From 2189f8e1145ee4b91f8d4b6e34d7591428b1d3d6 Mon Sep 17 00:00:00 2001 From: exp_table Date: Wed, 24 May 2023 11:35:35 +0200 Subject: [PATCH] Up to date template --- .gitignore | 108 +- README.md | 31 +- circuits/Verifier.toml | 7 +- circuits/contract/plonk_vk.sol | 2611 ++++ circuits/proofs/a.proof | 1 + contracts/Kevin.sol | 17 + contracts/Verifier.sol | 3447 ------ contracts/mocks/Kevin.sol | 18 - foundry.toml | 6 +- hardhat.config.ts | 22 - package-lock.json | 20045 ------------------------------- package.json | 38 - scripts/generateContract.ts | 36 - scripts/generateProof.ts | 33 - test/Kevin.t.sol | 25 +- test/test.ts | 47 - test/utils/ffiProof.ts | 27 - utils/safeGenerateContract.sh | 21 - utils/safeGenerateProof.sh | 19 - 19 files changed, 2656 insertions(+), 23903 deletions(-) create mode 100644 circuits/contract/plonk_vk.sol create mode 100644 circuits/proofs/a.proof create mode 100644 contracts/Kevin.sol delete mode 100644 contracts/Verifier.sol delete mode 100644 contracts/mocks/Kevin.sol delete mode 100644 hardhat.config.ts delete mode 100644 package-lock.json delete mode 100644 package.json delete mode 100644 scripts/generateContract.ts delete mode 100644 scripts/generateProof.ts delete mode 100644 test/test.ts delete mode 100644 test/utils/ffiProof.ts delete mode 100755 utils/safeGenerateContract.sh delete mode 100755 utils/safeGenerateProof.sh diff --git a/.gitignore b/.gitignore index fad6dab..a3aa6d1 100644 --- a/.gitignore +++ b/.gitignore @@ -1,109 +1,5 @@ out/ cache/ -circuits/build/ artifacts/ -circuits/proofs/ -# Logs -logs -*.log -npm-debug.log* -yarn-debug.log* -yarn-error.log* -lerna-debug.log* -typechain-types/ -# Diagnostic reports (https://nodejs.org/api/report.html) -report.[0-9]*.[0-9]*.[0-9]*.[0-9]*.json - -# Runtime data -pids -*.pid -*.seed -*.pid.lock - -# Directory for instrumented libs generated by jscoverage/JSCover -lib-cov - -# Coverage directory used by tools like istanbul -coverage -*.lcov - -# nyc test coverage -.nyc_output - -# Grunt intermediate storage (https://gruntjs.com/creating-plugins#storing-task-files) -.grunt - -# Bower dependency directory (https://bower.io/) -bower_components - -# node-waf configuration -.lock-wscript - -# Compiled binary addons (https://nodejs.org/api/addons.html) -build/Release - -# Dependency directories -node_modules/ -jspm_packages/ - -# TypeScript v1 declaration files -typings/ - -# TypeScript cache -*.tsbuildinfo - -# Optional npm cache directory -.npm - -# Optional eslint cache -.eslintcache - -# Microbundle cache -.rpt2_cache/ -.rts2_cache_cjs/ -.rts2_cache_es/ -.rts2_cache_umd/ - -# Optional REPL history -.node_repl_history - -# Output of 'npm pack' -*.tgz - -# Yarn Integrity file -.yarn-integrity - -# dotenv environment variables file -.env -.env.test - -# parcel-bundler cache (https://parceljs.org/) -.cache - -# Next.js build output -.next - -# Nuxt.js build / generate output -.nuxt -dist - -# Gatsby files -.cache/ -# Comment in the public line in if your project uses Gatsby and *not* Next.js -# https://nextjs.org/blog/next-9-1#public-directory-support -# public - -# vuepress build output -.vuepress/dist - -# Serverless directories -.serverless/ - -# FuseBox cache -.fusebox/ - -# DynamoDB Local files -.dynamodb/ - -# TernJS port file -.tern-port +circuits/build/ +circuits/target/ \ No newline at end of file diff --git a/README.md b/README.md index 3c100da..1ba3275 100644 --- a/README.md +++ b/README.md @@ -10,48 +10,39 @@ Click [`use this template`](https://github.com/whitenois3/nplate/generate) to cr ## Development -Both hardhat and foundry are supported. -With the help of the `ffi`, you can write complex JS/TS scripts, feed them inputs FROM the foundry test contract and use the output in the test contract. - **Setup** -```bash -npm install -``` + +You need both `nargo` and `foundry` installed. + Regarding the installation of `nargo`, please refer to its repo [here](https://github.com/noir-lang/noir). **Building** + ```bash cd circuits -nargo build -nargo compile BUILD_NAME +# generates the Solidity contract +nargo nargo codegen-verifier +# generates a file "p.proof" in circuits/proofs +nargo prove p ``` **Testing** -```bash -npx hardhat test -``` -```bash -forge test --ffi -``` -We have provided two bash scripts in `utils/` to make your life easier when it comes to generating the Verifier contract and a proof. +Before testing, be sure you have generated the updated Solidity verifier contract as well as a valid proof! -``` -./utils/safeGenerateContract.sh -./utils/safeGenerateProof.sh +```bash +forge test --ffi ``` ## License [AGPL-3.0-only](https://github.com/abigger87/femplate/blob/master/LICENSE) - ## Acknowledgements - [femplate](https://github.com/abigger87/femplate) - [basic_mul_noir_example](https://github.com/vezenovm/basic_mul_noir_example) - ## Disclaimer _These smart contracts are being provided as is. No guarantee, representation or warranty is being made, express or implied, as to the safety or correctness of the user interface or the smart contracts. They have not been audited and as such there can be no assurance they will work as intended, and users may experience delays, failures, errors, omissions, loss of transmitted information or loss of funds. The creators are not liable for any of the foregoing. Users should proceed with caution and use at their own risk._ diff --git a/circuits/Verifier.toml b/circuits/Verifier.toml index 8ca02a9..a5c1f4b 100644 --- a/circuits/Verifier.toml +++ b/circuits/Verifier.toml @@ -1,4 +1,3 @@ -setpub = [] -x = "1" -y = "2" -return = "3" \ No newline at end of file +return = "0x0000000000000000000000000000000000000000000000000000000000000003" +x = "0x0000000000000000000000000000000000000000000000000000000000000001" +y = "0x0000000000000000000000000000000000000000000000000000000000000002" diff --git a/circuits/contract/plonk_vk.sol b/circuits/contract/plonk_vk.sol new file mode 100644 index 0000000..fafe46d --- /dev/null +++ b/circuits/contract/plonk_vk.sol @@ -0,0 +1,2611 @@ +// Verification Key Hash: a0e940165bfc708013d5b4f7940f3b07f3bcf3c0f57ee21d8b4bdb78630817a3 +// SPDX-License-Identifier: Apache-2.0 +// Copyright 2022 Aztec +pragma solidity >=0.8.4; + +library UltraVerificationKey { + function verificationKeyHash() internal pure returns(bytes32) { + return 0xa0e940165bfc708013d5b4f7940f3b07f3bcf3c0f57ee21d8b4bdb78630817a3; + } + + function loadVerificationKey(uint256 _vk, uint256 _omegaInverseLoc) internal pure { + assembly { + mstore(add(_vk, 0x00), 0x0000000000000000000000000000000000000000000000000000000000000010) // vk.circuit_size + mstore(add(_vk, 0x20), 0x0000000000000000000000000000000000000000000000000000000000000003) // vk.num_inputs + mstore(add(_vk, 0x40), 0x21082ca216cbbf4e1c6e4f4594dd508c996dfbe1174efb98b11509c6e306460b) // vk.work_root + mstore(add(_vk, 0x60), 0x2d5e098bb31e86271ccb415b196942d755b0a9c3f21dd9882fa3d63ab1000001) // vk.domain_inverse + mstore(add(_vk, 0x80), 0x0fe8527a8494f827e4b332060e5569bdfe47aadc475cb1f03b4d222b0804e463) // vk.Q1.x + mstore(add(_vk, 0xa0), 0x2d051f6d8a9eec7ae2622b4b259fb91d942a8892632cffcdad4c03e2c9081593) // vk.Q1.y + mstore(add(_vk, 0xc0), 0x21be04985f898ef5e2a80f32fbaa16cd3eb8c451c243db46144b97113c8e556a) // vk.Q2.x + mstore(add(_vk, 0xe0), 0x2913bcdde62d6d2143aa6a0fed511ca527994df2cba6a780baa29dddac161de9) // vk.Q2.y + mstore(add(_vk, 0x100), 0x15bf0818d578953a624a127aa04d4b0aa1b09d3fe69b9a29e2546a41e9b08049) // vk.Q3.x + mstore(add(_vk, 0x120), 0x0148f0d2abf2ca1fe6cc20fdef0a8d4a88eb9602eaf48f0c1c02445c27cb9592) // vk.Q3.y + mstore(add(_vk, 0x140), 0x02d6fd9e84dbe74b7531e1801405a1c292117b1a17fefe9de0bfd9edf1a84bf9) // vk.Q4.x + mstore(add(_vk, 0x160), 0x293c6ab3c06a0669af13393a82c60a459a3b2a0b768da45ac7af7f2aec40fc42) // vk.Q4.y + mstore(add(_vk, 0x180), 0x2950076760523510abcfe90fa550b964e84b338f73af5222cdbbaefdacd4484e) // vk.Q_M.x + mstore(add(_vk, 0x1a0), 0x2e4e3e272c7b78ad894559812d7766e05615a8f7050a43d7ed1367adf30a9319) // vk.Q_M.y + mstore(add(_vk, 0x1c0), 0x1798c37010a4285e1774c1ad35779886380ee5ceee0ba183927e2a2103301a68) // vk.Q_C.x + mstore(add(_vk, 0x1e0), 0x2935f9e4d47a8e39aa0107f31a84584b47d903cfeb9690f6d850dc8ea7d2f4ea) // vk.Q_C.y + mstore(add(_vk, 0x200), 0x205aff7186f2cedc99e9cadb7930ef25f296991e5a7b574a33d6249f0a5db1f9) // vk.Q_ARITHMETIC.x + mstore(add(_vk, 0x220), 0x0beadc757bee3a2be1f6425385547099fc1eeeb1fed5a8552b07e997251d7c45) // vk.Q_ARITHMETIC.y + mstore(add(_vk, 0x240), 0x2cbce7beee3076b78dace04943d69d0d9e28aa6d00e046852781a5f20816645c) // vk.QSORT.x + mstore(add(_vk, 0x260), 0x2bc27ec2e1612ea284b08bcc55b6f2fd915d11bfedbdc0e59de09e5b28952080) // vk.QSORT.y + mstore(add(_vk, 0x280), 0x0ad34b5e8db72a5acf4427546c7294be6ed4f4d252a79059e505f9abc1bdf3ed) // vk.Q_ELLIPTIC.x + mstore(add(_vk, 0x2a0), 0x1e5b26790a26eb340217dd9ad28dbf90a049f42a3852acd45e6f521f24b4900e) // vk.Q_ELLIPTIC.y + mstore(add(_vk, 0x2c0), 0x155a0f51fec78c33ffceb7364d69d7ac27e570ae50bc180509764eb3fef94815) // vk.Q_AUX.x + mstore(add(_vk, 0x2e0), 0x1c1c4720bed44a591d97cbc72b6e44b644999713a8d3c66e9054aa5726324c76) // vk.Q_AUX.y + mstore(add(_vk, 0x300), 0x01d8b8ff3b1674e57a7d30ce1d9e07c686174c643eb20d38e604eec7095248a9) // vk.SIGMA1.x + mstore(add(_vk, 0x320), 0x261015d69327a58810e6eb1052ed694914b7a89034e1334c50b9e70a161489b7) // vk.SIGMA1.y + mstore(add(_vk, 0x340), 0x1987df111730a8a6a650423757dbf048f3f43860a7d24a5e2e8bd67b6931ca67) // vk.SIGMA2.x + mstore(add(_vk, 0x360), 0x1fe074ff24b35d7830bec2a3fad7e53038ffb5e2a3f718a23660d68daffc2953) // vk.SIGMA2.y + mstore(add(_vk, 0x380), 0x191d6881b9369e50141da3f2009a2f2dfc9adba276e874eb9f7f3183a0ea8f89) // vk.SIGMA3.x + mstore(add(_vk, 0x3a0), 0x2cbfbdd75526be7e9f2830cb1fd99457227f90fb024902635e342344cb6b2926) // vk.SIGMA3.y + mstore(add(_vk, 0x3c0), 0x2e7fe658b8f1f34dc561568e4ef6c74bb36330404967952b1e15390c1e2443cf) // vk.SIGMA4.x + mstore(add(_vk, 0x3e0), 0x293a5337eedc88329f10aa45a11e4adbb77f74717345987d70ed726e3e4556f1) // vk.SIGMA4.y + mstore(add(_vk, 0x400), 0x02c397073c8abce6d4140c9b961209dd783bff1a1cfc999bb29859cfb16c46fc) // vk.TABLE1.x + mstore(add(_vk, 0x420), 0x2b7bba2d1efffce0d033f596b4d030750599be670db593af86e1923fe8a1bb18) // vk.TABLE1.y + mstore(add(_vk, 0x440), 0x2c71c58b66498f903b3bbbda3d05ce8ffb571a4b3cf83533f3f71b99a04f6e6b) // vk.TABLE2.x + mstore(add(_vk, 0x460), 0x039dce37f94d1bbd97ccea32a224fe2afaefbcbd080c84dcea90b54f4e0a858f) // vk.TABLE2.y + mstore(add(_vk, 0x480), 0x27dc44977efe6b3746a290706f4f7275783c73cfe56847d848fd93b63bf32083) // vk.TABLE3.x + mstore(add(_vk, 0x4a0), 0x0a5366266dd7b71a10b356030226a2de0cbf2edc8f085b16d73652b15eced8f5) // vk.TABLE3.y + mstore(add(_vk, 0x4c0), 0x136097d79e1b0ae373255e8760c49900a7588ec4d6809c90bb451005a3de3077) // vk.TABLE4.x + mstore(add(_vk, 0x4e0), 0x13dd7515ccac4095302d204f06f0bff2595d77bdf72e4acdb0b0b43969860d98) // vk.TABLE4.y + mstore(add(_vk, 0x500), 0x16ff3501369121d410b445929239ba057fe211dad1b706e49a3b55920fac20ec) // vk.TABLE_TYPE.x + mstore(add(_vk, 0x520), 0x1e190987ebd9cf480f608b82134a00eb8007673c1ed10b834a695adf0068522a) // vk.TABLE_TYPE.y + mstore(add(_vk, 0x540), 0x0baaf073a203ba4ba0093c827bb5b3f7a55611765f111ecf80c456f631e99f29) // vk.ID1.x + mstore(add(_vk, 0x560), 0x27cd34cafd5735ec970278202765e0f1e9da3494b30b948ebce3414d078cef9e) // vk.ID1.y + mstore(add(_vk, 0x580), 0x0868357b28039385c5a5058b6d358ebb29f26f9890d6cc6401f4921d5884edca) // vk.ID2.x + mstore(add(_vk, 0x5a0), 0x1060afe929554ca473103f5e68193c36fb6e229dde8edf7ec858b12d7e8be485) // vk.ID2.y + mstore(add(_vk, 0x5c0), 0x0b1c02619282755533457230b19b4a15226e07e207744c0857074dcab883af4a) // vk.ID3.x + mstore(add(_vk, 0x5e0), 0x0d928deafed363659688ed4ccdef521f2a0277e4807e6e1cbabca21dde5eb5e1) // vk.ID3.y + mstore(add(_vk, 0x600), 0x2eea648c8732596b1314fe2a4d2f05363f0c994e91cecad25835338edee2294f) // vk.ID4.x + mstore(add(_vk, 0x620), 0x0ab49886c2b94bd0bd3f6ed1dbbe2cb2671d2ae51d31c1210433c3972bb64578) // vk.ID4.y + mstore(add(_vk, 0x640), 0x00) // vk.contains_recursive_proof + mstore(add(_vk, 0x660), 0) // vk.recursive_proof_public_input_indices + mstore(add(_vk, 0x680), 0x260e01b251f6f1c7e7ff4e580791dee8ea51d87a358e038b4efe30fac09383c1) // vk.g2_x.X.c1 + mstore(add(_vk, 0x6a0), 0x0118c4d5b837bcc2bc89b5b398b5974e9f5944073b32078b7e231fec938883b0) // vk.g2_x.X.c0 + mstore(add(_vk, 0x6c0), 0x04fc6369f7110fe3d25156c1bb9a72859cf2a04641f99ba4ee413c80da6a5fe4) // vk.g2_x.Y.c1 + mstore(add(_vk, 0x6e0), 0x22febda3c0c0632a56475b4214e5615e11e6dd3f96e6cea2854a87d4dacc5e55) // vk.g2_x.Y.c0 + mstore(_omegaInverseLoc, 0x02e40daf409556c02bfc85eb303402b774954d30aeb0337eb85a71e6373428de) // vk.work_root_inverse + } + } +} + +/** + * @title Ultra Plonk proof verification contract + * @dev Top level Plonk proof verification contract, which allows Plonk proof to be verified + */ +abstract contract BaseUltraVerifier { + // VERIFICATION KEY MEMORY LOCATIONS + uint256 internal constant N_LOC = 0x380; + uint256 internal constant NUM_INPUTS_LOC = 0x3a0; + uint256 internal constant OMEGA_LOC = 0x3c0; + uint256 internal constant DOMAIN_INVERSE_LOC = 0x3e0; + uint256 internal constant Q1_X_LOC = 0x400; + uint256 internal constant Q1_Y_LOC = 0x420; + uint256 internal constant Q2_X_LOC = 0x440; + uint256 internal constant Q2_Y_LOC = 0x460; + uint256 internal constant Q3_X_LOC = 0x480; + uint256 internal constant Q3_Y_LOC = 0x4a0; + uint256 internal constant Q4_X_LOC = 0x4c0; + uint256 internal constant Q4_Y_LOC = 0x4e0; + uint256 internal constant QM_X_LOC = 0x500; + uint256 internal constant QM_Y_LOC = 0x520; + uint256 internal constant QC_X_LOC = 0x540; + uint256 internal constant QC_Y_LOC = 0x560; + uint256 internal constant QARITH_X_LOC = 0x580; + uint256 internal constant QARITH_Y_LOC = 0x5a0; + uint256 internal constant QSORT_X_LOC = 0x5c0; + uint256 internal constant QSORT_Y_LOC = 0x5e0; + uint256 internal constant QELLIPTIC_X_LOC = 0x600; + uint256 internal constant QELLIPTIC_Y_LOC = 0x620; + uint256 internal constant QAUX_X_LOC = 0x640; + uint256 internal constant QAUX_Y_LOC = 0x660; + uint256 internal constant SIGMA1_X_LOC = 0x680; + uint256 internal constant SIGMA1_Y_LOC = 0x6a0; + uint256 internal constant SIGMA2_X_LOC = 0x6c0; + uint256 internal constant SIGMA2_Y_LOC = 0x6e0; + uint256 internal constant SIGMA3_X_LOC = 0x700; + uint256 internal constant SIGMA3_Y_LOC = 0x720; + uint256 internal constant SIGMA4_X_LOC = 0x740; + uint256 internal constant SIGMA4_Y_LOC = 0x760; + uint256 internal constant TABLE1_X_LOC = 0x780; + uint256 internal constant TABLE1_Y_LOC = 0x7a0; + uint256 internal constant TABLE2_X_LOC = 0x7c0; + uint256 internal constant TABLE2_Y_LOC = 0x7e0; + uint256 internal constant TABLE3_X_LOC = 0x800; + uint256 internal constant TABLE3_Y_LOC = 0x820; + uint256 internal constant TABLE4_X_LOC = 0x840; + uint256 internal constant TABLE4_Y_LOC = 0x860; + uint256 internal constant TABLE_TYPE_X_LOC = 0x880; + uint256 internal constant TABLE_TYPE_Y_LOC = 0x8a0; + uint256 internal constant ID1_X_LOC = 0x8c0; + uint256 internal constant ID1_Y_LOC = 0x8e0; + uint256 internal constant ID2_X_LOC = 0x900; + uint256 internal constant ID2_Y_LOC = 0x920; + uint256 internal constant ID3_X_LOC = 0x940; + uint256 internal constant ID3_Y_LOC = 0x960; + uint256 internal constant ID4_X_LOC = 0x980; + uint256 internal constant ID4_Y_LOC = 0x9a0; + uint256 internal constant CONTAINS_RECURSIVE_PROOF_LOC = 0x9c0; + uint256 internal constant RECURSIVE_PROOF_PUBLIC_INPUT_INDICES_LOC = 0x9e0; + uint256 internal constant G2X_X0_LOC = 0xa00; + uint256 internal constant G2X_X1_LOC = 0xa20; + uint256 internal constant G2X_Y0_LOC = 0xa40; + uint256 internal constant G2X_Y1_LOC = 0xa60; + + // ### PROOF DATA MEMORY LOCATIONS + uint256 internal constant W1_X_LOC = 0x1200; + uint256 internal constant W1_Y_LOC = 0x1220; + uint256 internal constant W2_X_LOC = 0x1240; + uint256 internal constant W2_Y_LOC = 0x1260; + uint256 internal constant W3_X_LOC = 0x1280; + uint256 internal constant W3_Y_LOC = 0x12a0; + uint256 internal constant W4_X_LOC = 0x12c0; + uint256 internal constant W4_Y_LOC = 0x12e0; + uint256 internal constant S_X_LOC = 0x1300; + uint256 internal constant S_Y_LOC = 0x1320; + uint256 internal constant Z_X_LOC = 0x1340; + uint256 internal constant Z_Y_LOC = 0x1360; + uint256 internal constant Z_LOOKUP_X_LOC = 0x1380; + uint256 internal constant Z_LOOKUP_Y_LOC = 0x13a0; + uint256 internal constant T1_X_LOC = 0x13c0; + uint256 internal constant T1_Y_LOC = 0x13e0; + uint256 internal constant T2_X_LOC = 0x1400; + uint256 internal constant T2_Y_LOC = 0x1420; + uint256 internal constant T3_X_LOC = 0x1440; + uint256 internal constant T3_Y_LOC = 0x1460; + uint256 internal constant T4_X_LOC = 0x1480; + uint256 internal constant T4_Y_LOC = 0x14a0; + + uint256 internal constant W1_EVAL_LOC = 0x1600; + uint256 internal constant W2_EVAL_LOC = 0x1620; + uint256 internal constant W3_EVAL_LOC = 0x1640; + uint256 internal constant W4_EVAL_LOC = 0x1660; + uint256 internal constant S_EVAL_LOC = 0x1680; + uint256 internal constant Z_EVAL_LOC = 0x16a0; + uint256 internal constant Z_LOOKUP_EVAL_LOC = 0x16c0; + uint256 internal constant Q1_EVAL_LOC = 0x16e0; + uint256 internal constant Q2_EVAL_LOC = 0x1700; + uint256 internal constant Q3_EVAL_LOC = 0x1720; + uint256 internal constant Q4_EVAL_LOC = 0x1740; + uint256 internal constant QM_EVAL_LOC = 0x1760; + uint256 internal constant QC_EVAL_LOC = 0x1780; + uint256 internal constant QARITH_EVAL_LOC = 0x17a0; + uint256 internal constant QSORT_EVAL_LOC = 0x17c0; + uint256 internal constant QELLIPTIC_EVAL_LOC = 0x17e0; + uint256 internal constant QAUX_EVAL_LOC = 0x1800; + uint256 internal constant TABLE1_EVAL_LOC = 0x1840; + uint256 internal constant TABLE2_EVAL_LOC = 0x1860; + uint256 internal constant TABLE3_EVAL_LOC = 0x1880; + uint256 internal constant TABLE4_EVAL_LOC = 0x18a0; + uint256 internal constant TABLE_TYPE_EVAL_LOC = 0x18c0; + uint256 internal constant ID1_EVAL_LOC = 0x18e0; + uint256 internal constant ID2_EVAL_LOC = 0x1900; + uint256 internal constant ID3_EVAL_LOC = 0x1920; + uint256 internal constant ID4_EVAL_LOC = 0x1940; + uint256 internal constant SIGMA1_EVAL_LOC = 0x1960; + uint256 internal constant SIGMA2_EVAL_LOC = 0x1980; + uint256 internal constant SIGMA3_EVAL_LOC = 0x19a0; + uint256 internal constant SIGMA4_EVAL_LOC = 0x19c0; + uint256 internal constant W1_OMEGA_EVAL_LOC = 0x19e0; + uint256 internal constant W2_OMEGA_EVAL_LOC = 0x2000; + uint256 internal constant W3_OMEGA_EVAL_LOC = 0x2020; + uint256 internal constant W4_OMEGA_EVAL_LOC = 0x2040; + uint256 internal constant S_OMEGA_EVAL_LOC = 0x2060; + uint256 internal constant Z_OMEGA_EVAL_LOC = 0x2080; + uint256 internal constant Z_LOOKUP_OMEGA_EVAL_LOC = 0x20a0; + uint256 internal constant TABLE1_OMEGA_EVAL_LOC = 0x20c0; + uint256 internal constant TABLE2_OMEGA_EVAL_LOC = 0x20e0; + uint256 internal constant TABLE3_OMEGA_EVAL_LOC = 0x2100; + uint256 internal constant TABLE4_OMEGA_EVAL_LOC = 0x2120; + + uint256 internal constant PI_Z_X_LOC = 0x2300; + uint256 internal constant PI_Z_Y_LOC = 0x2320; + uint256 internal constant PI_Z_OMEGA_X_LOC = 0x2340; + uint256 internal constant PI_Z_OMEGA_Y_LOC = 0x2360; + + // Used for elliptic widget. These are alias names for wire + shifted wire evaluations + uint256 internal constant X1_EVAL_LOC = W2_EVAL_LOC; + uint256 internal constant X2_EVAL_LOC = W1_OMEGA_EVAL_LOC; + uint256 internal constant X3_EVAL_LOC = W2_OMEGA_EVAL_LOC; + uint256 internal constant Y1_EVAL_LOC = W3_EVAL_LOC; + uint256 internal constant Y2_EVAL_LOC = W4_OMEGA_EVAL_LOC; + uint256 internal constant Y3_EVAL_LOC = W3_OMEGA_EVAL_LOC; + uint256 internal constant QBETA_LOC = Q3_EVAL_LOC; + uint256 internal constant QBETA_SQR_LOC = Q4_EVAL_LOC; + uint256 internal constant QSIGN_LOC = Q1_EVAL_LOC; + + // ### CHALLENGES MEMORY OFFSETS + + uint256 internal constant C_BETA_LOC = 0x2600; + uint256 internal constant C_GAMMA_LOC = 0x2620; + uint256 internal constant C_ALPHA_LOC = 0x2640; + uint256 internal constant C_ETA_LOC = 0x2660; + uint256 internal constant C_ETA_SQR_LOC = 0x2680; + uint256 internal constant C_ETA_CUBE_LOC = 0x26a0; + + uint256 internal constant C_ZETA_LOC = 0x26c0; + uint256 internal constant C_CURRENT_LOC = 0x26e0; + uint256 internal constant C_V0_LOC = 0x2700; + uint256 internal constant C_V1_LOC = 0x2720; + uint256 internal constant C_V2_LOC = 0x2740; + uint256 internal constant C_V3_LOC = 0x2760; + uint256 internal constant C_V4_LOC = 0x2780; + uint256 internal constant C_V5_LOC = 0x27a0; + uint256 internal constant C_V6_LOC = 0x27c0; + uint256 internal constant C_V7_LOC = 0x27e0; + uint256 internal constant C_V8_LOC = 0x2800; + uint256 internal constant C_V9_LOC = 0x2820; + uint256 internal constant C_V10_LOC = 0x2840; + uint256 internal constant C_V11_LOC = 0x2860; + uint256 internal constant C_V12_LOC = 0x2880; + uint256 internal constant C_V13_LOC = 0x28a0; + uint256 internal constant C_V14_LOC = 0x28c0; + uint256 internal constant C_V15_LOC = 0x28e0; + uint256 internal constant C_V16_LOC = 0x2900; + uint256 internal constant C_V17_LOC = 0x2920; + uint256 internal constant C_V18_LOC = 0x2940; + uint256 internal constant C_V19_LOC = 0x2960; + uint256 internal constant C_V20_LOC = 0x2980; + uint256 internal constant C_V21_LOC = 0x29a0; + uint256 internal constant C_V22_LOC = 0x29c0; + uint256 internal constant C_V23_LOC = 0x29e0; + uint256 internal constant C_V24_LOC = 0x2a00; + uint256 internal constant C_V25_LOC = 0x2a20; + uint256 internal constant C_V26_LOC = 0x2a40; + uint256 internal constant C_V27_LOC = 0x2a60; + uint256 internal constant C_V28_LOC = 0x2a80; + uint256 internal constant C_V29_LOC = 0x2aa0; + uint256 internal constant C_V30_LOC = 0x2ac0; + + uint256 internal constant C_U_LOC = 0x2b00; + + // ### LOCAL VARIABLES MEMORY OFFSETS + uint256 internal constant DELTA_NUMERATOR_LOC = 0x3000; + uint256 internal constant DELTA_DENOMINATOR_LOC = 0x3020; + uint256 internal constant ZETA_POW_N_LOC = 0x3040; + uint256 internal constant PUBLIC_INPUT_DELTA_LOC = 0x3060; + uint256 internal constant ZERO_POLY_LOC = 0x3080; + uint256 internal constant L_START_LOC = 0x30a0; + uint256 internal constant L_END_LOC = 0x30c0; + uint256 internal constant R_ZERO_EVAL_LOC = 0x30e0; + + uint256 internal constant PLOOKUP_DELTA_NUMERATOR_LOC = 0x3100; + uint256 internal constant PLOOKUP_DELTA_DENOMINATOR_LOC = 0x3120; + uint256 internal constant PLOOKUP_DELTA_LOC = 0x3140; + + uint256 internal constant ACCUMULATOR_X_LOC = 0x3160; + uint256 internal constant ACCUMULATOR_Y_LOC = 0x3180; + uint256 internal constant ACCUMULATOR2_X_LOC = 0x31a0; + uint256 internal constant ACCUMULATOR2_Y_LOC = 0x31c0; + uint256 internal constant PAIRING_LHS_X_LOC = 0x31e0; + uint256 internal constant PAIRING_LHS_Y_LOC = 0x3200; + uint256 internal constant PAIRING_RHS_X_LOC = 0x3220; + uint256 internal constant PAIRING_RHS_Y_LOC = 0x3240; + + // ### SUCCESS FLAG MEMORY LOCATIONS + uint256 internal constant GRAND_PRODUCT_SUCCESS_FLAG = 0x3300; + uint256 internal constant ARITHMETIC_TERM_SUCCESS_FLAG = 0x3020; + uint256 internal constant BATCH_OPENING_SUCCESS_FLAG = 0x3340; + uint256 internal constant OPENING_COMMITMENT_SUCCESS_FLAG = 0x3360; + uint256 internal constant PAIRING_PREAMBLE_SUCCESS_FLAG = 0x3380; + uint256 internal constant PAIRING_SUCCESS_FLAG = 0x33a0; + uint256 internal constant RESULT_FLAG = 0x33c0; + + // misc stuff + uint256 internal constant OMEGA_INVERSE_LOC = 0x3400; + uint256 internal constant C_ALPHA_SQR_LOC = 0x3420; + uint256 internal constant C_ALPHA_CUBE_LOC = 0x3440; + uint256 internal constant C_ALPHA_QUAD_LOC = 0x3460; + uint256 internal constant C_ALPHA_BASE_LOC = 0x3480; + + // ### RECURSION VARIABLE MEMORY LOCATIONS + uint256 internal constant RECURSIVE_P1_X_LOC = 0x3500; + uint256 internal constant RECURSIVE_P1_Y_LOC = 0x3520; + uint256 internal constant RECURSIVE_P2_X_LOC = 0x3540; + uint256 internal constant RECURSIVE_P2_Y_LOC = 0x3560; + + uint256 internal constant PUBLIC_INPUTS_HASH_LOCATION = 0x3580; + + // sub-identity storage + uint256 internal constant PERMUTATION_IDENTITY = 0x3600; + uint256 internal constant PLOOKUP_IDENTITY = 0x3620; + uint256 internal constant ARITHMETIC_IDENTITY = 0x3640; + uint256 internal constant SORT_IDENTITY = 0x3660; + uint256 internal constant ELLIPTIC_IDENTITY = 0x3680; + uint256 internal constant AUX_IDENTITY = 0x36a0; + uint256 internal constant AUX_NON_NATIVE_FIELD_EVALUATION = 0x36c0; + uint256 internal constant AUX_LIMB_ACCUMULATOR_EVALUATION = 0x36e0; + uint256 internal constant AUX_RAM_CONSISTENCY_EVALUATION = 0x3700; + uint256 internal constant AUX_ROM_CONSISTENCY_EVALUATION = 0x3720; + uint256 internal constant AUX_MEMORY_EVALUATION = 0x3740; + + uint256 internal constant QUOTIENT_EVAL_LOC = 0x3760; + uint256 internal constant ZERO_POLY_INVERSE_LOC = 0x3780; + + // when hashing public inputs we use memory at NU_CHALLENGE_INPUT_LOC_A, as the hash input size is unknown at compile time + uint256 internal constant NU_CHALLENGE_INPUT_LOC_A = 0x37a0; + uint256 internal constant NU_CHALLENGE_INPUT_LOC_B = 0x37c0; + uint256 internal constant NU_CHALLENGE_INPUT_LOC_C = 0x37e0; + + bytes4 internal constant PUBLIC_INPUT_INVALID_BN128_G1_POINT_SELECTOR = 0xeba9f4a6; + bytes4 internal constant PUBLIC_INPUT_GE_P_SELECTOR = 0x374a972f; + bytes4 internal constant MOD_EXP_FAILURE_SELECTOR = 0xf894a7bc; + bytes4 internal constant EC_SCALAR_MUL_FAILURE_SELECTOR = 0xf755f369; + bytes4 internal constant PROOF_FAILURE_SELECTOR = 0x0711fcec; + + uint256 internal constant ETA_INPUT_LENGTH = 0xc0; // W1, W2, W3 = 6 * 0x20 bytes + + // We need to hash 41 field elements when generating the NU challenge + // w1, w2, w3, w4, s, z, z_lookup, q1, q2, q3, q4, qm, qc, qarith (14) + // qsort, qelliptic, qaux, sigma1, sigma2, sigma, sigma4, (7) + // table1, table2, table3, table4, tabletype, id1, id2, id3, id4, (9) + // w1_omega, w2_omega, w3_omega, w4_omega, s_omega, z_omega, z_lookup_omega, (7) + // table1_omega, table2_omega, table3_omega, table4_omega (4) + uint256 internal constant NU_INPUT_LENGTH = 0x520; // 0x520 = 41 * 0x20 + + // There are ELEVEN G1 group elements added into the transcript in the `beta` round, that we need to skip over + // W1, W2, W3, W4, S, Z, Z_LOOKUP, T1, T2, T3, T4 + uint256 internal constant NU_CALLDATA_SKIP_LENGTH = 0x2c0; // 11 * 0x40 = 0x2c0 + + uint256 internal constant NEGATIVE_INVERSE_OF_2_MODULO_P = + 0x183227397098d014dc2822db40c0ac2e9419f4243cdcb848a1f0fac9f8000000; + uint256 internal constant LIMB_SIZE = 0x100000000000000000; // 2<<68 + uint256 internal constant SUBLIMB_SHIFT = 0x4000; // 2<<14 + + error PUBLIC_INPUT_COUNT_INVALID(uint256 expected, uint256 actual); + error PUBLIC_INPUT_INVALID_BN128_G1_POINT(); + error PUBLIC_INPUT_GE_P(); + error MOD_EXP_FAILURE(); + error EC_SCALAR_MUL_FAILURE(); + error PROOF_FAILURE(); + + function getVerificationKeyHash() public pure virtual returns (bytes32); + + function loadVerificationKey(uint256 _vk, uint256 _omegaInverseLoc) internal pure virtual; + + /** + * @notice Verify a Ultra Plonk proof + * @param _proof - The serialized proof + * @param _publicInputs - An array of the public inputs + * @return True if proof is valid, reverts otherwise + */ + function verify(bytes calldata _proof, bytes32[] calldata _publicInputs) external view returns (bool) { + loadVerificationKey(N_LOC, OMEGA_INVERSE_LOC); + + uint256 requiredPublicInputCount; + assembly { + requiredPublicInputCount := mload(NUM_INPUTS_LOC) + } + if (requiredPublicInputCount != _publicInputs.length) { + revert PUBLIC_INPUT_COUNT_INVALID(requiredPublicInputCount, _publicInputs.length); + } + + assembly { + let q := 21888242871839275222246405745257275088696311157297823662689037894645226208583 // EC group order + let p := 21888242871839275222246405745257275088548364400416034343698204186575808495617 // Prime field order + + /** + * LOAD PROOF FROM CALLDATA + */ + { + let data_ptr := add(calldataload(0x04), 0x24) + + mstore(W1_Y_LOC, mod(calldataload(data_ptr), q)) + mstore(W1_X_LOC, mod(calldataload(add(data_ptr, 0x20)), q)) + + mstore(W2_Y_LOC, mod(calldataload(add(data_ptr, 0x40)), q)) + mstore(W2_X_LOC, mod(calldataload(add(data_ptr, 0x60)), q)) + + mstore(W3_Y_LOC, mod(calldataload(add(data_ptr, 0x80)), q)) + mstore(W3_X_LOC, mod(calldataload(add(data_ptr, 0xa0)), q)) + + mstore(W4_Y_LOC, mod(calldataload(add(data_ptr, 0xc0)), q)) + mstore(W4_X_LOC, mod(calldataload(add(data_ptr, 0xe0)), q)) + + mstore(S_Y_LOC, mod(calldataload(add(data_ptr, 0x100)), q)) + mstore(S_X_LOC, mod(calldataload(add(data_ptr, 0x120)), q)) + mstore(Z_Y_LOC, mod(calldataload(add(data_ptr, 0x140)), q)) + mstore(Z_X_LOC, mod(calldataload(add(data_ptr, 0x160)), q)) + mstore(Z_LOOKUP_Y_LOC, mod(calldataload(add(data_ptr, 0x180)), q)) + mstore(Z_LOOKUP_X_LOC, mod(calldataload(add(data_ptr, 0x1a0)), q)) + mstore(T1_Y_LOC, mod(calldataload(add(data_ptr, 0x1c0)), q)) + mstore(T1_X_LOC, mod(calldataload(add(data_ptr, 0x1e0)), q)) + + mstore(T2_Y_LOC, mod(calldataload(add(data_ptr, 0x200)), q)) + mstore(T2_X_LOC, mod(calldataload(add(data_ptr, 0x220)), q)) + + mstore(T3_Y_LOC, mod(calldataload(add(data_ptr, 0x240)), q)) + mstore(T3_X_LOC, mod(calldataload(add(data_ptr, 0x260)), q)) + + mstore(T4_Y_LOC, mod(calldataload(add(data_ptr, 0x280)), q)) + mstore(T4_X_LOC, mod(calldataload(add(data_ptr, 0x2a0)), q)) + + mstore(W1_EVAL_LOC, mod(calldataload(add(data_ptr, 0x2c0)), p)) + mstore(W2_EVAL_LOC, mod(calldataload(add(data_ptr, 0x2e0)), p)) + mstore(W3_EVAL_LOC, mod(calldataload(add(data_ptr, 0x300)), p)) + mstore(W4_EVAL_LOC, mod(calldataload(add(data_ptr, 0x320)), p)) + mstore(S_EVAL_LOC, mod(calldataload(add(data_ptr, 0x340)), p)) + mstore(Z_EVAL_LOC, mod(calldataload(add(data_ptr, 0x360)), p)) + mstore(Z_LOOKUP_EVAL_LOC, mod(calldataload(add(data_ptr, 0x380)), p)) + mstore(Q1_EVAL_LOC, mod(calldataload(add(data_ptr, 0x3a0)), p)) + mstore(Q2_EVAL_LOC, mod(calldataload(add(data_ptr, 0x3c0)), p)) + mstore(Q3_EVAL_LOC, mod(calldataload(add(data_ptr, 0x3e0)), p)) + mstore(Q4_EVAL_LOC, mod(calldataload(add(data_ptr, 0x400)), p)) + mstore(QM_EVAL_LOC, mod(calldataload(add(data_ptr, 0x420)), p)) + mstore(QC_EVAL_LOC, mod(calldataload(add(data_ptr, 0x440)), p)) + mstore(QARITH_EVAL_LOC, mod(calldataload(add(data_ptr, 0x460)), p)) + mstore(QSORT_EVAL_LOC, mod(calldataload(add(data_ptr, 0x480)), p)) + mstore(QELLIPTIC_EVAL_LOC, mod(calldataload(add(data_ptr, 0x4a0)), p)) + mstore(QAUX_EVAL_LOC, mod(calldataload(add(data_ptr, 0x4c0)), p)) + + mstore(SIGMA1_EVAL_LOC, mod(calldataload(add(data_ptr, 0x4e0)), p)) + mstore(SIGMA2_EVAL_LOC, mod(calldataload(add(data_ptr, 0x500)), p)) + + mstore(SIGMA3_EVAL_LOC, mod(calldataload(add(data_ptr, 0x520)), p)) + mstore(SIGMA4_EVAL_LOC, mod(calldataload(add(data_ptr, 0x540)), p)) + + mstore(TABLE1_EVAL_LOC, mod(calldataload(add(data_ptr, 0x560)), p)) + mstore(TABLE2_EVAL_LOC, mod(calldataload(add(data_ptr, 0x580)), p)) + mstore(TABLE3_EVAL_LOC, mod(calldataload(add(data_ptr, 0x5a0)), p)) + mstore(TABLE4_EVAL_LOC, mod(calldataload(add(data_ptr, 0x5c0)), p)) + mstore(TABLE_TYPE_EVAL_LOC, mod(calldataload(add(data_ptr, 0x5e0)), p)) + + mstore(ID1_EVAL_LOC, mod(calldataload(add(data_ptr, 0x600)), p)) + mstore(ID2_EVAL_LOC, mod(calldataload(add(data_ptr, 0x620)), p)) + mstore(ID3_EVAL_LOC, mod(calldataload(add(data_ptr, 0x640)), p)) + mstore(ID4_EVAL_LOC, mod(calldataload(add(data_ptr, 0x660)), p)) + + mstore(W1_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x680)), p)) + mstore(W2_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x6a0)), p)) + mstore(W3_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x6c0)), p)) + mstore(W4_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x6e0)), p)) + mstore(S_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x700)), p)) + + mstore(Z_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x720)), p)) + + mstore(Z_LOOKUP_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x740)), p)) + mstore(TABLE1_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x760)), p)) + mstore(TABLE2_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x780)), p)) + mstore(TABLE3_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x7a0)), p)) + mstore(TABLE4_OMEGA_EVAL_LOC, mod(calldataload(add(data_ptr, 0x7c0)), p)) + + mstore(PI_Z_Y_LOC, mod(calldataload(add(data_ptr, 0x7e0)), q)) + mstore(PI_Z_X_LOC, mod(calldataload(add(data_ptr, 0x800)), q)) + + mstore(PI_Z_OMEGA_Y_LOC, mod(calldataload(add(data_ptr, 0x820)), q)) + mstore(PI_Z_OMEGA_X_LOC, mod(calldataload(add(data_ptr, 0x840)), q)) + } + + /** + * LOAD RECURSIVE PROOF INTO MEMORY + */ + { + if mload(CONTAINS_RECURSIVE_PROOF_LOC) { + let public_inputs_ptr := add(calldataload(0x24), 0x24) + let index_counter := add(shl(5, mload(RECURSIVE_PROOF_PUBLIC_INPUT_INDICES_LOC)), public_inputs_ptr) + + let x0 := calldataload(index_counter) + x0 := add(x0, shl(68, calldataload(add(index_counter, 0x20)))) + x0 := add(x0, shl(136, calldataload(add(index_counter, 0x40)))) + x0 := add(x0, shl(204, calldataload(add(index_counter, 0x60)))) + let y0 := calldataload(add(index_counter, 0x80)) + y0 := add(y0, shl(68, calldataload(add(index_counter, 0xa0)))) + y0 := add(y0, shl(136, calldataload(add(index_counter, 0xc0)))) + y0 := add(y0, shl(204, calldataload(add(index_counter, 0xe0)))) + let x1 := calldataload(add(index_counter, 0x100)) + x1 := add(x1, shl(68, calldataload(add(index_counter, 0x120)))) + x1 := add(x1, shl(136, calldataload(add(index_counter, 0x140)))) + x1 := add(x1, shl(204, calldataload(add(index_counter, 0x160)))) + let y1 := calldataload(add(index_counter, 0x180)) + y1 := add(y1, shl(68, calldataload(add(index_counter, 0x1a0)))) + y1 := add(y1, shl(136, calldataload(add(index_counter, 0x1c0)))) + y1 := add(y1, shl(204, calldataload(add(index_counter, 0x1e0)))) + mstore(RECURSIVE_P1_X_LOC, x0) + mstore(RECURSIVE_P1_Y_LOC, y0) + mstore(RECURSIVE_P2_X_LOC, x1) + mstore(RECURSIVE_P2_Y_LOC, y1) + + // validate these are valid bn128 G1 points + if iszero(and(and(lt(x0, q), lt(x1, q)), and(lt(y0, q), lt(y1, q)))) { + mstore(0x00, PUBLIC_INPUT_INVALID_BN128_G1_POINT_SELECTOR) + revert(0x00, 0x04) + } + } + } + + { + /** + * Generate initial challenge + */ + mstore(0x00, shl(224, mload(N_LOC))) + mstore(0x04, shl(224, mload(NUM_INPUTS_LOC))) + let challenge := keccak256(0x00, 0x08) + + /** + * Generate eta challenge + */ + mstore(PUBLIC_INPUTS_HASH_LOCATION, challenge) + // The public input location is stored at 0x24, we then add 0x24 to skip selector and the length of public inputs + let public_inputs_start := add(calldataload(0x24), 0x24) + // copy the public inputs over + let public_input_size := mul(mload(NUM_INPUTS_LOC), 0x20) + calldatacopy(add(PUBLIC_INPUTS_HASH_LOCATION, 0x20), public_inputs_start, public_input_size) + + // copy W1, W2, W3 into challenge. Each point is 0x40 bytes, so load 0xc0 = 3 * 0x40 bytes (ETA input length) + let w_start := add(calldataload(0x04), 0x24) + calldatacopy(add(add(PUBLIC_INPUTS_HASH_LOCATION, 0x20), public_input_size), w_start, ETA_INPUT_LENGTH) + + // Challenge is the old challenge + public inputs + W1, W2, W3 (0x20 + public_input_size + 0xc0) + let challenge_bytes_size := add(0x20, add(public_input_size, ETA_INPUT_LENGTH)) + + challenge := keccak256(PUBLIC_INPUTS_HASH_LOCATION, challenge_bytes_size) + { + let eta := mod(challenge, p) + mstore(C_ETA_LOC, eta) + mstore(C_ETA_SQR_LOC, mulmod(eta, eta, p)) + mstore(C_ETA_CUBE_LOC, mulmod(mload(C_ETA_SQR_LOC), eta, p)) + } + + /** + * Generate beta challenge + */ + mstore(0x00, challenge) + mstore(0x20, mload(W4_Y_LOC)) + mstore(0x40, mload(W4_X_LOC)) + mstore(0x60, mload(S_Y_LOC)) + mstore(0x80, mload(S_X_LOC)) + challenge := keccak256(0x00, 0xa0) + mstore(C_BETA_LOC, mod(challenge, p)) + + /** + * Generate gamma challenge + */ + mstore(0x00, challenge) + mstore8(0x20, 0x01) + challenge := keccak256(0x00, 0x21) + mstore(C_GAMMA_LOC, mod(challenge, p)) + + /** + * Generate alpha challenge + */ + mstore(0x00, challenge) + mstore(0x20, mload(Z_Y_LOC)) + mstore(0x40, mload(Z_X_LOC)) + mstore(0x60, mload(Z_LOOKUP_Y_LOC)) + mstore(0x80, mload(Z_LOOKUP_X_LOC)) + challenge := keccak256(0x00, 0xa0) + mstore(C_ALPHA_LOC, mod(challenge, p)) + + /** + * Compute and store some powers of alpha for future computations + */ + let alpha := mload(C_ALPHA_LOC) + mstore(C_ALPHA_SQR_LOC, mulmod(alpha, alpha, p)) + mstore(C_ALPHA_CUBE_LOC, mulmod(mload(C_ALPHA_SQR_LOC), alpha, p)) + mstore(C_ALPHA_QUAD_LOC, mulmod(mload(C_ALPHA_CUBE_LOC), alpha, p)) + mstore(C_ALPHA_BASE_LOC, alpha) + + /** + * Generate zeta challenge + */ + mstore(0x00, challenge) + mstore(0x20, mload(T1_Y_LOC)) + mstore(0x40, mload(T1_X_LOC)) + mstore(0x60, mload(T2_Y_LOC)) + mstore(0x80, mload(T2_X_LOC)) + mstore(0xa0, mload(T3_Y_LOC)) + mstore(0xc0, mload(T3_X_LOC)) + mstore(0xe0, mload(T4_Y_LOC)) + mstore(0x100, mload(T4_X_LOC)) + + challenge := keccak256(0x00, 0x120) + + mstore(C_ZETA_LOC, mod(challenge, p)) + mstore(C_CURRENT_LOC, challenge) + } + + /** + * EVALUATE FIELD OPERATIONS + */ + + /** + * COMPUTE PUBLIC INPUT DELTA + * ΔPI = ∏ᵢ∈ℓ(wᵢ + β σ(i) + γ) / ∏ᵢ∈ℓ(wᵢ + β σ'(i) + γ) + */ + { + let beta := mload(C_BETA_LOC) // β + let gamma := mload(C_GAMMA_LOC) // γ + let work_root := mload(OMEGA_LOC) // ω + let numerator_value := 1 + let denominator_value := 1 + + let p_clone := p // move p to the front of the stack + let valid_inputs := true + + // Load the starting point of the public inputs (jump over the selector and the length of public inputs [0x24]) + let public_inputs_ptr := add(calldataload(0x24), 0x24) + + // endpoint_ptr = public_inputs_ptr + num_inputs * 0x20. // every public input is 0x20 bytes + let endpoint_ptr := add(public_inputs_ptr, mul(mload(NUM_INPUTS_LOC), 0x20)) + + // root_1 = β * 0x05 + let root_1 := mulmod(beta, 0x05, p_clone) // k1.β + // root_2 = β * 0x0c + let root_2 := mulmod(beta, 0x0c, p_clone) + // @note 0x05 + 0x07 == 0x0c == external coset generator + + for {} lt(public_inputs_ptr, endpoint_ptr) { public_inputs_ptr := add(public_inputs_ptr, 0x20) } { + /** + * input = public_input[i] + * valid_inputs &= input < p + * temp = input + gamma + * numerator_value *= (β.σ(i) + wᵢ + γ) // σ(i) = 0x05.ωⁱ + * denominator_value *= (β.σ'(i) + wᵢ + γ) // σ'(i) = 0x0c.ωⁱ + * root_1 *= ω + * root_2 *= ω + */ + + let input := calldataload(public_inputs_ptr) + valid_inputs := and(valid_inputs, lt(input, p_clone)) + let temp := addmod(input, gamma, p_clone) + + numerator_value := mulmod(numerator_value, add(root_1, temp), p_clone) + denominator_value := mulmod(denominator_value, add(root_2, temp), p_clone) + + root_1 := mulmod(root_1, work_root, p_clone) + root_2 := mulmod(root_2, work_root, p_clone) + } + + // Revert if not all public inputs are field elements (i.e. < p) + if iszero(valid_inputs) { + mstore(0x00, PUBLIC_INPUT_GE_P_SELECTOR) + revert(0x00, 0x04) + } + + mstore(DELTA_NUMERATOR_LOC, numerator_value) + mstore(DELTA_DENOMINATOR_LOC, denominator_value) + } + + /** + * Compute Plookup delta factor [γ(1 + β)]^{n-k} + * k = num roots cut out of Z_H = 4 + */ + { + let delta_base := mulmod(mload(C_GAMMA_LOC), addmod(mload(C_BETA_LOC), 1, p), p) + let delta_numerator := delta_base + { + let exponent := mload(N_LOC) + let count := 1 + for {} lt(count, exponent) { count := add(count, count) } { + delta_numerator := mulmod(delta_numerator, delta_numerator, p) + } + } + mstore(PLOOKUP_DELTA_NUMERATOR_LOC, delta_numerator) + + let delta_denominator := mulmod(delta_base, delta_base, p) + delta_denominator := mulmod(delta_denominator, delta_denominator, p) + mstore(PLOOKUP_DELTA_DENOMINATOR_LOC, delta_denominator) + } + /** + * Compute lagrange poly and vanishing poly fractions + */ + { + /** + * vanishing_numerator = zeta + * ZETA_POW_N = zeta^n + * vanishing_numerator -= 1 + * accumulating_root = omega_inverse + * work_root = p - accumulating_root + * domain_inverse = domain_inverse + * vanishing_denominator = zeta + work_root + * work_root *= accumulating_root + * vanishing_denominator *= (zeta + work_root) + * work_root *= accumulating_root + * vanishing_denominator *= (zeta + work_root) + * vanishing_denominator *= (zeta + (zeta + accumulating_root)) + * work_root = omega + * lagrange_numerator = vanishing_numerator * domain_inverse + * l_start_denominator = zeta - 1 + * accumulating_root = work_root^2 + * l_end_denominator = accumulating_root^2 * work_root * zeta - 1 + * Note: l_end_denominator term contains a term \omega^5 to cut out 5 roots of unity from vanishing poly + */ + + let zeta := mload(C_ZETA_LOC) + + // compute zeta^n, where n is a power of 2 + let vanishing_numerator := zeta + { + // pow_small + let exponent := mload(N_LOC) + let count := 1 + for {} lt(count, exponent) { count := add(count, count) } { + vanishing_numerator := mulmod(vanishing_numerator, vanishing_numerator, p) + } + } + mstore(ZETA_POW_N_LOC, vanishing_numerator) + vanishing_numerator := addmod(vanishing_numerator, sub(p, 1), p) + + let accumulating_root := mload(OMEGA_INVERSE_LOC) + let work_root := sub(p, accumulating_root) + let domain_inverse := mload(DOMAIN_INVERSE_LOC) + + let vanishing_denominator := addmod(zeta, work_root, p) + work_root := mulmod(work_root, accumulating_root, p) + vanishing_denominator := mulmod(vanishing_denominator, addmod(zeta, work_root, p), p) + work_root := mulmod(work_root, accumulating_root, p) + vanishing_denominator := mulmod(vanishing_denominator, addmod(zeta, work_root, p), p) + vanishing_denominator := + mulmod(vanishing_denominator, addmod(zeta, mulmod(work_root, accumulating_root, p), p), p) + + work_root := mload(OMEGA_LOC) + + let lagrange_numerator := mulmod(vanishing_numerator, domain_inverse, p) + let l_start_denominator := addmod(zeta, sub(p, 1), p) + + accumulating_root := mulmod(work_root, work_root, p) + + let l_end_denominator := + addmod( + mulmod(mulmod(mulmod(accumulating_root, accumulating_root, p), work_root, p), zeta, p), sub(p, 1), p + ) + + /** + * Compute inversions using Montgomery's batch inversion trick + */ + let accumulator := mload(DELTA_DENOMINATOR_LOC) + let t0 := accumulator + accumulator := mulmod(accumulator, vanishing_denominator, p) + let t1 := accumulator + accumulator := mulmod(accumulator, vanishing_numerator, p) + let t2 := accumulator + accumulator := mulmod(accumulator, l_start_denominator, p) + let t3 := accumulator + accumulator := mulmod(accumulator, mload(PLOOKUP_DELTA_DENOMINATOR_LOC), p) + let t4 := accumulator + { + mstore(0, 0x20) + mstore(0x20, 0x20) + mstore(0x40, 0x20) + mstore(0x60, mulmod(accumulator, l_end_denominator, p)) + mstore(0x80, sub(p, 2)) + mstore(0xa0, p) + if iszero(staticcall(gas(), 0x05, 0x00, 0xc0, 0x00, 0x20)) { + mstore(0x0, MOD_EXP_FAILURE_SELECTOR) + revert(0x00, 0x04) + } + accumulator := mload(0x00) + } + + t4 := mulmod(accumulator, t4, p) + accumulator := mulmod(accumulator, l_end_denominator, p) + + t3 := mulmod(accumulator, t3, p) + accumulator := mulmod(accumulator, mload(PLOOKUP_DELTA_DENOMINATOR_LOC), p) + + t2 := mulmod(accumulator, t2, p) + accumulator := mulmod(accumulator, l_start_denominator, p) + + t1 := mulmod(accumulator, t1, p) + accumulator := mulmod(accumulator, vanishing_numerator, p) + + t0 := mulmod(accumulator, t0, p) + accumulator := mulmod(accumulator, vanishing_denominator, p) + + accumulator := mulmod(mulmod(accumulator, accumulator, p), mload(DELTA_DENOMINATOR_LOC), p) + + mstore(PUBLIC_INPUT_DELTA_LOC, mulmod(mload(DELTA_NUMERATOR_LOC), accumulator, p)) + mstore(ZERO_POLY_LOC, mulmod(vanishing_numerator, t0, p)) + mstore(ZERO_POLY_INVERSE_LOC, mulmod(vanishing_denominator, t1, p)) + mstore(L_START_LOC, mulmod(lagrange_numerator, t2, p)) + mstore(PLOOKUP_DELTA_LOC, mulmod(mload(PLOOKUP_DELTA_NUMERATOR_LOC), t3, p)) + mstore(L_END_LOC, mulmod(lagrange_numerator, t4, p)) + } + + /** + * UltraPlonk Widget Ordering: + * + * 1. Permutation widget + * 2. Plookup widget + * 3. Arithmetic widget + * 4. Fixed base widget (?) + * 5. GenPermSort widget + * 6. Elliptic widget + * 7. Auxiliary widget + */ + + /** + * COMPUTE PERMUTATION WIDGET EVALUATION + */ + { + let alpha := mload(C_ALPHA_LOC) + let beta := mload(C_BETA_LOC) + let gamma := mload(C_GAMMA_LOC) + + /** + * t1 = (W1 + gamma + beta * ID1) * (W2 + gamma + beta * ID2) + * t2 = (W3 + gamma + beta * ID3) * (W4 + gamma + beta * ID4) + * result = alpha_base * z_eval * t1 * t2 + * t1 = (W1 + gamma + beta * sigma_1_eval) * (W2 + gamma + beta * sigma_2_eval) + * t2 = (W2 + gamma + beta * sigma_3_eval) * (W3 + gamma + beta * sigma_4_eval) + * result -= (alpha_base * z_omega_eval * t1 * t2) + */ + let t1 := + mulmod( + add(add(mload(W1_EVAL_LOC), gamma), mulmod(beta, mload(ID1_EVAL_LOC), p)), + add(add(mload(W2_EVAL_LOC), gamma), mulmod(beta, mload(ID2_EVAL_LOC), p)), + p + ) + let t2 := + mulmod( + add(add(mload(W3_EVAL_LOC), gamma), mulmod(beta, mload(ID3_EVAL_LOC), p)), + add(add(mload(W4_EVAL_LOC), gamma), mulmod(beta, mload(ID4_EVAL_LOC), p)), + p + ) + let result := mulmod(mload(C_ALPHA_BASE_LOC), mulmod(mload(Z_EVAL_LOC), mulmod(t1, t2, p), p), p) + t1 := + mulmod( + add(add(mload(W1_EVAL_LOC), gamma), mulmod(beta, mload(SIGMA1_EVAL_LOC), p)), + add(add(mload(W2_EVAL_LOC), gamma), mulmod(beta, mload(SIGMA2_EVAL_LOC), p)), + p + ) + t2 := + mulmod( + add(add(mload(W3_EVAL_LOC), gamma), mulmod(beta, mload(SIGMA3_EVAL_LOC), p)), + add(add(mload(W4_EVAL_LOC), gamma), mulmod(beta, mload(SIGMA4_EVAL_LOC), p)), + p + ) + result := + addmod( + result, + sub(p, mulmod(mload(C_ALPHA_BASE_LOC), mulmod(mload(Z_OMEGA_EVAL_LOC), mulmod(t1, t2, p), p), p)), + p + ) + + /** + * alpha_base *= alpha + * result += alpha_base . (L_{n-k}(ʓ) . (z(ʓ.ω) - ∆_{PI})) + * alpha_base *= alpha + * result += alpha_base . (L_1(ʓ)(Z(ʓ) - 1)) + * alpha_Base *= alpha + */ + mstore(C_ALPHA_BASE_LOC, mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_LOC), p)) + result := + addmod( + result, + mulmod( + mload(C_ALPHA_BASE_LOC), + mulmod( + mload(L_END_LOC), + addmod(mload(Z_OMEGA_EVAL_LOC), sub(p, mload(PUBLIC_INPUT_DELTA_LOC)), p), + p + ), + p + ), + p + ) + mstore(C_ALPHA_BASE_LOC, mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_LOC), p)) + mstore( + PERMUTATION_IDENTITY, + addmod( + result, + mulmod( + mload(C_ALPHA_BASE_LOC), + mulmod(mload(L_START_LOC), addmod(mload(Z_EVAL_LOC), sub(p, 1), p), p), + p + ), + p + ) + ) + mstore(C_ALPHA_BASE_LOC, mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_LOC), p)) + } + + /** + * COMPUTE PLOOKUP WIDGET EVALUATION + */ + { + /** + * Goal: f = (w1(z) + q2.w1(zω)) + η(w2(z) + qm.w2(zω)) + η²(w3(z) + qc.w_3(zω)) + q3(z).η³ + * f = η.q3(z) + * f += (w3(z) + qc.w_3(zω)) + * f *= η + * f += (w2(z) + qm.w2(zω)) + * f *= η + * f += (w1(z) + q2.w1(zω)) + */ + let f := mulmod(mload(C_ETA_LOC), mload(Q3_EVAL_LOC), p) + f := + addmod(f, addmod(mload(W3_EVAL_LOC), mulmod(mload(QC_EVAL_LOC), mload(W3_OMEGA_EVAL_LOC), p), p), p) + f := mulmod(f, mload(C_ETA_LOC), p) + f := + addmod(f, addmod(mload(W2_EVAL_LOC), mulmod(mload(QM_EVAL_LOC), mload(W2_OMEGA_EVAL_LOC), p), p), p) + f := mulmod(f, mload(C_ETA_LOC), p) + f := + addmod(f, addmod(mload(W1_EVAL_LOC), mulmod(mload(Q2_EVAL_LOC), mload(W1_OMEGA_EVAL_LOC), p), p), p) + + // t(z) = table4(z).η³ + table3(z).η² + table2(z).η + table1(z) + let t := + addmod( + addmod( + addmod( + mulmod(mload(TABLE4_EVAL_LOC), mload(C_ETA_CUBE_LOC), p), + mulmod(mload(TABLE3_EVAL_LOC), mload(C_ETA_SQR_LOC), p), + p + ), + mulmod(mload(TABLE2_EVAL_LOC), mload(C_ETA_LOC), p), + p + ), + mload(TABLE1_EVAL_LOC), + p + ) + + // t(zw) = table4(zw).η³ + table3(zw).η² + table2(zw).η + table1(zw) + let t_omega := + addmod( + addmod( + addmod( + mulmod(mload(TABLE4_OMEGA_EVAL_LOC), mload(C_ETA_CUBE_LOC), p), + mulmod(mload(TABLE3_OMEGA_EVAL_LOC), mload(C_ETA_SQR_LOC), p), + p + ), + mulmod(mload(TABLE2_OMEGA_EVAL_LOC), mload(C_ETA_LOC), p), + p + ), + mload(TABLE1_OMEGA_EVAL_LOC), + p + ) + + /** + * Goal: numerator = (TABLE_TYPE_EVAL * f(z) + γ) * (t(z) + βt(zω) + γ(β + 1)) * (β + 1) + * gamma_beta_constant = γ(β + 1) + * numerator = f * TABLE_TYPE_EVAL + gamma + * temp0 = t(z) + t(zω) * β + gamma_beta_constant + * numerator *= temp0 + * numerator *= (β + 1) + * temp0 = alpha * l_1 + * numerator += temp0 + * numerator *= z_lookup(z) + * numerator -= temp0 + */ + let gamma_beta_constant := mulmod(mload(C_GAMMA_LOC), addmod(mload(C_BETA_LOC), 1, p), p) + let numerator := addmod(mulmod(f, mload(TABLE_TYPE_EVAL_LOC), p), mload(C_GAMMA_LOC), p) + let temp0 := addmod(addmod(t, mulmod(t_omega, mload(C_BETA_LOC), p), p), gamma_beta_constant, p) + numerator := mulmod(numerator, temp0, p) + numerator := mulmod(numerator, addmod(mload(C_BETA_LOC), 1, p), p) + temp0 := mulmod(mload(C_ALPHA_LOC), mload(L_START_LOC), p) + numerator := addmod(numerator, temp0, p) + numerator := mulmod(numerator, mload(Z_LOOKUP_EVAL_LOC), p) + numerator := addmod(numerator, sub(p, temp0), p) + + /** + * Goal: denominator = z_lookup(zω)*[s(z) + βs(zω) + γ(1 + β)] - [z_lookup(zω) - [γ(1 + β)]^{n-k}]*α²L_end(z) + * note: delta_factor = [γ(1 + β)]^{n-k} + * denominator = s(z) + βs(zω) + γ(β + 1) + * temp1 = α²L_end(z) + * denominator -= temp1 + * denominator *= z_lookup(zω) + * denominator += temp1 * delta_factor + * PLOOKUP_IDENTITY = (numerator - denominator).alpha_base + * alpha_base *= alpha^3 + */ + let denominator := + addmod( + addmod(mload(S_EVAL_LOC), mulmod(mload(S_OMEGA_EVAL_LOC), mload(C_BETA_LOC), p), p), + gamma_beta_constant, + p + ) + let temp1 := mulmod(mload(C_ALPHA_SQR_LOC), mload(L_END_LOC), p) + denominator := addmod(denominator, sub(p, temp1), p) + denominator := mulmod(denominator, mload(Z_LOOKUP_OMEGA_EVAL_LOC), p) + denominator := addmod(denominator, mulmod(temp1, mload(PLOOKUP_DELTA_LOC), p), p) + + mstore(PLOOKUP_IDENTITY, mulmod(addmod(numerator, sub(p, denominator), p), mload(C_ALPHA_BASE_LOC), p)) + + // update alpha + mstore(C_ALPHA_BASE_LOC, mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_CUBE_LOC), p)) + } + + /** + * COMPUTE ARITHMETIC WIDGET EVALUATION + */ + { + /** + * The basic arithmetic gate identity in standard plonk is as follows. + * (w_1 . w_2 . q_m) + (w_1 . q_1) + (w_2 . q_2) + (w_3 . q_3) + (w_4 . q_4) + q_c = 0 + * However, for Ultraplonk, we extend this to support "passing" wires between rows (shown without alpha scaling below): + * q_arith * ( ( (-1/2) * (q_arith - 3) * q_m * w_1 * w_2 + q_1 * w_1 + q_2 * w_2 + q_3 * w_3 + q_4 * w_4 + q_c ) + + * (q_arith - 1)*( α * (q_arith - 2) * (w_1 + w_4 - w_1_omega + q_m) + w_4_omega) ) = 0 + * + * This formula results in several cases depending on q_arith: + * 1. q_arith == 0: Arithmetic gate is completely disabled + * + * 2. q_arith == 1: Everything in the minigate on the right is disabled. The equation is just a standard plonk equation + * with extra wires: q_m * w_1 * w_2 + q_1 * w_1 + q_2 * w_2 + q_3 * w_3 + q_4 * w_4 + q_c = 0 + * + * 3. q_arith == 2: The (w_1 + w_4 - ...) term is disabled. THe equation is: + * (1/2) * q_m * w_1 * w_2 + q_1 * w_1 + q_2 * w_2 + q_3 * w_3 + q_4 * w_4 + q_c + w_4_omega = 0 + * It allows defining w_4 at next index (w_4_omega) in terms of current wire values + * + * 4. q_arith == 3: The product of w_1 and w_2 is disabled, but a mini addition gate is enabled. α allows us to split + * the equation into two: + * + * q_1 * w_1 + q_2 * w_2 + q_3 * w_3 + q_4 * w_4 + q_c + 2 * w_4_omega = 0 + * and + * w_1 + w_4 - w_1_omega + q_m = 0 (we are reusing q_m here) + * + * 5. q_arith > 3: The product of w_1 and w_2 is scaled by (q_arith - 3), while the w_4_omega term is scaled by (q_arith - 1). + * The equation can be split into two: + * + * (q_arith - 3)* q_m * w_1 * w_ 2 + q_1 * w_1 + q_2 * w_2 + q_3 * w_3 + q_4 * w_4 + q_c + (q_arith - 1) * w_4_omega = 0 + * and + * w_1 + w_4 - w_1_omega + q_m = 0 + * + * The problem that q_m is used both in both equations can be dealt with by appropriately changing selector values at + * the next gate. Then we can treat (q_arith - 1) as a simulated q_6 selector and scale q_m to handle (q_arith - 3) at + * product. + */ + + let w1q1 := mulmod(mload(W1_EVAL_LOC), mload(Q1_EVAL_LOC), p) + let w2q2 := mulmod(mload(W2_EVAL_LOC), mload(Q2_EVAL_LOC), p) + let w3q3 := mulmod(mload(W3_EVAL_LOC), mload(Q3_EVAL_LOC), p) + let w4q3 := mulmod(mload(W4_EVAL_LOC), mload(Q4_EVAL_LOC), p) + + // @todo - Add a explicit test that hits QARITH == 3 + // w1w2qm := (w_1 . w_2 . q_m . (QARITH_EVAL_LOC - 3)) / 2 + let w1w2qm := + mulmod( + mulmod( + mulmod(mulmod(mload(W1_EVAL_LOC), mload(W2_EVAL_LOC), p), mload(QM_EVAL_LOC), p), + addmod(mload(QARITH_EVAL_LOC), sub(p, 3), p), + p + ), + NEGATIVE_INVERSE_OF_2_MODULO_P, + p + ) + + // (w_1 . w_2 . q_m . (q_arith - 3)) / -2) + (w_1 . q_1) + (w_2 . q_2) + (w_3 . q_3) + (w_4 . q_4) + q_c + let identity := + addmod( + mload(QC_EVAL_LOC), addmod(w4q3, addmod(w3q3, addmod(w2q2, addmod(w1q1, w1w2qm, p), p), p), p), p + ) + + // if q_arith == 3 we evaluate an additional mini addition gate (on top of the regular one), where: + // w_1 + w_4 - w_1_omega + q_m = 0 + // we use this gate to save an addition gate when adding or subtracting non-native field elements + // α * (q_arith - 2) * (w_1 + w_4 - w_1_omega + q_m) + let extra_small_addition_gate_identity := + mulmod( + mload(C_ALPHA_LOC), + mulmod( + addmod(mload(QARITH_EVAL_LOC), sub(p, 2), p), + addmod( + mload(QM_EVAL_LOC), + addmod( + sub(p, mload(W1_OMEGA_EVAL_LOC)), addmod(mload(W1_EVAL_LOC), mload(W4_EVAL_LOC), p), p + ), + p + ), + p + ), + p + ) + + // if q_arith == 2 OR q_arith == 3 we add the 4th wire of the NEXT gate into the arithmetic identity + // N.B. if q_arith > 2, this wire value will be scaled by (q_arith - 1) relative to the other gate wires! + // alpha_base * q_arith * (identity + (q_arith - 1) * (w_4_omega + extra_small_addition_gate_identity)) + mstore( + ARITHMETIC_IDENTITY, + mulmod( + mload(C_ALPHA_BASE_LOC), + mulmod( + mload(QARITH_EVAL_LOC), + addmod( + identity, + mulmod( + addmod(mload(QARITH_EVAL_LOC), sub(p, 1), p), + addmod(mload(W4_OMEGA_EVAL_LOC), extra_small_addition_gate_identity, p), + p + ), + p + ), + p + ), + p + ) + ) + + // update alpha + mstore(C_ALPHA_BASE_LOC, mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_SQR_LOC), p)) + } + + /** + * COMPUTE GENPERMSORT WIDGET EVALUATION + */ + { + /** + * D1 = (w2 - w1) + * D2 = (w3 - w2) + * D3 = (w4 - w3) + * D4 = (w1_omega - w4) + * + * α_a = alpha_base + * α_b = alpha_base * α + * α_c = alpha_base * α^2 + * α_d = alpha_base * α^3 + * + * range_accumulator = ( + * D1(D1 - 1)(D1 - 2)(D1 - 3).α_a + + * D2(D2 - 1)(D2 - 2)(D2 - 3).α_b + + * D3(D3 - 1)(D3 - 2)(D3 - 3).α_c + + * D4(D4 - 1)(D4 - 2)(D4 - 3).α_d + + * ) . q_sort + */ + let minus_two := sub(p, 2) + let minus_three := sub(p, 3) + let d1 := addmod(mload(W2_EVAL_LOC), sub(p, mload(W1_EVAL_LOC)), p) + let d2 := addmod(mload(W3_EVAL_LOC), sub(p, mload(W2_EVAL_LOC)), p) + let d3 := addmod(mload(W4_EVAL_LOC), sub(p, mload(W3_EVAL_LOC)), p) + let d4 := addmod(mload(W1_OMEGA_EVAL_LOC), sub(p, mload(W4_EVAL_LOC)), p) + + let range_accumulator := + mulmod( + mulmod( + mulmod(addmod(mulmod(d1, d1, p), sub(p, d1), p), addmod(d1, minus_two, p), p), + addmod(d1, minus_three, p), + p + ), + mload(C_ALPHA_BASE_LOC), + p + ) + range_accumulator := + addmod( + range_accumulator, + mulmod( + mulmod( + mulmod(addmod(mulmod(d2, d2, p), sub(p, d2), p), addmod(d2, minus_two, p), p), + addmod(d2, minus_three, p), + p + ), + mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_LOC), p), + p + ), + p + ) + range_accumulator := + addmod( + range_accumulator, + mulmod( + mulmod( + mulmod(addmod(mulmod(d3, d3, p), sub(p, d3), p), addmod(d3, minus_two, p), p), + addmod(d3, minus_three, p), + p + ), + mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_SQR_LOC), p), + p + ), + p + ) + range_accumulator := + addmod( + range_accumulator, + mulmod( + mulmod( + mulmod(addmod(mulmod(d4, d4, p), sub(p, d4), p), addmod(d4, minus_two, p), p), + addmod(d4, minus_three, p), + p + ), + mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_CUBE_LOC), p), + p + ), + p + ) + range_accumulator := mulmod(range_accumulator, mload(QSORT_EVAL_LOC), p) + + mstore(SORT_IDENTITY, range_accumulator) + + // update alpha + mstore(C_ALPHA_BASE_LOC, mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_QUAD_LOC), p)) + } + + /** + * COMPUTE ELLIPTIC WIDGET EVALUATION + */ + { + /** + * endo_term = (-x_2) * x_1 * (x_3 * 2 + x_1) * q_beta + * endo_sqr_term = x_2^2 + * endo_sqr_term *= (x_3 - x_1) + * endo_sqr_term *= q_beta^2 + * leftovers = x_2^2 + * leftovers *= x_2 + * leftovers += x_1^2 * (x_3 + x_1) @follow-up Invalid comment in BB widget + * leftovers -= (y_2^2 + y_1^2) + * sign_term = y_2 * y_1 + * sign_term += sign_term + * sign_term *= q_sign + */ + + let endo_term := + mulmod( + mulmod( + mulmod(sub(p, mload(X2_EVAL_LOC)), mload(X1_EVAL_LOC), p), + addmod(addmod(mload(X3_EVAL_LOC), mload(X3_EVAL_LOC), p), mload(X1_EVAL_LOC), p), + p + ), + mload(QBETA_LOC), + p + ) + + let endo_sqr_term := mulmod(mload(X2_EVAL_LOC), mload(X2_EVAL_LOC), p) + endo_sqr_term := mulmod(endo_sqr_term, addmod(mload(X3_EVAL_LOC), sub(p, mload(X1_EVAL_LOC)), p), p) + endo_sqr_term := mulmod(endo_sqr_term, mload(QBETA_SQR_LOC), p) + + let leftovers := mulmod(mload(X2_EVAL_LOC), mload(X2_EVAL_LOC), p) + leftovers := mulmod(leftovers, mload(X2_EVAL_LOC), p) + leftovers := + addmod( + leftovers, + mulmod( + mulmod(mload(X1_EVAL_LOC), mload(X1_EVAL_LOC), p), + addmod(mload(X3_EVAL_LOC), mload(X1_EVAL_LOC), p), + p + ), + p + ) + leftovers := + addmod( + leftovers, + sub( + p, + addmod( + mulmod(mload(Y2_EVAL_LOC), mload(Y2_EVAL_LOC), p), + mulmod(mload(Y1_EVAL_LOC), mload(Y1_EVAL_LOC), p), + p + ) + ), + p + ) + + let sign_term := mulmod(mload(Y2_EVAL_LOC), mload(Y1_EVAL_LOC), p) + sign_term := addmod(sign_term, sign_term, p) + sign_term := mulmod(sign_term, mload(QSIGN_LOC), p) + + /** + * x_identity = endo_term + endo_sqr_term + sign_term + leftovers + * x_identity *= alpha_base + * endo_term = (x_2 * q_beta) * (y_3 + y_1) + * sign_term = -((y2 * q_sign) * (x_1 + x_3)) + * leftovers = - x1 * (y_3 + y_1) + y_1 * (x_1 - x_3) + * y_identity = (endo_term + sign_term + leftovers) * (alpha_base * α) + */ + + let x_identity := addmod(addmod(endo_term, endo_sqr_term, p), addmod(sign_term, leftovers, p), p) + x_identity := mulmod(x_identity, mload(C_ALPHA_BASE_LOC), p) + endo_term := + mulmod( + mulmod(mload(X2_EVAL_LOC), mload(QBETA_LOC), p), + addmod(mload(Y3_EVAL_LOC), mload(Y1_EVAL_LOC), p), + p + ) + sign_term := + sub( + p, + mulmod( + mulmod(mload(Y2_EVAL_LOC), mload(QSIGN_LOC), p), + addmod(mload(X1_EVAL_LOC), sub(p, mload(X3_EVAL_LOC)), p), + p + ) + ) + leftovers := + addmod( + sub(p, mulmod(mload(X1_EVAL_LOC), addmod(mload(Y3_EVAL_LOC), mload(Y1_EVAL_LOC), p), p)), + mulmod(mload(Y1_EVAL_LOC), addmod(mload(X1_EVAL_LOC), sub(p, mload(X3_EVAL_LOC)), p), p), + p + ) + let y_identity := + mulmod( + addmod(addmod(endo_term, sign_term, p), leftovers, p), + mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_LOC), p), + p + ) + + // ELLIPTIC_IDENTITY = (x_identity + y_identity) * Q_ELLIPTIC_EVAL + mstore(ELLIPTIC_IDENTITY, mulmod(addmod(x_identity, y_identity, p), mload(QELLIPTIC_EVAL_LOC), p)) + + // update alpha + // The paper says to use ALPHA^2, we use ALPHA^4 this is a small oversight in the prover protocol + mstore(C_ALPHA_BASE_LOC, mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_QUAD_LOC), p)) + } + + /** + * COMPUTE AUXILIARY WIDGET EVALUATION + */ + { + { + /** + * Non native field arithmetic gate 2 + * _ _ + * / _ _ _ 14 \ + * q_2 . q_4 | (w_1 . w_2) + (w_1 . w_2) + (w_1 . w_4 + w_2 . w_3 - w_3) . 2 - w_3 - w_4 | + * \_ _/ + * + * limb_subproduct = w_1 . w_2_omega + w_1_omega . w_2 + * non_native_field_gate_2 = w_1 * w_4 + w_4 * w_3 - w_3_omega + * non_native_field_gate_2 = non_native_field_gate_2 * limb_size + * non_native_field_gate_2 -= w_4_omega + * non_native_field_gate_2 += limb_subproduct + * non_native_field_gate_2 *= q_4 + * limb_subproduct *= limb_size + * limb_subproduct += w_1_omega * w_2_omega + * non_native_field_gate_1 = (limb_subproduct + w_3 + w_4) * q_3 + * non_native_field_gate_3 = (limb_subproduct + w_4 - (w_3_omega + w_4_omega)) * q_m + * non_native_field_identity = (non_native_field_gate_1 + non_native_field_gate_2 + non_native_field_gate_3) * q_2 + */ + + let limb_subproduct := + addmod( + mulmod(mload(W1_EVAL_LOC), mload(W2_OMEGA_EVAL_LOC), p), + mulmod(mload(W1_OMEGA_EVAL_LOC), mload(W2_EVAL_LOC), p), + p + ) + + let non_native_field_gate_2 := + addmod( + addmod( + mulmod(mload(W1_EVAL_LOC), mload(W4_EVAL_LOC), p), + mulmod(mload(W2_EVAL_LOC), mload(W3_EVAL_LOC), p), + p + ), + sub(p, mload(W3_OMEGA_EVAL_LOC)), + p + ) + non_native_field_gate_2 := mulmod(non_native_field_gate_2, LIMB_SIZE, p) + non_native_field_gate_2 := addmod(non_native_field_gate_2, sub(p, mload(W4_OMEGA_EVAL_LOC)), p) + non_native_field_gate_2 := addmod(non_native_field_gate_2, limb_subproduct, p) + non_native_field_gate_2 := mulmod(non_native_field_gate_2, mload(Q4_EVAL_LOC), p) + limb_subproduct := mulmod(limb_subproduct, LIMB_SIZE, p) + limb_subproduct := + addmod(limb_subproduct, mulmod(mload(W1_OMEGA_EVAL_LOC), mload(W2_OMEGA_EVAL_LOC), p), p) + let non_native_field_gate_1 := + mulmod( + addmod(limb_subproduct, sub(p, addmod(mload(W3_EVAL_LOC), mload(W4_EVAL_LOC), p)), p), + mload(Q3_EVAL_LOC), + p + ) + let non_native_field_gate_3 := + mulmod( + addmod( + addmod(limb_subproduct, mload(W4_EVAL_LOC), p), + sub(p, addmod(mload(W3_OMEGA_EVAL_LOC), mload(W4_OMEGA_EVAL_LOC), p)), + p + ), + mload(QM_EVAL_LOC), + p + ) + let non_native_field_identity := + mulmod( + addmod(addmod(non_native_field_gate_1, non_native_field_gate_2, p), non_native_field_gate_3, p), + mload(Q2_EVAL_LOC), + p + ) + + mstore(AUX_NON_NATIVE_FIELD_EVALUATION, non_native_field_identity) + } + + { + /** + * limb_accumulator_1 = w_2_omega; + * limb_accumulator_1 *= SUBLIMB_SHIFT; + * limb_accumulator_1 += w_1_omega; + * limb_accumulator_1 *= SUBLIMB_SHIFT; + * limb_accumulator_1 += w_3; + * limb_accumulator_1 *= SUBLIMB_SHIFT; + * limb_accumulator_1 += w_2; + * limb_accumulator_1 *= SUBLIMB_SHIFT; + * limb_accumulator_1 += w_1; + * limb_accumulator_1 -= w_4; + * limb_accumulator_1 *= q_4; + */ + let limb_accumulator_1 := mulmod(mload(W2_OMEGA_EVAL_LOC), SUBLIMB_SHIFT, p) + limb_accumulator_1 := addmod(limb_accumulator_1, mload(W1_OMEGA_EVAL_LOC), p) + limb_accumulator_1 := mulmod(limb_accumulator_1, SUBLIMB_SHIFT, p) + limb_accumulator_1 := addmod(limb_accumulator_1, mload(W3_EVAL_LOC), p) + limb_accumulator_1 := mulmod(limb_accumulator_1, SUBLIMB_SHIFT, p) + limb_accumulator_1 := addmod(limb_accumulator_1, mload(W2_EVAL_LOC), p) + limb_accumulator_1 := mulmod(limb_accumulator_1, SUBLIMB_SHIFT, p) + limb_accumulator_1 := addmod(limb_accumulator_1, mload(W1_EVAL_LOC), p) + limb_accumulator_1 := addmod(limb_accumulator_1, sub(p, mload(W4_EVAL_LOC)), p) + limb_accumulator_1 := mulmod(limb_accumulator_1, mload(Q4_EVAL_LOC), p) + + /** + * limb_accumulator_2 = w_3_omega; + * limb_accumulator_2 *= SUBLIMB_SHIFT; + * limb_accumulator_2 += w_2_omega; + * limb_accumulator_2 *= SUBLIMB_SHIFT; + * limb_accumulator_2 += w_1_omega; + * limb_accumulator_2 *= SUBLIMB_SHIFT; + * limb_accumulator_2 += w_4; + * limb_accumulator_2 *= SUBLIMB_SHIFT; + * limb_accumulator_2 += w_3; + * limb_accumulator_2 -= w_4_omega; + * limb_accumulator_2 *= q_m; + */ + let limb_accumulator_2 := mulmod(mload(W3_OMEGA_EVAL_LOC), SUBLIMB_SHIFT, p) + limb_accumulator_2 := addmod(limb_accumulator_2, mload(W2_OMEGA_EVAL_LOC), p) + limb_accumulator_2 := mulmod(limb_accumulator_2, SUBLIMB_SHIFT, p) + limb_accumulator_2 := addmod(limb_accumulator_2, mload(W1_OMEGA_EVAL_LOC), p) + limb_accumulator_2 := mulmod(limb_accumulator_2, SUBLIMB_SHIFT, p) + limb_accumulator_2 := addmod(limb_accumulator_2, mload(W4_EVAL_LOC), p) + limb_accumulator_2 := mulmod(limb_accumulator_2, SUBLIMB_SHIFT, p) + limb_accumulator_2 := addmod(limb_accumulator_2, mload(W3_EVAL_LOC), p) + limb_accumulator_2 := addmod(limb_accumulator_2, sub(p, mload(W4_OMEGA_EVAL_LOC)), p) + limb_accumulator_2 := mulmod(limb_accumulator_2, mload(QM_EVAL_LOC), p) + + mstore( + AUX_LIMB_ACCUMULATOR_EVALUATION, + mulmod(addmod(limb_accumulator_1, limb_accumulator_2, p), mload(Q3_EVAL_LOC), p) + ) + } + + { + /** + * memory_record_check = w_3; + * memory_record_check *= eta; + * memory_record_check += w_2; + * memory_record_check *= eta; + * memory_record_check += w_1; + * memory_record_check *= eta; + * memory_record_check += q_c; + * + * partial_record_check = memory_record_check; + * + * memory_record_check -= w_4; + */ + + let memory_record_check := mulmod(mload(W3_EVAL_LOC), mload(C_ETA_LOC), p) + memory_record_check := addmod(memory_record_check, mload(W2_EVAL_LOC), p) + memory_record_check := mulmod(memory_record_check, mload(C_ETA_LOC), p) + memory_record_check := addmod(memory_record_check, mload(W1_EVAL_LOC), p) + memory_record_check := mulmod(memory_record_check, mload(C_ETA_LOC), p) + memory_record_check := addmod(memory_record_check, mload(QC_EVAL_LOC), p) + + let partial_record_check := memory_record_check + memory_record_check := addmod(memory_record_check, sub(p, mload(W4_EVAL_LOC)), p) + + mstore(AUX_MEMORY_EVALUATION, memory_record_check) + + // index_delta = w_1_omega - w_1 + let index_delta := addmod(mload(W1_OMEGA_EVAL_LOC), sub(p, mload(W1_EVAL_LOC)), p) + // record_delta = w_4_omega - w_4 + let record_delta := addmod(mload(W4_OMEGA_EVAL_LOC), sub(p, mload(W4_EVAL_LOC)), p) + // index_is_monotonically_increasing = index_delta * (index_delta - 1) + let index_is_monotonically_increasing := mulmod(index_delta, addmod(index_delta, sub(p, 1), p), p) + + // adjacent_values_match_if_adjacent_indices_match = record_delta * (1 - index_delta) + let adjacent_values_match_if_adjacent_indices_match := + mulmod(record_delta, addmod(1, sub(p, index_delta), p), p) + + // AUX_ROM_CONSISTENCY_EVALUATION = ((adjacent_values_match_if_adjacent_indices_match * alpha) + index_is_monotonically_increasing) * alpha + partial_record_check + mstore( + AUX_ROM_CONSISTENCY_EVALUATION, + addmod( + mulmod( + addmod( + mulmod(adjacent_values_match_if_adjacent_indices_match, mload(C_ALPHA_LOC), p), + index_is_monotonically_increasing, + p + ), + mload(C_ALPHA_LOC), + p + ), + memory_record_check, + p + ) + ) + + { + /** + * next_gate_access_type = w_3_omega; + * next_gate_access_type *= eta; + * next_gate_access_type += w_2_omega; + * next_gate_access_type *= eta; + * next_gate_access_type += w_1_omega; + * next_gate_access_type *= eta; + * next_gate_access_type = w_4_omega - next_gate_access_type; + */ + let next_gate_access_type := mulmod(mload(W3_OMEGA_EVAL_LOC), mload(C_ETA_LOC), p) + next_gate_access_type := addmod(next_gate_access_type, mload(W2_OMEGA_EVAL_LOC), p) + next_gate_access_type := mulmod(next_gate_access_type, mload(C_ETA_LOC), p) + next_gate_access_type := addmod(next_gate_access_type, mload(W1_OMEGA_EVAL_LOC), p) + next_gate_access_type := mulmod(next_gate_access_type, mload(C_ETA_LOC), p) + next_gate_access_type := addmod(mload(W4_OMEGA_EVAL_LOC), sub(p, next_gate_access_type), p) + + // value_delta = w_3_omega - w_3 + let value_delta := addmod(mload(W3_OMEGA_EVAL_LOC), sub(p, mload(W3_EVAL_LOC)), p) + // adjacent_values_match_if_adjacent_indices_match_and_next_access_is_a_read_operation = (1 - index_delta) * value_delta * (1 - next_gate_access_type); + + let adjacent_values_match_if_adjacent_indices_match_and_next_access_is_a_read_operation := + mulmod( + addmod(1, sub(p, index_delta), p), + mulmod(value_delta, addmod(1, sub(p, next_gate_access_type), p), p), + p + ) + + // AUX_RAM_CONSISTENCY_EVALUATION + + /** + * access_type = w_4 - partial_record_check + * access_check = access_type^2 - access_type + * next_gate_access_type_is_boolean = next_gate_access_type^2 - next_gate_access_type + * RAM_consistency_check_identity = adjacent_values_match_if_adjacent_indices_match_and_next_access_is_a_read_operation; + * RAM_consistency_check_identity *= alpha; + * RAM_consistency_check_identity += index_is_monotonically_increasing; + * RAM_consistency_check_identity *= alpha; + * RAM_consistency_check_identity += next_gate_access_type_is_boolean; + * RAM_consistency_check_identity *= alpha; + * RAM_consistency_check_identity += access_check; + */ + + let access_type := addmod(mload(W4_EVAL_LOC), sub(p, partial_record_check), p) + let access_check := mulmod(access_type, addmod(access_type, sub(p, 1), p), p) + let next_gate_access_type_is_boolean := + mulmod(next_gate_access_type, addmod(next_gate_access_type, sub(p, 1), p), p) + let RAM_cci := + mulmod( + adjacent_values_match_if_adjacent_indices_match_and_next_access_is_a_read_operation, + mload(C_ALPHA_LOC), + p + ) + RAM_cci := addmod(RAM_cci, index_is_monotonically_increasing, p) + RAM_cci := mulmod(RAM_cci, mload(C_ALPHA_LOC), p) + RAM_cci := addmod(RAM_cci, next_gate_access_type_is_boolean, p) + RAM_cci := mulmod(RAM_cci, mload(C_ALPHA_LOC), p) + RAM_cci := addmod(RAM_cci, access_check, p) + + mstore(AUX_RAM_CONSISTENCY_EVALUATION, RAM_cci) + } + + { + // timestamp_delta = w_2_omega - w_2 + let timestamp_delta := addmod(mload(W2_OMEGA_EVAL_LOC), sub(p, mload(W2_EVAL_LOC)), p) + + // RAM_timestamp_check_identity = (1 - index_delta) * timestamp_delta - w_3 + let RAM_timestamp_check_identity := + addmod( + mulmod(timestamp_delta, addmod(1, sub(p, index_delta), p), p), sub(p, mload(W3_EVAL_LOC)), p + ) + + /** + * memory_identity = ROM_consistency_check_identity * q_2; + * memory_identity += RAM_timestamp_check_identity * q_4; + * memory_identity += memory_record_check * q_m; + * memory_identity *= q_1; + * memory_identity += (RAM_consistency_check_identity * q_arith); + * + * auxiliary_identity = memory_identity + non_native_field_identity + limb_accumulator_identity; + * auxiliary_identity *= q_aux; + * auxiliary_identity *= alpha_base; + */ + let memory_identity := mulmod(mload(AUX_ROM_CONSISTENCY_EVALUATION), mload(Q2_EVAL_LOC), p) + memory_identity := + addmod(memory_identity, mulmod(RAM_timestamp_check_identity, mload(Q4_EVAL_LOC), p), p) + memory_identity := + addmod(memory_identity, mulmod(mload(AUX_MEMORY_EVALUATION), mload(QM_EVAL_LOC), p), p) + memory_identity := mulmod(memory_identity, mload(Q1_EVAL_LOC), p) + memory_identity := + addmod( + memory_identity, mulmod(mload(AUX_RAM_CONSISTENCY_EVALUATION), mload(QARITH_EVAL_LOC), p), p + ) + + let auxiliary_identity := addmod(memory_identity, mload(AUX_NON_NATIVE_FIELD_EVALUATION), p) + auxiliary_identity := addmod(auxiliary_identity, mload(AUX_LIMB_ACCUMULATOR_EVALUATION), p) + auxiliary_identity := mulmod(auxiliary_identity, mload(QAUX_EVAL_LOC), p) + auxiliary_identity := mulmod(auxiliary_identity, mload(C_ALPHA_BASE_LOC), p) + + mstore(AUX_IDENTITY, auxiliary_identity) + + // update alpha + mstore(C_ALPHA_BASE_LOC, mulmod(mload(C_ALPHA_BASE_LOC), mload(C_ALPHA_CUBE_LOC), p)) + } + } + } + + { + /** + * quotient = ARITHMETIC_IDENTITY + * quotient += PERMUTATION_IDENTITY + * quotient += PLOOKUP_IDENTITY + * quotient += SORT_IDENTITY + * quotient += ELLIPTIC_IDENTITY + * quotient += AUX_IDENTITY + * quotient *= ZERO_POLY_INVERSE + */ + mstore( + QUOTIENT_EVAL_LOC, + mulmod( + addmod( + addmod( + addmod( + addmod( + addmod(mload(PERMUTATION_IDENTITY), mload(PLOOKUP_IDENTITY), p), + mload(ARITHMETIC_IDENTITY), + p + ), + mload(SORT_IDENTITY), + p + ), + mload(ELLIPTIC_IDENTITY), + p + ), + mload(AUX_IDENTITY), + p + ), + mload(ZERO_POLY_INVERSE_LOC), + p + ) + ) + } + + /** + * GENERATE NU AND SEPARATOR CHALLENGES + */ + { + let current_challenge := mload(C_CURRENT_LOC) + // get a calldata pointer that points to the start of the data we want to copy + let calldata_ptr := add(calldataload(0x04), 0x24) + + calldata_ptr := add(calldata_ptr, NU_CALLDATA_SKIP_LENGTH) + + mstore(NU_CHALLENGE_INPUT_LOC_A, current_challenge) + mstore(NU_CHALLENGE_INPUT_LOC_B, mload(QUOTIENT_EVAL_LOC)) + calldatacopy(NU_CHALLENGE_INPUT_LOC_C, calldata_ptr, NU_INPUT_LENGTH) + + // hash length = (0x20 + num field elements), we include the previous challenge in the hash + let challenge := keccak256(NU_CHALLENGE_INPUT_LOC_A, add(NU_INPUT_LENGTH, 0x40)) + + mstore(C_V0_LOC, mod(challenge, p)) + // We need THIRTY-ONE independent nu challenges! + mstore(0x00, challenge) + mstore8(0x20, 0x01) + mstore(C_V1_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x02) + mstore(C_V2_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x03) + mstore(C_V3_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x04) + mstore(C_V4_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x05) + mstore(C_V5_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x06) + mstore(C_V6_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x07) + mstore(C_V7_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x08) + mstore(C_V8_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x09) + mstore(C_V9_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x0a) + mstore(C_V10_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x0b) + mstore(C_V11_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x0c) + mstore(C_V12_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x0d) + mstore(C_V13_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x0e) + mstore(C_V14_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x0f) + mstore(C_V15_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x10) + mstore(C_V16_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x11) + mstore(C_V17_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x12) + mstore(C_V18_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x13) + mstore(C_V19_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x14) + mstore(C_V20_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x15) + mstore(C_V21_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x16) + mstore(C_V22_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x17) + mstore(C_V23_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x18) + mstore(C_V24_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x19) + mstore(C_V25_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x1a) + mstore(C_V26_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x1b) + mstore(C_V27_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x1c) + mstore(C_V28_LOC, mod(keccak256(0x00, 0x21), p)) + mstore8(0x20, 0x1d) + mstore(C_V29_LOC, mod(keccak256(0x00, 0x21), p)) + + // @follow-up - Why are both v29 and v30 using appending 0x1d to the prior challenge and hashing, should it not change? + mstore8(0x20, 0x1d) + challenge := keccak256(0x00, 0x21) + mstore(C_V30_LOC, mod(challenge, p)) + + // separator + mstore(0x00, challenge) + mstore(0x20, mload(PI_Z_Y_LOC)) + mstore(0x40, mload(PI_Z_X_LOC)) + mstore(0x60, mload(PI_Z_OMEGA_Y_LOC)) + mstore(0x80, mload(PI_Z_OMEGA_X_LOC)) + + mstore(C_U_LOC, mod(keccak256(0x00, 0xa0), p)) + } + + let success := 0 + // VALIDATE T1 + { + let x := mload(T1_X_LOC) + let y := mload(T1_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q)) + mstore(ACCUMULATOR_X_LOC, x) + mstore(add(ACCUMULATOR_X_LOC, 0x20), y) + } + // VALIDATE T2 + { + let x := mload(T2_X_LOC) // 0x1400 + let y := mload(T2_Y_LOC) // 0x1420 + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(ZETA_POW_N_LOC)) + // accumulator_2 = [T2].zeta^n + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = [T1] + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE T3 + { + let x := mload(T3_X_LOC) + let y := mload(T3_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(mload(ZETA_POW_N_LOC), mload(ZETA_POW_N_LOC), p)) + // accumulator_2 = [T3].zeta^{2n} + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE T4 + { + let x := mload(T4_X_LOC) + let y := mload(T4_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(mulmod(mload(ZETA_POW_N_LOC), mload(ZETA_POW_N_LOC), p), mload(ZETA_POW_N_LOC), p)) + // accumulator_2 = [T4].zeta^{3n} + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE W1 + { + let x := mload(W1_X_LOC) + let y := mload(W1_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V0_LOC), p)) + // accumulator_2 = v0.(u + 1).[W1] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE W2 + { + let x := mload(W2_X_LOC) + let y := mload(W2_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V1_LOC), p)) + // accumulator_2 = v1.(u + 1).[W2] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE W3 + { + let x := mload(W3_X_LOC) + let y := mload(W3_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V2_LOC), p)) + // accumulator_2 = v2.(u + 1).[W3] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE W4 + { + let x := mload(W4_X_LOC) + let y := mload(W4_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V3_LOC), p)) + // accumulator_2 = v3.(u + 1).[W4] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE S + { + let x := mload(S_X_LOC) + let y := mload(S_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V4_LOC), p)) + // accumulator_2 = v4.(u + 1).[S] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE Z + { + let x := mload(Z_X_LOC) + let y := mload(Z_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V5_LOC), p)) + // accumulator_2 = v5.(u + 1).[Z] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE Z_LOOKUP + { + let x := mload(Z_LOOKUP_X_LOC) + let y := mload(Z_LOOKUP_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V6_LOC), p)) + // accumulator_2 = v6.(u + 1).[Z_LOOKUP] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE Q1 + { + let x := mload(Q1_X_LOC) + let y := mload(Q1_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V7_LOC)) + // accumulator_2 = v7.[Q1] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE Q2 + { + let x := mload(Q2_X_LOC) + let y := mload(Q2_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V8_LOC)) + // accumulator_2 = v8.[Q2] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE Q3 + { + let x := mload(Q3_X_LOC) + let y := mload(Q3_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V9_LOC)) + // accumulator_2 = v9.[Q3] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE Q4 + { + let x := mload(Q4_X_LOC) + let y := mload(Q4_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V10_LOC)) + // accumulator_2 = v10.[Q4] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE QM + { + let x := mload(QM_X_LOC) + let y := mload(QM_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V11_LOC)) + // accumulator_2 = v11.[Q;] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE QC + { + let x := mload(QC_X_LOC) + let y := mload(QC_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V12_LOC)) + // accumulator_2 = v12.[QC] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE QARITH + { + let x := mload(QARITH_X_LOC) + let y := mload(QARITH_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V13_LOC)) + // accumulator_2 = v13.[QARITH] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE QSORT + { + let x := mload(QSORT_X_LOC) + let y := mload(QSORT_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V14_LOC)) + // accumulator_2 = v14.[QSORT] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE QELLIPTIC + { + let x := mload(QELLIPTIC_X_LOC) + let y := mload(QELLIPTIC_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V15_LOC)) + // accumulator_2 = v15.[QELLIPTIC] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE QAUX + { + let x := mload(QAUX_X_LOC) + let y := mload(QAUX_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V16_LOC)) + // accumulator_2 = v15.[Q_AUX] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE SIGMA1 + { + let x := mload(SIGMA1_X_LOC) + let y := mload(SIGMA1_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V17_LOC)) + // accumulator_2 = v17.[sigma1] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE SIGMA2 + { + let x := mload(SIGMA2_X_LOC) + let y := mload(SIGMA2_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V18_LOC)) + // accumulator_2 = v18.[sigma2] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE SIGMA3 + { + let x := mload(SIGMA3_X_LOC) + let y := mload(SIGMA3_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V19_LOC)) + // accumulator_2 = v19.[sigma3] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE SIGMA4 + { + let x := mload(SIGMA4_X_LOC) + let y := mload(SIGMA4_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V20_LOC)) + // accumulator_2 = v20.[sigma4] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE TABLE1 + { + let x := mload(TABLE1_X_LOC) + let y := mload(TABLE1_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V21_LOC), p)) + // accumulator_2 = u.[table1] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE TABLE2 + { + let x := mload(TABLE2_X_LOC) + let y := mload(TABLE2_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V22_LOC), p)) + // accumulator_2 = u.[table2] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE TABLE3 + { + let x := mload(TABLE3_X_LOC) + let y := mload(TABLE3_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V23_LOC), p)) + // accumulator_2 = u.[table3] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE TABLE4 + { + let x := mload(TABLE4_X_LOC) + let y := mload(TABLE4_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(addmod(mload(C_U_LOC), 0x1, p), mload(C_V24_LOC), p)) + // accumulator_2 = u.[table4] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE TABLE_TYPE + { + let x := mload(TABLE_TYPE_X_LOC) + let y := mload(TABLE_TYPE_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V25_LOC)) + // accumulator_2 = v25.[TableType] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE ID1 + { + let x := mload(ID1_X_LOC) + let y := mload(ID1_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V26_LOC)) + // accumulator_2 = v26.[ID1] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE ID2 + { + let x := mload(ID2_X_LOC) + let y := mload(ID2_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V27_LOC)) + // accumulator_2 = v27.[ID2] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE ID3 + { + let x := mload(ID3_X_LOC) + let y := mload(ID3_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V28_LOC)) + // accumulator_2 = v28.[ID3] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE ID4 + { + let x := mload(ID4_X_LOC) + let y := mload(ID4_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mload(C_V29_LOC)) + // accumulator_2 = v29.[ID4] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + /** + * COMPUTE BATCH EVALUATION SCALAR MULTIPLIER + */ + { + /** + * batch_evaluation = v0 * (w_1_omega * u + w_1_eval) + * batch_evaluation += v1 * (w_2_omega * u + w_2_eval) + * batch_evaluation += v2 * (w_3_omega * u + w_3_eval) + * batch_evaluation += v3 * (w_4_omega * u + w_4_eval) + * batch_evaluation += v4 * (s_omega_eval * u + s_eval) + * batch_evaluation += v5 * (z_omega_eval * u + z_eval) + * batch_evaluation += v6 * (z_lookup_omega_eval * u + z_lookup_eval) + */ + let batch_evaluation := + mulmod( + mload(C_V0_LOC), + addmod(mulmod(mload(W1_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(W1_EVAL_LOC), p), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V1_LOC), + addmod(mulmod(mload(W2_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(W2_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V2_LOC), + addmod(mulmod(mload(W3_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(W3_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V3_LOC), + addmod(mulmod(mload(W4_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(W4_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V4_LOC), + addmod(mulmod(mload(S_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(S_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V5_LOC), + addmod(mulmod(mload(Z_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(Z_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V6_LOC), + addmod(mulmod(mload(Z_LOOKUP_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(Z_LOOKUP_EVAL_LOC), p), + p + ), + p + ) + + /** + * batch_evaluation += v7 * Q1_EVAL + * batch_evaluation += v8 * Q2_EVAL + * batch_evaluation += v9 * Q3_EVAL + * batch_evaluation += v10 * Q4_EVAL + * batch_evaluation += v11 * QM_EVAL + * batch_evaluation += v12 * QC_EVAL + * batch_evaluation += v13 * QARITH_EVAL + * batch_evaluation += v14 * QSORT_EVAL_LOC + * batch_evaluation += v15 * QELLIPTIC_EVAL_LOC + * batch_evaluation += v16 * QAUX_EVAL_LOC + * batch_evaluation += v17 * SIGMA1_EVAL_LOC + * batch_evaluation += v18 * SIGMA2_EVAL_LOC + * batch_evaluation += v19 * SIGMA3_EVAL_LOC + * batch_evaluation += v20 * SIGMA4_EVAL_LOC + */ + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V7_LOC), mload(Q1_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V8_LOC), mload(Q2_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V9_LOC), mload(Q3_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V10_LOC), mload(Q4_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V11_LOC), mload(QM_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V12_LOC), mload(QC_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V13_LOC), mload(QARITH_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V14_LOC), mload(QSORT_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V15_LOC), mload(QELLIPTIC_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V16_LOC), mload(QAUX_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V17_LOC), mload(SIGMA1_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V18_LOC), mload(SIGMA2_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V19_LOC), mload(SIGMA3_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V20_LOC), mload(SIGMA4_EVAL_LOC), p), p) + + /** + * batch_evaluation += v21 * (table1(zw) * u + table1(z)) + * batch_evaluation += v22 * (table2(zw) * u + table2(z)) + * batch_evaluation += v23 * (table3(zw) * u + table3(z)) + * batch_evaluation += v24 * (table4(zw) * u + table4(z)) + * batch_evaluation += v25 * table_type_eval + * batch_evaluation += v26 * id1_eval + * batch_evaluation += v27 * id2_eval + * batch_evaluation += v28 * id3_eval + * batch_evaluation += v29 * id4_eval + * batch_evaluation += quotient_eval + */ + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V21_LOC), + addmod(mulmod(mload(TABLE1_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(TABLE1_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V22_LOC), + addmod(mulmod(mload(TABLE2_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(TABLE2_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V23_LOC), + addmod(mulmod(mload(TABLE3_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(TABLE3_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := + addmod( + batch_evaluation, + mulmod( + mload(C_V24_LOC), + addmod(mulmod(mload(TABLE4_OMEGA_EVAL_LOC), mload(C_U_LOC), p), mload(TABLE4_EVAL_LOC), p), + p + ), + p + ) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V25_LOC), mload(TABLE_TYPE_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V26_LOC), mload(ID1_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V27_LOC), mload(ID2_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V28_LOC), mload(ID3_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mulmod(mload(C_V29_LOC), mload(ID4_EVAL_LOC), p), p) + batch_evaluation := addmod(batch_evaluation, mload(QUOTIENT_EVAL_LOC), p) + + mstore(0x00, 0x01) // [1].x + mstore(0x20, 0x02) // [1].y + mstore(0x40, sub(p, batch_evaluation)) + // accumulator_2 = -[1].(batch_evaluation) + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + mstore(OPENING_COMMITMENT_SUCCESS_FLAG, success) + } + + /** + * PERFORM PAIRING PREAMBLE + */ + { + let u := mload(C_U_LOC) + let zeta := mload(C_ZETA_LOC) + // VALIDATE PI_Z + { + let x := mload(PI_Z_X_LOC) + let y := mload(PI_Z_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q)) + mstore(0x00, x) + mstore(0x20, y) + } + // compute zeta.[PI_Z] and add into accumulator + mstore(0x40, zeta) + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // accumulator = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, ACCUMULATOR_X_LOC, 0x40)) + + // VALIDATE PI_Z_OMEGA + { + let x := mload(PI_Z_OMEGA_X_LOC) + let y := mload(PI_Z_OMEGA_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + mstore(0x40, mulmod(mulmod(u, zeta, p), mload(OMEGA_LOC), p)) + // accumulator_2 = u.zeta.omega.[PI_Z_OMEGA] + success := and(success, staticcall(gas(), 7, 0x00, 0x60, ACCUMULATOR2_X_LOC, 0x40)) + // PAIRING_RHS = accumulator + accumulator_2 + success := and(success, staticcall(gas(), 6, ACCUMULATOR_X_LOC, 0x80, PAIRING_RHS_X_LOC, 0x40)) + + mstore(0x00, mload(PI_Z_X_LOC)) + mstore(0x20, mload(PI_Z_Y_LOC)) + mstore(0x40, mload(PI_Z_OMEGA_X_LOC)) + mstore(0x60, mload(PI_Z_OMEGA_Y_LOC)) + mstore(0x80, u) + success := and(success, staticcall(gas(), 7, 0x40, 0x60, 0x40, 0x40)) + // PAIRING_LHS = [PI_Z] + [PI_Z_OMEGA] * u + success := and(success, staticcall(gas(), 6, 0x00, 0x80, PAIRING_LHS_X_LOC, 0x40)) + // negate lhs y-coordinate + mstore(PAIRING_LHS_Y_LOC, sub(q, mload(PAIRING_LHS_Y_LOC))) + + if mload(CONTAINS_RECURSIVE_PROOF_LOC) { + // VALIDATE RECURSIVE P1 + { + let x := mload(RECURSIVE_P1_X_LOC) + let y := mload(RECURSIVE_P1_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + + // compute u.u.[recursive_p1] and write into 0x60 + mstore(0x40, mulmod(u, u, p)) + success := and(success, staticcall(gas(), 7, 0x00, 0x60, 0x60, 0x40)) + // VALIDATE RECURSIVE P2 + { + let x := mload(RECURSIVE_P2_X_LOC) + let y := mload(RECURSIVE_P2_Y_LOC) + let xx := mulmod(x, x, q) + // validate on curve + success := and(success, eq(mulmod(y, y, q), addmod(mulmod(x, xx, q), 3, q))) + mstore(0x00, x) + mstore(0x20, y) + } + // compute u.u.[recursive_p2] and write into 0x00 + // 0x40 still contains u*u + success := and(success, staticcall(gas(), 7, 0x00, 0x60, 0x00, 0x40)) + + // compute u.u.[recursiveP1] + rhs and write into rhs + mstore(0xa0, mload(PAIRING_RHS_X_LOC)) + mstore(0xc0, mload(PAIRING_RHS_Y_LOC)) + success := and(success, staticcall(gas(), 6, 0x60, 0x80, PAIRING_RHS_X_LOC, 0x40)) + + // compute u.u.[recursiveP2] + lhs and write into lhs + mstore(0x40, mload(PAIRING_LHS_X_LOC)) + mstore(0x60, mload(PAIRING_LHS_Y_LOC)) + success := and(success, staticcall(gas(), 6, 0x00, 0x80, PAIRING_LHS_X_LOC, 0x40)) + } + + if iszero(success) { + mstore(0x0, EC_SCALAR_MUL_FAILURE_SELECTOR) + revert(0x00, 0x04) + } + mstore(PAIRING_PREAMBLE_SUCCESS_FLAG, success) + } + + /** + * PERFORM PAIRING + */ + { + // rhs paired with [1]_2 + // lhs paired with [x]_2 + + mstore(0x00, mload(PAIRING_RHS_X_LOC)) + mstore(0x20, mload(PAIRING_RHS_Y_LOC)) + mstore(0x40, 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2) // this is [1]_2 + mstore(0x60, 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed) + mstore(0x80, 0x090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b) + mstore(0xa0, 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa) + + mstore(0xc0, mload(PAIRING_LHS_X_LOC)) + mstore(0xe0, mload(PAIRING_LHS_Y_LOC)) + mstore(0x100, mload(G2X_X0_LOC)) + mstore(0x120, mload(G2X_X1_LOC)) + mstore(0x140, mload(G2X_Y0_LOC)) + mstore(0x160, mload(G2X_Y1_LOC)) + + success := staticcall(gas(), 8, 0x00, 0x180, 0x00, 0x20) + mstore(PAIRING_SUCCESS_FLAG, success) + mstore(RESULT_FLAG, mload(0x00)) + } + if iszero( + and( + and(and(mload(PAIRING_SUCCESS_FLAG), mload(RESULT_FLAG)), mload(PAIRING_PREAMBLE_SUCCESS_FLAG)), + mload(OPENING_COMMITMENT_SUCCESS_FLAG) + ) + ) { + mstore(0x0, PROOF_FAILURE_SELECTOR) + revert(0x00, 0x04) + } + { + mstore(0x00, 0x01) + return(0x00, 0x20) // Proof succeeded! + } + } + } +} + +contract UltraVerifier is BaseUltraVerifier { + function getVerificationKeyHash() public pure override(BaseUltraVerifier) returns (bytes32) { + return UltraVerificationKey.verificationKeyHash(); + } + + function loadVerificationKey(uint256 vk, uint256 _omegaInverseLoc) internal pure virtual override(BaseUltraVerifier) { + UltraVerificationKey.loadVerificationKey(vk, _omegaInverseLoc); + } +} diff --git a/circuits/proofs/a.proof b/circuits/proofs/a.proof new file mode 100644 index 0000000..8de1970 --- /dev/null +++ b/circuits/proofs/a.proof @@ -0,0 +1 @@ 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 \ No newline at end of file diff --git a/contracts/Kevin.sol b/contracts/Kevin.sol new file mode 100644 index 0000000..f7f214b --- /dev/null +++ b/contracts/Kevin.sol @@ -0,0 +1,17 @@ +pragma solidity ^0.8.15; + +import { UltraVerifier } from "circuits/contract/plonk_vk.sol"; + +contract Kevin is UltraVerifier { + + event Banana(uint256 x, uint256 y, uint256 result); + + uint256 public last; + + function set(bytes calldata proof, bytes32[] calldata inputs) public { + require(this.verify(proof, inputs)); + last = uint256(inputs[2]); + emit Banana(uint256(inputs[0]), uint256(inputs[1]), uint256(inputs[2])); + } + +} \ No newline at end of file diff --git a/contracts/Verifier.sol b/contracts/Verifier.sol deleted file mode 100644 index dc46e57..0000000 --- a/contracts/Verifier.sol +++ /dev/null @@ -1,3447 +0,0 @@ - - -// SPDX-License-Identifier: GPL-2.0-only -// Copyright 2020 Spilsbury Holdings Ltd - -pragma solidity >=0.6.0; -pragma experimental ABIEncoderV2; - -/** - * @title Turbo Plonk proof verification contract - * @dev Top level Plonk proof verification contract, which allows Plonk proof to be verified - * - * Copyright 2020 Spilsbury Holdings Ltd - * - * Licensed under the GNU General Public License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * - * This program is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * You should have received a copy of the GNU General Public License - * along with this program. If not, see . - */ -contract TurboVerifier { - using Bn254Crypto for Types.G1Point; - using Bn254Crypto for Types.G2Point; - using Transcript for Transcript.TranscriptData; - - /** - Calldata formatting: - - 0x00 - 0x04 : function signature - 0x04 - 0x24 : proof_data pointer (location in calldata that contains the proof_data array) - 0x44 - 0x64 : length of `proof_data` array - 0x64 - ???? : array containing our zk proof data - **/ - /** - * @dev Verify a Plonk proof - * @param - array of serialized proof data - */ - function verify(bytes calldata) - external - view - returns (bool result) - { - - Types.VerificationKey memory vk = get_verification_key(); - uint256 num_public_inputs = vk.num_inputs; - - // parse the input calldata and construct a Proof object - Types.Proof memory decoded_proof = deserialize_proof( - num_public_inputs, - vk - ); - - Transcript.TranscriptData memory transcript; - transcript.generate_initial_challenge(vk.circuit_size, vk.num_inputs); - - // reconstruct the beta, gamma, alpha and zeta challenges - Types.ChallengeTranscript memory challenges; - transcript.generate_beta_gamma_challenges(challenges, vk.num_inputs); - transcript.generate_alpha_challenge(challenges, decoded_proof.Z); - transcript.generate_zeta_challenge( - challenges, - decoded_proof.T1, - decoded_proof.T2, - decoded_proof.T3, - decoded_proof.T4 - ); - - /** - * Compute all inverses that will be needed throughout the program here. - * - * This is an efficiency improvement - it allows us to make use of the batch inversion Montgomery trick, - * which allows all inversions to be replaced with one inversion operation, at the expense of a few - * additional multiplications - **/ - (uint256 r_0, uint256 L1) = evalaute_field_operations( - decoded_proof, - vk, - challenges - ); - decoded_proof.r_0 = r_0; - - // reconstruct the nu and u challenges - // Need to change nu and u according to the simplified Plonk - transcript.generate_nu_challenges(challenges, vk.num_inputs); - - transcript.generate_separator_challenge( - challenges, - decoded_proof.PI_Z, - decoded_proof.PI_Z_OMEGA - ); - - //reset 'alpha base' - challenges.alpha_base = challenges.alpha; - // Computes step 9 -> [D]_1 - Types.G1Point memory linearised_contribution = PolynomialEval - .compute_linearised_opening_terms( - challenges, - L1, - vk, - decoded_proof - ); - // Computes step 10 -> [F]_1 - Types.G1Point memory batch_opening_commitment = PolynomialEval - .compute_batch_opening_commitment( - challenges, - vk, - linearised_contribution, - decoded_proof - ); - - uint256 batch_evaluation_g1_scalar = PolynomialEval - .compute_batch_evaluation_scalar_multiplier( - decoded_proof, - challenges - ); - - result = perform_pairing( - batch_opening_commitment, - batch_evaluation_g1_scalar, - challenges, - decoded_proof, - vk - ); - require(result, "Proof failed"); - } - - - function get_verification_key() internal pure returns (Types.VerificationKey memory) { - Types.VerificationKey memory vk; - - assembly { - mstore(add(vk, 0x00), 16) // vk.circuit_size - mstore(add(vk, 0x20), 3) // vk.num_inputs - mstore(add(vk, 0x40),0x21082ca216cbbf4e1c6e4f4594dd508c996dfbe1174efb98b11509c6e306460b) // vk.work_root - mstore(add(vk, 0x60),0x2d5e098bb31e86271ccb415b196942d755b0a9c3f21dd9882fa3d63ab1000001) // vk.domain_inverse - mstore(add(vk, 0x80),0x02e40daf409556c02bfc85eb303402b774954d30aeb0337eb85a71e6373428de) // vk.work_root_inverse - mstore(mload(add(vk, 0xa0)), 0x21d19f9a2e422fdf54281aba2841ca2b7ac7d47e06927da134da437e69b256d4)//vk.Q1 - mstore(add(mload(add(vk, 0xa0)), 0x20), 0x2731bfdcdd703c7fd8f9304efbf8698a7f7a6e00d9869c6ccf5d0992ba1c0925) - mstore(mload(add(vk, 0xc0)), 0x2d2da582f417ed5a42b104282a8768520b231c1507cb3f153375c9d64b1327a4)//vk.Q2 - mstore(add(mload(add(vk, 0xc0)), 0x20), 0x18c5218449c3d8d7a6073303f43fbe541552ce8ea126e38ea360cc2119e29aa7) - mstore(mload(add(vk, 0xe0)), 0x0ed20f0f8bafcbfa128b662e7ab8632c21287a3a148aeaec961976dee4a2a5f9)//vk.Q3 - mstore(add(mload(add(vk, 0xe0)), 0x20), 0x2f628d633ac6c8c6e4ddb0aa96000c4fcdee16856692d710a48623c45ff634de) - mstore(mload(add(vk, 0x100)), 0x2950076760523510abcfe90fa550b964e84b338f73af5222cdbbaefdacd4484e)//vk.Q4 - mstore(add(mload(add(vk, 0x100)), 0x20), 0x2e4e3e272c7b78ad894559812d7766e05615a8f7050a43d7ed1367adf30a9319) - mstore(mload(add(vk, 0x120)), 0x2950076760523510abcfe90fa550b964e84b338f73af5222cdbbaefdacd4484e)//vk.Q5 - mstore(add(mload(add(vk, 0x120)), 0x20), 0x2e4e3e272c7b78ad894559812d7766e05615a8f7050a43d7ed1367adf30a9319) - mstore(mload(add(vk, 0x140)), 0x10edf0eceb57978a9fcb47f4f3aca73be62974b9f4bcecbdf8b31370a0b0ac87)//vk.QM - mstore(add(mload(add(vk, 0x140)), 0x20), 0x09d5f4ba46e3137e3a5140001a8d00714069cb62cea9f25e76ca190c2441fb88) - mstore(mload(add(vk, 0x160)), 0x2950076760523510abcfe90fa550b964e84b338f73af5222cdbbaefdacd4484e)//vk.QC - mstore(add(mload(add(vk, 0x160)), 0x20), 0x2e4e3e272c7b78ad894559812d7766e05615a8f7050a43d7ed1367adf30a9319) - mstore(mload(add(vk, 0x180)), 0x0d071546f621d210d6666b6f0be14b57f319fe53d3a700d4bd98108cde5cafef)//vk.QARITH - mstore(add(mload(add(vk, 0x180)), 0x20), 0x09889531fea632235929915d4c46531278387ba2c1e25ea195155b6ce12468fb) - mstore(mload(add(vk, 0x1a0)), 0x2950076760523510abcfe90fa550b964e84b338f73af5222cdbbaefdacd4484e)//vk.QECC - mstore(add(mload(add(vk, 0x1a0)), 0x20), 0x2e4e3e272c7b78ad894559812d7766e05615a8f7050a43d7ed1367adf30a9319) - mstore(mload(add(vk, 0x1c0)), 0x2950076760523510abcfe90fa550b964e84b338f73af5222cdbbaefdacd4484e)//vk.QRANGE - mstore(add(mload(add(vk, 0x1c0)), 0x20), 0x2e4e3e272c7b78ad894559812d7766e05615a8f7050a43d7ed1367adf30a9319) - mstore(mload(add(vk, 0x1e0)), 0x2950076760523510abcfe90fa550b964e84b338f73af5222cdbbaefdacd4484e)//vk.QLOGIC - mstore(add(mload(add(vk, 0x1e0)), 0x20), 0x2e4e3e272c7b78ad894559812d7766e05615a8f7050a43d7ed1367adf30a9319) - mstore(mload(add(vk, 0x200)), 0x1a8d351d2e6954169d85d79caee093a1ce9a184b647b0a65349eff0f74869277)//vk.SIGMA1 - mstore(add(mload(add(vk, 0x200)), 0x20), 0x08adb7fb43ae70b37518b90f69889b3b96e5ae6c2a8d21605e289deb6acb7514) - mstore(mload(add(vk, 0x220)), 0x1eed4ab7f02dd2a46511bc4e0bf1126783f745c116b18c26625eeefbeb199561)//vk.SIGMA2 - mstore(add(mload(add(vk, 0x220)), 0x20), 0x2a61ee046ee1b01df35632f175dae62a3c3a458ea7b96d71184bc9f6c5dac1c8) - mstore(mload(add(vk, 0x240)), 0x17eb4448a82712353da6409cb97b2a3bb246af54d3b22e1250123ad8d1188d16)//vk.SIGMA3 - mstore(add(mload(add(vk, 0x240)), 0x20), 0x1e702c2da29525658efa992bb372676479cb0ba80e595d31aac2a6b1a046f254) - mstore(mload(add(vk, 0x260)), 0x10fb943eb02defee38be5eb1cbdb206190f0bb85bf2d967a2fea4cd6bf716577)//vk.SIGMA4 - mstore(add(mload(add(vk, 0x260)), 0x20), 0x127d3dfe3dfbf916177b5d53f86b2b2729e150b0b20b973718c1741048da753d) - mstore(add(vk, 0x280), 0x00) // vk.contains_recursive_proof - mstore(add(vk, 0x2a0), 0) // vk.recursive_proof_public_input_indices - mstore(mload(add(vk, 0x2c0)), 0x260e01b251f6f1c7e7ff4e580791dee8ea51d87a358e038b4efe30fac09383c1) // vk.g2_x.X.c1 - mstore(add(mload(add(vk, 0x2c0)), 0x20), 0x0118c4d5b837bcc2bc89b5b398b5974e9f5944073b32078b7e231fec938883b0) // vk.g2_x.X.c0 - mstore(add(mload(add(vk, 0x2c0)), 0x40), 0x04fc6369f7110fe3d25156c1bb9a72859cf2a04641f99ba4ee413c80da6a5fe4) // vk.g2_x.Y.c1 - mstore(add(mload(add(vk, 0x2c0)), 0x60), 0x22febda3c0c0632a56475b4214e5615e11e6dd3f96e6cea2854a87d4dacc5e55) // vk.g2_x.Y.c0 - } - return vk; - } - - - /** - * @dev Compute partial state of the verifier, specifically: public input delta evaluation, zero polynomial - * evaluation, the lagrange evaluations and the quotient polynomial evaluations - * - * Note: This uses the batch inversion Montgomery trick to reduce the number of - * inversions, and therefore the number of calls to the bn128 modular exponentiation - * precompile. - * - * Specifically, each function call: compute_public_input_delta() etc. at some point needs to invert a - * value to calculate a denominator in a fraction. Instead of performing this inversion as it is needed, we - * instead 'save up' the denominator calculations. The inputs to this are returned from the various functions - * and then we perform all necessary inversions in one go at the end of `evalaute_field_operations()`. This - * gives us the various variables that need to be returned. - * - * @param decoded_proof - deserialised proof - * @param vk - verification key - * @param challenges - all challenges (alpha, beta, gamma, zeta, nu[NUM_NU_CHALLENGES], u) stored in - * ChallengeTranscript struct form - * @return quotient polynomial evaluation (field element) and lagrange 1 evaluation (field element) - */ - function evalaute_field_operations( - Types.Proof memory decoded_proof, - Types.VerificationKey memory vk, - Types.ChallengeTranscript memory challenges - ) internal view returns (uint256, uint256) { - uint256 public_input_delta; - uint256 zero_polynomial_eval; - uint256 l_start; - uint256 l_end; - { - ( - uint256 public_input_numerator, - uint256 public_input_denominator - ) = PolynomialEval.compute_public_input_delta(challenges, vk); - - ( - uint256 vanishing_numerator, - uint256 vanishing_denominator, - uint256 lagrange_numerator, - uint256 l_start_denominator, - uint256 l_end_denominator - ) = PolynomialEval.compute_lagrange_and_vanishing_fractions( - vk, - challenges.zeta - ); - - ( - zero_polynomial_eval, - public_input_delta, - l_start, - l_end - ) = PolynomialEval.compute_batch_inversions( - public_input_numerator, - public_input_denominator, - vanishing_numerator, - vanishing_denominator, - lagrange_numerator, - l_start_denominator, - l_end_denominator - ); - vk.zero_polynomial_eval = zero_polynomial_eval; - } - - uint256 r_0 = PolynomialEval.compute_linear_polynomial_constant( - zero_polynomial_eval, - public_input_delta, - challenges, - l_start, - l_end, - decoded_proof - ); - - return (r_0, l_start); - } - - /** - * @dev Perform the pairing check - * @param batch_opening_commitment - G1 point representing the calculated batch opening commitment - * @param batch_evaluation_g1_scalar - uint256 representing the batch evaluation scalar multiplier to be applied to the G1 generator point - * @param challenges - all challenges (alpha, beta, gamma, zeta, nu[NUM_NU_CHALLENGES], u) stored in - * ChallengeTranscript struct form - * @param vk - verification key - * @param decoded_proof - deserialised proof - * @return bool specifying whether the pairing check was successful - */ - function perform_pairing( - Types.G1Point memory batch_opening_commitment, - uint256 batch_evaluation_g1_scalar, - Types.ChallengeTranscript memory challenges, - Types.Proof memory decoded_proof, - Types.VerificationKey memory vk - ) internal view returns (bool) { - uint256 u = challenges.u; - bool success; - uint256 p = Bn254Crypto.r_mod; - Types.G1Point memory rhs; - Types.G1Point memory PI_Z_OMEGA = decoded_proof.PI_Z_OMEGA; - Types.G1Point memory PI_Z = decoded_proof.PI_Z; - PI_Z.validateG1Point(); - PI_Z_OMEGA.validateG1Point(); - - // rhs = zeta.[PI_Z] + u.zeta.omega.[PI_Z_OMEGA] + [batch_opening_commitment] - batch_evaluation_g1_scalar.[1] - // scope this block to prevent stack depth errors - { - uint256 zeta = challenges.zeta; - uint256 pi_z_omega_scalar = vk.work_root; - assembly { - pi_z_omega_scalar := mulmod(pi_z_omega_scalar, zeta, p) - pi_z_omega_scalar := mulmod(pi_z_omega_scalar, u, p) - batch_evaluation_g1_scalar := sub(p, batch_evaluation_g1_scalar) - - // store accumulator point at mptr - let mPtr := mload(0x40) - - // set accumulator = batch_opening_commitment - mstore(mPtr, mload(batch_opening_commitment)) - mstore( - add(mPtr, 0x20), - mload(add(batch_opening_commitment, 0x20)) - ) - - // compute zeta.[PI_Z] and add into accumulator - mstore(add(mPtr, 0x40), mload(PI_Z)) - mstore(add(mPtr, 0x60), mload(add(PI_Z, 0x20))) - mstore(add(mPtr, 0x80), zeta) - success := staticcall( - gas(), - 7, - add(mPtr, 0x40), - 0x60, - add(mPtr, 0x40), - 0x40 - ) - success := and( - success, - staticcall(gas(), 6, mPtr, 0x80, mPtr, 0x40) - ) - - // compute u.zeta.omega.[PI_Z_OMEGA] and add into accumulator - mstore(add(mPtr, 0x40), mload(PI_Z_OMEGA)) - mstore(add(mPtr, 0x60), mload(add(PI_Z_OMEGA, 0x20))) - mstore(add(mPtr, 0x80), pi_z_omega_scalar) - success := and( - success, - staticcall( - gas(), - 7, - add(mPtr, 0x40), - 0x60, - add(mPtr, 0x40), - 0x40 - ) - ) - success := and( - success, - staticcall(gas(), 6, mPtr, 0x80, mPtr, 0x40) - ) - - // compute -batch_evaluation_g1_scalar.[1] - mstore(add(mPtr, 0x40), 0x01) // hardcoded generator point (1, 2) - mstore(add(mPtr, 0x60), 0x02) - mstore(add(mPtr, 0x80), batch_evaluation_g1_scalar) - success := and( - success, - staticcall( - gas(), - 7, - add(mPtr, 0x40), - 0x60, - add(mPtr, 0x40), - 0x40 - ) - ) - - // add -batch_evaluation_g1_scalar.[1] and the accumulator point, write result into rhs - success := and( - success, - staticcall(gas(), 6, mPtr, 0x80, rhs, 0x40) - ) - } - } - - Types.G1Point memory lhs; - assembly { - // store accumulator point at mptr - let mPtr := mload(0x40) - - // copy [PI_Z] into mPtr - mstore(mPtr, mload(PI_Z)) - mstore(add(mPtr, 0x20), mload(add(PI_Z, 0x20))) - - // compute u.[PI_Z_OMEGA] and write to (mPtr + 0x40) - mstore(add(mPtr, 0x40), mload(PI_Z_OMEGA)) - mstore(add(mPtr, 0x60), mload(add(PI_Z_OMEGA, 0x20))) - mstore(add(mPtr, 0x80), u) - success := and( - success, - staticcall( - gas(), - 7, - add(mPtr, 0x40), - 0x60, - add(mPtr, 0x40), - 0x40 - ) - ) - - // add [PI_Z] + u.[PI_Z_OMEGA] and write result into lhs - success := and(success, staticcall(gas(), 6, mPtr, 0x80, lhs, 0x40)) - } - - // negate lhs y-coordinate - uint256 q = Bn254Crypto.p_mod; - assembly { - mstore(add(lhs, 0x20), sub(q, mload(add(lhs, 0x20)))) - } - - if (vk.contains_recursive_proof) { - // If the proof itself contains an accumulated proof, - // we will have extracted two G1 elements `recursive_P1`, `recursive_p2` from the public inputs - - // We need to evaluate that e(recursive_P1, [x]_2) == e(recursive_P2, [1]_2) to finish verifying the inner proof - // We do this by creating a random linear combination between (lhs, recursive_P1) and (rhs, recursivee_P2) - // That way we still only need to evaluate one pairing product - - // We use `challenge.u * challenge.u` as the randomness to create a linear combination - // challenge.u is produced by hashing the entire transcript, which contains the public inputs (and by extension the recursive proof) - - // i.e. [lhs] = [lhs] + u.u.[recursive_P1] - // [rhs] = [rhs] + u.u.[recursive_P2] - Types.G1Point memory recursive_P1 = decoded_proof.recursive_P1; - Types.G1Point memory recursive_P2 = decoded_proof.recursive_P2; - recursive_P1.validateG1Point(); - recursive_P2.validateG1Point(); - assembly { - let mPtr := mload(0x40) - - // compute u.u.[recursive_P1] - mstore(mPtr, mload(recursive_P1)) - mstore(add(mPtr, 0x20), mload(add(recursive_P1, 0x20))) - mstore(add(mPtr, 0x40), mulmod(u, u, p)) // separator_challenge = u * u - success := and( - success, - staticcall(gas(), 7, mPtr, 0x60, add(mPtr, 0x60), 0x40) - ) - - // compute u.u.[recursive_P2] (u*u is still in memory at (mPtr + 0x40), no need to re-write it) - mstore(mPtr, mload(recursive_P2)) - mstore(add(mPtr, 0x20), mload(add(recursive_P2, 0x20))) - success := and( - success, - staticcall(gas(), 7, mPtr, 0x60, mPtr, 0x40) - ) - - // compute u.u.[recursiveP2] + rhs and write into rhs - mstore(add(mPtr, 0xa0), mload(rhs)) - mstore(add(mPtr, 0xc0), mload(add(rhs, 0x20))) - success := and( - success, - staticcall(gas(), 6, add(mPtr, 0x60), 0x80, rhs, 0x40) - ) - - // compute u.u.[recursiveP1] + lhs and write into lhs - mstore(add(mPtr, 0x40), mload(lhs)) - mstore(add(mPtr, 0x60), mload(add(lhs, 0x20))) - success := and( - success, - staticcall(gas(), 6, mPtr, 0x80, lhs, 0x40) - ) - } - } - - require(success, "perform_pairing G1 operations preamble fail"); - - return Bn254Crypto.pairingProd2(rhs, Bn254Crypto.P2(), lhs, vk.g2_x); - } - - /** - * @dev Deserialize a proof into a Proof struct - * @param num_public_inputs - number of public inputs in the proof. Taken from verification key - * @return proof - proof deserialized into the proof struct - */ - function deserialize_proof( - uint256 num_public_inputs, - Types.VerificationKey memory vk - ) internal pure returns (Types.Proof memory proof) { - uint256 p = Bn254Crypto.r_mod; - uint256 q = Bn254Crypto.p_mod; - uint256 data_ptr; - uint256 proof_ptr; - // first 32 bytes of bytes array contains length, skip it - assembly { - data_ptr := add(calldataload(0x04), 0x24) - proof_ptr := proof - } - - if (vk.contains_recursive_proof) { - uint256 index_counter = vk.recursive_proof_indices * 32; - uint256 x0 = 0; - uint256 y0 = 0; - uint256 x1 = 0; - uint256 y1 = 0; - assembly { - index_counter := add(index_counter, data_ptr) - x0 := calldataload(index_counter) - x0 := add(x0, shl(68, calldataload(add(index_counter, 0x20)))) - x0 := add(x0, shl(136, calldataload(add(index_counter, 0x40)))) - x0 := add(x0, shl(204, calldataload(add(index_counter, 0x60)))) - y0 := calldataload(add(index_counter, 0x80)) - y0 := add(y0, shl(68, calldataload(add(index_counter, 0xa0)))) - y0 := add(y0, shl(136, calldataload(add(index_counter, 0xc0)))) - y0 := add(y0, shl(204, calldataload(add(index_counter, 0xe0)))) - x1 := calldataload(add(index_counter, 0x100)) - x1 := add(x1, shl(68, calldataload(add(index_counter, 0x120)))) - x1 := add(x1, shl(136, calldataload(add(index_counter, 0x140)))) - x1 := add(x1, shl(204, calldataload(add(index_counter, 0x160)))) - y1 := calldataload(add(index_counter, 0x180)) - y1 := add(y1, shl(68, calldataload(add(index_counter, 0x1a0)))) - y1 := add(y1, shl(136, calldataload(add(index_counter, 0x1c0)))) - y1 := add(y1, shl(204, calldataload(add(index_counter, 0x1e0)))) - } - - proof.recursive_P1 = Bn254Crypto.new_g1(x0, y0); - proof.recursive_P2 = Bn254Crypto.new_g1(x1, y1); - } - - assembly { - let public_input_byte_length := mul(num_public_inputs, 0x20) - data_ptr := add(data_ptr, public_input_byte_length) - - // proof.W1 - mstore(mload(proof_ptr), mod(calldataload(add(data_ptr, 0x20)), q)) - mstore(add(mload(proof_ptr), 0x20), mod(calldataload(data_ptr), q)) - - // proof.W2 - mstore( - mload(add(proof_ptr, 0x20)), - mod(calldataload(add(data_ptr, 0x60)), q) - ) - mstore( - add(mload(add(proof_ptr, 0x20)), 0x20), - mod(calldataload(add(data_ptr, 0x40)), q) - ) - - // proof.W3 - mstore( - mload(add(proof_ptr, 0x40)), - mod(calldataload(add(data_ptr, 0xa0)), q) - ) - mstore( - add(mload(add(proof_ptr, 0x40)), 0x20), - mod(calldataload(add(data_ptr, 0x80)), q) - ) - - // proof.W4 - mstore( - mload(add(proof_ptr, 0x60)), - mod(calldataload(add(data_ptr, 0xe0)), q) - ) - mstore( - add(mload(add(proof_ptr, 0x60)), 0x20), - mod(calldataload(add(data_ptr, 0xc0)), q) - ) - - // proof.Z - mstore( - mload(add(proof_ptr, 0x80)), - mod(calldataload(add(data_ptr, 0x120)), q) - ) - mstore( - add(mload(add(proof_ptr, 0x80)), 0x20), - mod(calldataload(add(data_ptr, 0x100)), q) - ) - - // proof.T1 - mstore( - mload(add(proof_ptr, 0xa0)), - mod(calldataload(add(data_ptr, 0x160)), q) - ) - mstore( - add(mload(add(proof_ptr, 0xa0)), 0x20), - mod(calldataload(add(data_ptr, 0x140)), q) - ) - - // proof.T2 - mstore( - mload(add(proof_ptr, 0xc0)), - mod(calldataload(add(data_ptr, 0x1a0)), q) - ) - mstore( - add(mload(add(proof_ptr, 0xc0)), 0x20), - mod(calldataload(add(data_ptr, 0x180)), q) - ) - - // proof.T3 - mstore( - mload(add(proof_ptr, 0xe0)), - mod(calldataload(add(data_ptr, 0x1e0)), q) - ) - mstore( - add(mload(add(proof_ptr, 0xe0)), 0x20), - mod(calldataload(add(data_ptr, 0x1c0)), q) - ) - - // proof.T4 - mstore( - mload(add(proof_ptr, 0x100)), - mod(calldataload(add(data_ptr, 0x220)), q) - ) - mstore( - add(mload(add(proof_ptr, 0x100)), 0x20), - mod(calldataload(add(data_ptr, 0x200)), q) - ) - - // proof.w1 to proof.w4 - mstore( - add(proof_ptr, 0x120), - mod(calldataload(add(data_ptr, 0x240)), p) - ) - mstore( - add(proof_ptr, 0x140), - mod(calldataload(add(data_ptr, 0x260)), p) - ) - mstore( - add(proof_ptr, 0x160), - mod(calldataload(add(data_ptr, 0x280)), p) - ) - mstore( - add(proof_ptr, 0x180), - mod(calldataload(add(data_ptr, 0x2a0)), p) - ) - - // proof.sigma1 - mstore( - add(proof_ptr, 0x1a0), - mod(calldataload(add(data_ptr, 0x2c0)), p) - ) - - // proof.sigma2 - mstore( - add(proof_ptr, 0x1c0), - mod(calldataload(add(data_ptr, 0x2e0)), p) - ) - - // proof.sigma3 - mstore( - add(proof_ptr, 0x1e0), - mod(calldataload(add(data_ptr, 0x300)), p) - ) - - // proof.q_arith - mstore( - add(proof_ptr, 0x200), - mod(calldataload(add(data_ptr, 0x320)), p) - ) - - // proof.q_ecc - mstore( - add(proof_ptr, 0x220), - mod(calldataload(add(data_ptr, 0x340)), p) - ) - - // proof.q_c - mstore( - add(proof_ptr, 0x240), - mod(calldataload(add(data_ptr, 0x360)), p) - ) - - // proof.linearization_polynomial - // mstore(add(proof_ptr, 0x260), mod(calldataload(add(data_ptr, 0x380)), p)) - - // proof.grand_product_at_z_omega - mstore( - add(proof_ptr, 0x260), - mod(calldataload(add(data_ptr, 0x380)), p) - ) - - // proof.w1_omega to proof.w4_omega - mstore( - add(proof_ptr, 0x280), - mod(calldataload(add(data_ptr, 0x3a0)), p) - ) - mstore( - add(proof_ptr, 0x2a0), - mod(calldataload(add(data_ptr, 0x3c0)), p) - ) - mstore( - add(proof_ptr, 0x2c0), - mod(calldataload(add(data_ptr, 0x3e0)), p) - ) - mstore( - add(proof_ptr, 0x2e0), - mod(calldataload(add(data_ptr, 0x400)), p) - ) - - // proof.PI_Z - //Order of x and y coordinate are reverse in case of serialization - mstore( - mload(add(proof_ptr, 0x300)), - mod(calldataload(add(data_ptr, 0x440)), q) - ) - mstore( - add(mload(add(proof_ptr, 0x300)), 0x20), - mod(calldataload(add(data_ptr, 0x420)), q) - ) - - // proof.PI_Z_OMEGA - mstore( - mload(add(proof_ptr, 0x320)), - mod(calldataload(add(data_ptr, 0x480)), q) - ) - mstore( - add(mload(add(proof_ptr, 0x320)), 0x20), - mod(calldataload(add(data_ptr, 0x460)), q) - ) - } - } -} - - - - - -/** - * @title Bn254Crypto library used for the fr, g1 and g2 point types - * @dev Used to manipulate fr, g1, g2 types, perform modular arithmetic on them and call - * the precompiles add, scalar mul and pairing - * - * Notes on optimisations - * 1) Perform addmod, mulmod etc. in assembly - removes the check that Solidity performs to confirm that - * the supplied modulus is not 0. This is safe as the modulus's used (r_mod, q_mod) are hard coded - * inside the contract and not supplied by the user - */ -library Types { - uint256 constant PROGRAM_WIDTH = 4; - uint256 constant NUM_NU_CHALLENGES = 11; - - uint256 constant coset_generator0 = - 0x0000000000000000000000000000000000000000000000000000000000000005; - uint256 constant coset_generator1 = - 0x0000000000000000000000000000000000000000000000000000000000000006; - uint256 constant coset_generator2 = - 0x0000000000000000000000000000000000000000000000000000000000000007; - - // TODO: add external_coset_generator() method to compute this - uint256 constant coset_generator7 = - 0x000000000000000000000000000000000000000000000000000000000000000c; - - struct G1Point { - uint256 x; - uint256 y; - } - - // G2 group element where x \in Fq2 = x0 * z + x1 - struct G2Point { - uint256 x0; - uint256 x1; - uint256 y0; - uint256 y1; - } - - // N>B. Do not re-order these fields! They must appear in the same order as they - // appear in the proof data - struct Proof { - G1Point W1; - G1Point W2; - G1Point W3; - G1Point W4; - G1Point Z; - G1Point T1; - G1Point T2; - G1Point T3; - G1Point T4; - uint256 w1; - uint256 w2; - uint256 w3; - uint256 w4; - uint256 sigma1; - uint256 sigma2; - uint256 sigma3; - uint256 q_arith; - uint256 q_ecc; - uint256 q_c; - // uint256 linearization_polynomial; - uint256 grand_product_at_z_omega; - uint256 w1_omega; - uint256 w2_omega; - uint256 w3_omega; - uint256 w4_omega; - G1Point PI_Z; - G1Point PI_Z_OMEGA; - G1Point recursive_P1; - G1Point recursive_P2; - // uint256 quotient_polynomial_eval; - uint256 r_0; - } - - struct ChallengeTranscript { - uint256 alpha_base; - uint256 alpha; - uint256 zeta; - uint256 beta; - uint256 gamma; - uint256 u; - uint256 v0; - uint256 v1; - uint256 v2; - uint256 v3; - uint256 v4; - uint256 v5; - uint256 v6; - uint256 v7; - uint256 v8; - uint256 v9; - uint256 v10; - } - - struct VerificationKey { - uint256 circuit_size; - uint256 num_inputs; - uint256 work_root; - uint256 domain_inverse; - uint256 work_root_inverse; - G1Point Q1; - G1Point Q2; - G1Point Q3; - G1Point Q4; - G1Point Q5; - G1Point QM; - G1Point QC; - G1Point QARITH; - G1Point QECC; - G1Point QRANGE; - G1Point QLOGIC; - G1Point SIGMA1; - G1Point SIGMA2; - G1Point SIGMA3; - G1Point SIGMA4; - bool contains_recursive_proof; - uint256 recursive_proof_indices; - G2Point g2_x; - // zeta challenge raised to the power of the circuit size. - // Not actually part of the verification key, but we put it here to prevent stack depth errors - uint256 zeta_pow_n; - // necessary fot the simplified plonk - uint256 zero_polynomial_eval; - } -} - - - - - - -/** - * @title Bn254 elliptic curve crypto - * @dev Provides some basic methods to compute bilinear pairings, construct group elements and misc numerical methods - */ -library Bn254Crypto { - uint256 constant p_mod = - 21888242871839275222246405745257275088696311157297823662689037894645226208583; - uint256 constant r_mod = - 21888242871839275222246405745257275088548364400416034343698204186575808495617; - - // Perform a modular exponentiation. This method is ideal for small exponents (~64 bits or less), as - // it is cheaper than using the pow precompile - function pow_small( - uint256 base, - uint256 exponent, - uint256 modulus - ) internal pure returns (uint256) { - uint256 result = 1; - uint256 input = base; - uint256 count = 1; - - assembly { - let endpoint := add(exponent, 0x01) - for { - - } lt(count, endpoint) { - count := add(count, count) - } { - if and(exponent, count) { - result := mulmod(result, input, modulus) - } - input := mulmod(input, input, modulus) - } - } - - return result; - } - - function invert(uint256 fr) internal view returns (uint256) { - uint256 output; - bool success; - uint256 p = r_mod; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, 0x20) - mstore(add(mPtr, 0x20), 0x20) - mstore(add(mPtr, 0x40), 0x20) - mstore(add(mPtr, 0x60), fr) - mstore(add(mPtr, 0x80), sub(p, 2)) - mstore(add(mPtr, 0xa0), p) - success := staticcall(gas(), 0x05, mPtr, 0xc0, 0x00, 0x20) - output := mload(0x00) - } - require(success, "pow precompile call failed!"); - return output; - } - - function new_g1(uint256 x, uint256 y) - internal - pure - returns (Types.G1Point memory) - { - uint256 xValue; - uint256 yValue; - assembly { - xValue := mod(x, r_mod) - yValue := mod(y, r_mod) - } - return Types.G1Point(xValue, yValue); - } - - function new_g2( - uint256 x0, - uint256 x1, - uint256 y0, - uint256 y1 - ) internal pure returns (Types.G2Point memory) { - return Types.G2Point(x0, x1, y0, y1); - } - - function P1() internal pure returns (Types.G1Point memory) { - return Types.G1Point(1, 2); - } - - function P2() internal pure returns (Types.G2Point memory) { - return - Types.G2Point({ - x0: 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2, - x1: 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed, - y0: 0x090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b, - y1: 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa - }); - } - - /// Evaluate the following pairing product: - /// e(a1, a2).e(-b1, b2) == 1 - function pairingProd2( - Types.G1Point memory a1, - Types.G2Point memory a2, - Types.G1Point memory b1, - Types.G2Point memory b2 - ) internal view returns (bool) { - validateG1Point(a1); - validateG1Point(b1); - bool success; - uint256 out; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(a1)) - mstore(add(mPtr, 0x20), mload(add(a1, 0x20))) - mstore(add(mPtr, 0x40), mload(a2)) - mstore(add(mPtr, 0x60), mload(add(a2, 0x20))) - mstore(add(mPtr, 0x80), mload(add(a2, 0x40))) - mstore(add(mPtr, 0xa0), mload(add(a2, 0x60))) - - mstore(add(mPtr, 0xc0), mload(b1)) - mstore(add(mPtr, 0xe0), mload(add(b1, 0x20))) - mstore(add(mPtr, 0x100), mload(b2)) - mstore(add(mPtr, 0x120), mload(add(b2, 0x20))) - mstore(add(mPtr, 0x140), mload(add(b2, 0x40))) - mstore(add(mPtr, 0x160), mload(add(b2, 0x60))) - success := staticcall(gas(), 8, mPtr, 0x180, 0x00, 0x20) - out := mload(0x00) - } - require(success, "Pairing check failed!"); - return (out != 0); - } - - /** - * validate the following: - * x != 0 - * y != 0 - * x < p - * y < p - * y^2 = x^3 + 3 mod p - */ - function validateG1Point(Types.G1Point memory point) internal pure { - bool is_well_formed; - uint256 p = p_mod; - assembly { - let x := mload(point) - let y := mload(add(point, 0x20)) - - is_well_formed := and( - and(and(lt(x, p), lt(y, p)), not(or(iszero(x), iszero(y)))), - eq(mulmod(y, y, p), addmod(mulmod(x, mulmod(x, x, p), p), 3, p)) - ) - } - require( - is_well_formed, - "Bn254: G1 point not on curve, or is malformed" - ); - } -} - - - - -/** - * @title Turbo Plonk polynomial evaluation - * @dev Implementation of Turbo Plonk's polynomial evaluation algorithms - * - * Expected to be inherited by `TurboPlonk.sol` - * - * Copyright 2020 Spilsbury Holdings Ltd - * - * Licensed under the GNU General Public License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * - * This program is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * You should have received a copy of the GNU General Public License - * along with this program. If not, see . - */ -library PolynomialEval { - using Bn254Crypto for Types.G1Point; - using Bn254Crypto for Types.G2Point; - - /** - * @dev Use batch inversion (so called Montgomery's trick). Circuit size is the domain - * Allows multiple inversions to be performed in one inversion, at the expense of additional multiplications - * - * Returns a struct containing the inverted elements - */ - function compute_batch_inversions( - uint256 public_input_delta_numerator, - uint256 public_input_delta_denominator, - uint256 vanishing_numerator, - uint256 vanishing_denominator, - uint256 lagrange_numerator, - uint256 l_start_denominator, - uint256 l_end_denominator - ) - internal - view - returns ( - uint256 zero_polynomial_eval, - uint256 public_input_delta, - uint256 l_start, - uint256 l_end - ) - { - uint256 mPtr; - uint256 p = Bn254Crypto.r_mod; - uint256 accumulator = 1; - assembly { - mPtr := mload(0x40) - mstore(0x40, add(mPtr, 0x200)) - } - - // store denominators in mPtr -> mPtr + 0x80 - assembly { - mstore(mPtr, public_input_delta_denominator) // store denominator - mstore(add(mPtr, 0x20), vanishing_denominator) // store denominator - mstore(add(mPtr, 0x40), l_start_denominator) // store denominator - mstore(add(mPtr, 0x60), l_end_denominator) // store denominator - - // store temporary product terms at mPtr + 0x80 -> mPtr + 0x100 - mstore(add(mPtr, 0x80), accumulator) - accumulator := mulmod(accumulator, mload(mPtr), p) - mstore(add(mPtr, 0xa0), accumulator) - accumulator := mulmod(accumulator, mload(add(mPtr, 0x20)), p) - mstore(add(mPtr, 0xc0), accumulator) - accumulator := mulmod(accumulator, mload(add(mPtr, 0x40)), p) - mstore(add(mPtr, 0xe0), accumulator) - accumulator := mulmod(accumulator, mload(add(mPtr, 0x60)), p) - } - - accumulator = Bn254Crypto.invert(accumulator); - assembly { - let intermediate := mulmod(accumulator, mload(add(mPtr, 0xe0)), p) - accumulator := mulmod(accumulator, mload(add(mPtr, 0x60)), p) - mstore(add(mPtr, 0x60), intermediate) - - intermediate := mulmod(accumulator, mload(add(mPtr, 0xc0)), p) - accumulator := mulmod(accumulator, mload(add(mPtr, 0x40)), p) - mstore(add(mPtr, 0x40), intermediate) - - intermediate := mulmod(accumulator, mload(add(mPtr, 0xa0)), p) - accumulator := mulmod(accumulator, mload(add(mPtr, 0x20)), p) - mstore(add(mPtr, 0x20), intermediate) - - intermediate := mulmod(accumulator, mload(add(mPtr, 0x80)), p) - accumulator := mulmod(accumulator, mload(mPtr), p) - mstore(mPtr, intermediate) - - public_input_delta := mulmod( - public_input_delta_numerator, - mload(mPtr), - p - ) - - zero_polynomial_eval := mulmod( - vanishing_numerator, - mload(add(mPtr, 0x20)), - p - ) - - l_start := mulmod(lagrange_numerator, mload(add(mPtr, 0x40)), p) - - l_end := mulmod(lagrange_numerator, mload(add(mPtr, 0x60)), p) - } - } - - function compute_public_input_delta( - Types.ChallengeTranscript memory challenges, - Types.VerificationKey memory vk - ) internal pure returns (uint256, uint256) { - uint256 gamma = challenges.gamma; - uint256 work_root = vk.work_root; - - uint256 endpoint = (vk.num_inputs * 0x20) - 0x20; - uint256 public_inputs; - uint256 root_1 = challenges.beta; - uint256 root_2 = challenges.beta; - uint256 numerator_value = 1; - uint256 denominator_value = 1; - - // we multiply length by 0x20 because our loop step size is 0x20 not 0x01 - // we subtract 0x20 because our loop is unrolled 2 times an we don't want to overshoot - - // perform this computation in assembly to improve efficiency. We are sensitive to the cost of this loop as - // it scales with the number of public inputs - uint256 p = Bn254Crypto.r_mod; - bool valid = true; - assembly { - root_1 := mulmod(root_1, 0x05, p) - root_2 := mulmod(root_2, 0x07, p) - public_inputs := add(calldataload(0x04), 0x24) - - // get public inputs from calldata. N.B. If Contract ABI Changes this code will need to be updated! - endpoint := add(endpoint, public_inputs) - // Do some loop unrolling to reduce number of conditional jump operations - for { - - } lt(public_inputs, endpoint) { - - } { - let input0 := calldataload(public_inputs) - let N0 := add(root_1, add(input0, gamma)) - let D0 := add(root_2, N0) // 4x overloaded - - root_1 := mulmod(root_1, work_root, p) - root_2 := mulmod(root_2, work_root, p) - - let input1 := calldataload(add(public_inputs, 0x20)) - let N1 := add(root_1, add(input1, gamma)) - - denominator_value := mulmod( - mulmod(D0, denominator_value, p), - add(N1, root_2), - p - ) - numerator_value := mulmod(mulmod(N1, N0, p), numerator_value, p) - - root_1 := mulmod(root_1, work_root, p) - root_2 := mulmod(root_2, work_root, p) - - valid := and(valid, and(lt(input0, p), lt(input1, p))) - public_inputs := add(public_inputs, 0x40) - } - - endpoint := add(endpoint, 0x20) - for { - - } lt(public_inputs, endpoint) { - public_inputs := add(public_inputs, 0x20) - } { - let input0 := calldataload(public_inputs) - valid := and(valid, lt(input0, p)) - let T0 := addmod(input0, gamma, p) - numerator_value := mulmod( - numerator_value, - add(root_1, T0), // 0x05 = coset_generator0 - p - ) - denominator_value := mulmod( - denominator_value, - add(add(root_1, root_2), T0), // 0x0c = coset_generator7 - p - ) - root_1 := mulmod(root_1, work_root, p) - root_2 := mulmod(root_2, work_root, p) - } - } - require(valid, "public inputs are greater than circuit modulus"); - return (numerator_value, denominator_value); - } - - /** - * @dev Computes the vanishing polynoimal and lagrange evaluations L1 and Ln. - * @return Returns fractions as numerators and denominators. We combine with the public input fraction and compute inverses as a batch - */ - function compute_lagrange_and_vanishing_fractions( - Types.VerificationKey memory vk, - uint256 zeta - ) - internal - pure - returns ( - uint256, - uint256, - uint256, - uint256, - uint256 - ) - { - uint256 p = Bn254Crypto.r_mod; - uint256 vanishing_numerator = Bn254Crypto.pow_small( - zeta, - vk.circuit_size, - p - ); - vk.zeta_pow_n = vanishing_numerator; - assembly { - vanishing_numerator := addmod(vanishing_numerator, sub(p, 1), p) - } - - uint256 accumulating_root = vk.work_root_inverse; - uint256 work_root = vk.work_root_inverse; - uint256 vanishing_denominator; - uint256 domain_inverse = vk.domain_inverse; - uint256 l_start_denominator; - uint256 l_end_denominator; - uint256 z = zeta; // copy input var to prevent stack depth errors - assembly { - // vanishing_denominator = (z - w^{n-1})(z - w^{n-2})(z - w^{n-3})(z - w^{n-4}) - // we need to cut 4 roots of unity out of the vanishing poly, the last 4 constraints are not satisfied due to randomness - // added to ensure the proving system is zero-knowledge - vanishing_denominator := addmod(z, sub(p, work_root), p) - work_root := mulmod(work_root, accumulating_root, p) - vanishing_denominator := mulmod( - vanishing_denominator, - addmod(z, sub(p, work_root), p), - p - ) - work_root := mulmod(work_root, accumulating_root, p) - vanishing_denominator := mulmod( - vanishing_denominator, - addmod(z, sub(p, work_root), p), - p - ) - work_root := mulmod(work_root, accumulating_root, p) - vanishing_denominator := mulmod( - vanishing_denominator, - addmod(z, sub(p, work_root), p), - p - ) - } - - work_root = vk.work_root; - uint256 lagrange_numerator; - assembly { - lagrange_numerator := mulmod(vanishing_numerator, domain_inverse, p) - // l_start_denominator = z - 1 - // l_end_denominator = z * \omega^5 - 1 - l_start_denominator := addmod(z, sub(p, 1), p) - - accumulating_root := mulmod(work_root, work_root, p) - accumulating_root := mulmod(accumulating_root, accumulating_root, p) - accumulating_root := mulmod(accumulating_root, work_root, p) - - l_end_denominator := addmod( - mulmod(accumulating_root, z, p), - sub(p, 1), - p - ) - } - - return ( - vanishing_numerator, - vanishing_denominator, - lagrange_numerator, - l_start_denominator, - l_end_denominator - ); - } - - function compute_arithmetic_gate_quotient_contribution( - Types.ChallengeTranscript memory challenges, - Types.Proof memory proof - ) internal view returns (uint256) { - uint256 q_arith = proof.q_arith; - uint256 wire3 = proof.w3; - uint256 wire4 = proof.w4; - uint256 alpha_base = challenges.alpha_base; - uint256 alpha = challenges.alpha; - uint256 t1; - uint256 p = Bn254Crypto.r_mod; - assembly { - t1 := addmod(mulmod(q_arith, q_arith, p), sub(p, q_arith), p) - - let t2 := addmod(sub(p, mulmod(wire4, 0x04, p)), wire3, p) - - let t3 := mulmod(mulmod(t2, t2, p), 0x02, p) - - let t4 := mulmod(t2, 0x09, p) - t4 := addmod(t4, addmod(sub(p, t3), sub(p, 0x07), p), p) - - t2 := mulmod(t2, t4, p) - - t1 := mulmod(mulmod(t1, t2, p), alpha_base, p) - - alpha_base := mulmod(alpha_base, alpha, p) - alpha_base := mulmod(alpha_base, alpha, p) - } - - challenges.alpha_base = alpha_base; - - return t1; - } - - function compute_pedersen_gate_quotient_contribution( - Types.ChallengeTranscript memory challenges, - Types.Proof memory proof - ) internal view returns (uint256) { - uint256 alpha = challenges.alpha; - uint256 gate_id = 0; - uint256 alpha_base = challenges.alpha_base; - - { - uint256 p = Bn254Crypto.r_mod; - uint256 delta = 0; - - uint256 wire_t0 = proof.w4; // w4 - uint256 wire_t1 = proof.w4_omega; // w4_omega - uint256 wire_t2 = proof.w3_omega; // w3_omega - assembly { - let wire4_neg := sub(p, wire_t0) - delta := addmod(wire_t1, mulmod(wire4_neg, 0x04, p), p) - - gate_id := mulmod( - mulmod( - mulmod( - mulmod(add(delta, 0x01), add(delta, 0x03), p), - add(delta, sub(p, 0x01)), - p - ), - add(delta, sub(p, 0x03)), - p - ), - alpha_base, - p - ) - alpha_base := mulmod(alpha_base, alpha, p) - - gate_id := addmod( - gate_id, - sub(p, mulmod(wire_t2, alpha_base, p)), - p - ) - - alpha_base := mulmod(alpha_base, alpha, p) - } - - uint256 selector_value = proof.q_ecc; - - wire_t0 = proof.w1; // w1 - wire_t1 = proof.w1_omega; // w1_omega - wire_t2 = proof.w2; // w2 - uint256 wire_t3 = proof.w3_omega; // w3_omega - uint256 t0; - uint256 t1; - uint256 t2; - assembly { - t0 := addmod(wire_t1, addmod(wire_t0, wire_t3, p), p) - - t1 := addmod(wire_t3, sub(p, wire_t0), p) - t1 := mulmod(t1, t1, p) - - t0 := mulmod(t0, t1, p) - - t1 := mulmod(wire_t3, mulmod(wire_t3, wire_t3, p), p) - - t2 := mulmod(wire_t2, wire_t2, p) - - t1 := sub(p, addmod(addmod(t1, t2, p), sub(p, 17), p)) - - t2 := mulmod(mulmod(delta, wire_t2, p), selector_value, p) - t2 := addmod(t2, t2, p) - - t0 := mulmod(addmod(t0, addmod(t1, t2, p), p), alpha_base, p) - gate_id := addmod(gate_id, t0, p) - - alpha_base := mulmod(alpha_base, alpha, p) - } - - wire_t0 = proof.w1; // w1 - wire_t1 = proof.w2_omega; // w2_omega - wire_t2 = proof.w2; // w2 - wire_t3 = proof.w3_omega; // w3_omega - uint256 wire_t4 = proof.w1_omega; // w1_omega - assembly { - t0 := mulmod( - addmod(wire_t1, wire_t2, p), - addmod(wire_t3, sub(p, wire_t0), p), - p - ) - - t1 := addmod(wire_t0, sub(p, wire_t4), p) - - t2 := addmod( - sub(p, mulmod(selector_value, delta, p)), - wire_t2, - p - ) - - gate_id := addmod( - gate_id, - mulmod(add(t0, mulmod(t1, t2, p)), alpha_base, p), - p - ) - - alpha_base := mulmod(alpha_base, alpha, p) - } - - selector_value = proof.q_c; - - wire_t1 = proof.w4; // w4 - wire_t2 = proof.w3; // w3 - assembly { - let acc_init_id := addmod(wire_t1, sub(p, 0x01), p) - - t1 := addmod(acc_init_id, sub(p, wire_t2), p) - - acc_init_id := mulmod(acc_init_id, mulmod(t1, alpha_base, p), p) - acc_init_id := mulmod(acc_init_id, selector_value, p) - - gate_id := addmod(gate_id, acc_init_id, p) - - alpha_base := mulmod(alpha_base, alpha, p) - } - - assembly { - let x_init_id := sub( - p, - mulmod( - mulmod(wire_t0, selector_value, p), - mulmod(wire_t2, alpha_base, p), - p - ) - ) - - gate_id := addmod(gate_id, x_init_id, p) - - alpha_base := mulmod(alpha_base, alpha, p) - } - - wire_t0 = proof.w2; // w2 - wire_t1 = proof.w3; // w3 - wire_t2 = proof.w4; // w4 - assembly { - let y_init_id := mulmod( - add(0x01, sub(p, wire_t2)), - selector_value, - p - ) - - t1 := sub(p, mulmod(wire_t0, wire_t1, p)) - - y_init_id := mulmod( - add(y_init_id, t1), - mulmod(alpha_base, selector_value, p), - p - ) - - gate_id := addmod(gate_id, y_init_id, p) - - alpha_base := mulmod(alpha_base, alpha, p) - } - selector_value = proof.q_ecc; - assembly { - gate_id := mulmod(gate_id, selector_value, p) - } - } - challenges.alpha_base = alpha_base; - return gate_id; - } - - function compute_permutation_quotient_contribution( - uint256 public_input_delta, - Types.ChallengeTranscript memory challenges, - uint256 lagrange_start, - uint256 lagrange_end, - Types.Proof memory proof - ) internal view returns (uint256) { - uint256 numerator_collector; - uint256 alpha = challenges.alpha; - uint256 beta = challenges.beta; - uint256 p = Bn254Crypto.r_mod; - uint256 grand_product = proof.grand_product_at_z_omega; - { - uint256 gamma = challenges.gamma; - uint256 wire1 = proof.w1; - uint256 wire2 = proof.w2; - uint256 wire3 = proof.w3; - uint256 wire4 = proof.w4; - uint256 sigma1 = proof.sigma1; - uint256 sigma2 = proof.sigma2; - uint256 sigma3 = proof.sigma3; - assembly { - let t0 := add(add(wire1, gamma), mulmod(beta, sigma1, p)) - - let t1 := add(add(wire2, gamma), mulmod(beta, sigma2, p)) - - let t2 := add(add(wire3, gamma), mulmod(beta, sigma3, p)) - - t0 := mulmod(t0, mulmod(t1, t2, p), p) - - t0 := mulmod(t0, add(wire4, gamma), p) - - t0 := mulmod(t0, grand_product, p) - - t0 := mulmod(t0, alpha, p) - - numerator_collector := sub(p, t0) - } - } - - uint256 alpha_base = challenges.alpha_base; - { - uint256 lstart = lagrange_start; - uint256 lend = lagrange_end; - uint256 public_delta = public_input_delta; - assembly { - let alpha_squared := mulmod(alpha, alpha, p) - let alpha_cubed := mulmod(alpha, alpha_squared, p) - - let t0 := mulmod(lstart, alpha_cubed, p) - let t1 := mulmod(lend, alpha_squared, p) - let t2 := addmod(grand_product, sub(p, public_delta), p) - t1 := mulmod(t1, t2, p) - - numerator_collector := addmod( - numerator_collector, - sub(p, t0), - p - ) - numerator_collector := addmod(numerator_collector, t1, p) - alpha_base := mulmod(alpha_base, alpha_cubed, p) - } - } - - challenges.alpha_base = alpha_base; - - return numerator_collector; - } - - // compute_r_0 - function compute_linear_polynomial_constant( - uint256 zero_poly_inverse, - uint256 public_input_delta, - Types.ChallengeTranscript memory challenges, - uint256 lagrange_start, - uint256 lagrange_end, - Types.Proof memory proof - ) internal view returns (uint256) { - uint256 t0 = compute_permutation_quotient_contribution( - public_input_delta, - challenges, - lagrange_start, - lagrange_end, - proof - ); - - uint256 t1 = compute_arithmetic_gate_quotient_contribution( - challenges, - proof - ); - - uint256 t2 = compute_pedersen_gate_quotient_contribution( - challenges, - proof - ); - - uint256 r_0; - uint256 p = Bn254Crypto.r_mod; - assembly { - r_0 := addmod(t0, addmod(t1, t2, p), p) - // r_0 := mulmod(r_0, zero_poly_inverse, p) // not necessary for the simplified Plonk - } - return r_0; - } - - function compute_linearised_opening_terms( - Types.ChallengeTranscript memory challenges, - uint256 L1_fr, - Types.VerificationKey memory vk, - Types.Proof memory proof - ) internal view returns (Types.G1Point memory) { - Types.G1Point - memory accumulator = compute_grand_product_opening_group_element( - proof, - vk, - challenges, - L1_fr - ); - Types.G1Point - memory arithmetic_term = compute_arithmetic_selector_opening_group_element( - proof, - vk, - challenges - ); - uint256 range_multiplier = compute_range_gate_opening_scalar( - proof, - challenges - ); - uint256 logic_multiplier = compute_logic_gate_opening_scalar( - proof, - challenges - ); - - Types.G1Point memory QRANGE = vk.QRANGE; - Types.G1Point memory QLOGIC = vk.QLOGIC; - QRANGE.validateG1Point(); - QLOGIC.validateG1Point(); - - // compute range_multiplier.[QRANGE] + logic_multiplier.[QLOGIC] + [accumulator] + [grand_product_term] - bool success; - assembly { - let mPtr := mload(0x40) - - // range_multiplier.[QRANGE] - mstore(mPtr, mload(QRANGE)) - mstore(add(mPtr, 0x20), mload(add(QRANGE, 0x20))) - mstore(add(mPtr, 0x40), range_multiplier) - success := staticcall(gas(), 7, mPtr, 0x60, mPtr, 0x40) - - // add scalar mul output into accumulator - // we use mPtr to store accumulated point - mstore(add(mPtr, 0x40), mload(accumulator)) - mstore(add(mPtr, 0x60), mload(add(accumulator, 0x20))) - success := and( - success, - staticcall(gas(), 6, mPtr, 0x80, mPtr, 0x40) - ) - - // logic_multiplier.[QLOGIC] - mstore(add(mPtr, 0x40), mload(QLOGIC)) - mstore(add(mPtr, 0x60), mload(add(QLOGIC, 0x20))) - mstore(add(mPtr, 0x80), logic_multiplier) - success := and( - success, - staticcall( - gas(), - 7, - add(mPtr, 0x40), - 0x60, - add(mPtr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall(gas(), 6, mPtr, 0x80, mPtr, 0x40) - ) - - // add arithmetic into accumulator - mstore(add(mPtr, 0x40), mload(arithmetic_term)) - mstore(add(mPtr, 0x60), mload(add(arithmetic_term, 0x20))) - success := and( - success, - staticcall(gas(), 6, mPtr, 0x80, accumulator, 0x40) - ) - } - require( - success, - "compute_linearised_opening_terms group operations fail" - ); - - return accumulator; - } - - function compute_batch_opening_commitment( - Types.ChallengeTranscript memory challenges, - Types.VerificationKey memory vk, - Types.G1Point memory partial_opening_commitment, - Types.Proof memory proof - ) internal view returns (Types.G1Point memory) { - // Computes the Kate opening proof group operations, for commitments that are not linearised - bool success; - // Reserve 0xa0 bytes of memory to perform group operations - uint256 accumulator_ptr; - uint256 p = Bn254Crypto.r_mod; - assembly { - accumulator_ptr := mload(0x40) - mstore(0x40, add(accumulator_ptr, 0xa0)) - } - // For the simplified plonk, we need to multiply -Z_H(z) with [T1], - // proof.zero_poly_eval = Z_H(z) - uint256 zero_poly_eval_neg = p - vk.zero_polynomial_eval; - // [T2], [T3], [T4] - // first term - Types.G1Point memory work_point = proof.T1; - work_point.validateG1Point(); - assembly { - mstore(accumulator_ptr, mload(work_point)) - mstore(add(accumulator_ptr, 0x20), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x40), zero_poly_eval_neg) - // computing zero_poly_eval_neg * [T1] - success := staticcall( - gas(), - 7, - accumulator_ptr, - 0x60, - accumulator_ptr, - 0x40 - ) - } - - // second term - uint256 scalar_multiplier = vk.zeta_pow_n; // zeta_pow_n is computed in compute_lagrange_and_vanishing_fractions - uint256 zeta_n = scalar_multiplier; - work_point = proof.T2; - work_point.validateG1Point(); - assembly { - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore( - add(accumulator_ptr, 0x80), - mulmod(scalar_multiplier, zero_poly_eval_neg, p) - ) - - // compute zero_poly_eval_neg * zeta_n * [T2] - success := staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // third term - work_point = proof.T3; - work_point.validateG1Point(); - assembly { - scalar_multiplier := mulmod(scalar_multiplier, scalar_multiplier, p) - - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore( - add(accumulator_ptr, 0x80), - mulmod(scalar_multiplier, zero_poly_eval_neg, p) - ) - - // compute zero_poly_eval_neg * zeta_n^2 * [T3] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // fourth term - work_point = proof.T4; - work_point.validateG1Point(); - assembly { - scalar_multiplier := mulmod(scalar_multiplier, zeta_n, p) - - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore( - add(accumulator_ptr, 0x80), - mulmod(scalar_multiplier, zero_poly_eval_neg, p) - ) - - // compute zero_poly_eval_neg * zeta_n^3 * [T4] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // fifth term - work_point = partial_opening_commitment; - work_point.validateG1Point(); - assembly { - // add partial opening commitment into accumulator - mstore( - add(accumulator_ptr, 0x40), - mload(partial_opening_commitment) - ) - mstore( - add(accumulator_ptr, 0x60), - mload(add(partial_opening_commitment, 0x20)) - ) - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - uint256 u_plus_one = challenges.u; - uint256 v_challenge = challenges.v0; - - // W1 - work_point = proof.W1; - work_point.validateG1Point(); - assembly { - u_plus_one := addmod(u_plus_one, 0x01, p) - - scalar_multiplier := mulmod(v_challenge, u_plus_one, p) - - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v0(u + 1).[W1] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // W2 - v_challenge = challenges.v1; - work_point = proof.W2; - work_point.validateG1Point(); - assembly { - scalar_multiplier := mulmod(v_challenge, u_plus_one, p) - - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v1(u + 1).[W2] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // W3 - v_challenge = challenges.v2; - work_point = proof.W3; - work_point.validateG1Point(); - assembly { - scalar_multiplier := mulmod(v_challenge, u_plus_one, p) - - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v2(u + 1).[W3] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // W4 - v_challenge = challenges.v3; - work_point = proof.W4; - work_point.validateG1Point(); - assembly { - scalar_multiplier := mulmod(v_challenge, u_plus_one, p) - - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v3(u + 1).[W4] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // SIGMA1 - scalar_multiplier = challenges.v4; - work_point = vk.SIGMA1; - work_point.validateG1Point(); - assembly { - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v4.[SIGMA1] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // SIGMA2 - scalar_multiplier = challenges.v5; - work_point = vk.SIGMA2; - work_point.validateG1Point(); - assembly { - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v5.[SIGMA2] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // SIGMA3 - scalar_multiplier = challenges.v6; - work_point = vk.SIGMA3; - work_point.validateG1Point(); - assembly { - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v6.[SIGMA3] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - // QARITH - scalar_multiplier = challenges.v7; - work_point = vk.QARITH; - work_point.validateG1Point(); - assembly { - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v7.[QARITH] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - - Types.G1Point memory output; - // QECC - scalar_multiplier = challenges.v8; - work_point = vk.QECC; - work_point.validateG1Point(); - assembly { - mstore(add(accumulator_ptr, 0x40), mload(work_point)) - mstore(add(accumulator_ptr, 0x60), mload(add(work_point, 0x20))) - mstore(add(accumulator_ptr, 0x80), scalar_multiplier) - - // compute v8.[QECC] - success := and( - success, - staticcall( - gas(), - 7, - add(accumulator_ptr, 0x40), - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - ) - - // add scalar mul output into output point - success := and( - success, - staticcall(gas(), 6, accumulator_ptr, 0x80, output, 0x40) - ) - } - - require( - success, - "compute_batch_opening_commitment group operations error" - ); - - return output; - } - - function compute_batch_evaluation_scalar_multiplier( - Types.Proof memory proof, - Types.ChallengeTranscript memory challenges - ) internal view returns (uint256) { - uint256 p = Bn254Crypto.r_mod; - uint256 opening_scalar; - uint256 lhs; // stores nu challenges - uint256 rhs; // stores evaluations of polynomials - - lhs = challenges.v0; - rhs = proof.w1; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v1; - rhs = proof.w2; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v2; - rhs = proof.w3; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v3; - rhs = proof.w4; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v4; - rhs = proof.sigma1; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v5; - rhs = proof.sigma2; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v6; - rhs = proof.sigma3; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v7; - rhs = proof.q_arith; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v8; - rhs = proof.q_ecc; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - lhs = challenges.v9; - rhs = proof.q_c; - assembly { - opening_scalar := addmod(opening_scalar, mulmod(lhs, rhs, p), p) - } - - // lhs = 1; //challenges.v10; (should be -1 for simplified Plonk) - rhs = proof.r_0; // linearization_polynomial should be r_0 for simplified Plonk - assembly { - opening_scalar := addmod(opening_scalar, sub(p, rhs), p) - } - // should be removed for simplified Plonk - // lhs = proof.quotient_polynomial_eval; - // assembly { - // opening_scalar := addmod(opening_scalar, lhs, p) - // } - - lhs = challenges.v0; - rhs = proof.w1_omega; - uint256 shifted_opening_scalar; - assembly { - shifted_opening_scalar := mulmod(lhs, rhs, p) - } - - lhs = challenges.v1; - rhs = proof.w2_omega; - assembly { - shifted_opening_scalar := addmod( - shifted_opening_scalar, - mulmod(lhs, rhs, p), - p - ) - } - - lhs = challenges.v2; - rhs = proof.w3_omega; - assembly { - shifted_opening_scalar := addmod( - shifted_opening_scalar, - mulmod(lhs, rhs, p), - p - ) - } - - lhs = challenges.v3; - rhs = proof.w4_omega; - assembly { - shifted_opening_scalar := addmod( - shifted_opening_scalar, - mulmod(lhs, rhs, p), - p - ) - } - - lhs = proof.grand_product_at_z_omega; - assembly { - shifted_opening_scalar := addmod(shifted_opening_scalar, lhs, p) - } - - lhs = challenges.u; - assembly { - shifted_opening_scalar := mulmod(shifted_opening_scalar, lhs, p) - - opening_scalar := addmod(opening_scalar, shifted_opening_scalar, p) - } - - return opening_scalar; - } - - // Compute kate opening scalar for arithmetic gate selectors and pedersen gate selectors - // (both the arithmetic gate and pedersen hash gate reuse the same selectors) - function compute_arithmetic_selector_opening_group_element( - Types.Proof memory proof, - Types.VerificationKey memory vk, - Types.ChallengeTranscript memory challenges - ) internal view returns (Types.G1Point memory) { - uint256 q_arith = proof.q_arith; - uint256 q_ecc = proof.q_ecc; - uint256 alpha_base = challenges.alpha_base; - uint256 scaling_alpha = challenges.alpha_base; - uint256 alpha = challenges.alpha; - uint256 p = Bn254Crypto.r_mod; - uint256 scalar_multiplier; - uint256 accumulator_ptr; // reserve 0xa0 bytes of memory to multiply and add points - assembly { - accumulator_ptr := mload(0x40) - mstore(0x40, add(accumulator_ptr, 0xa0)) - } - { - uint256 delta; - // Q1 Selector - { - { - uint256 w4 = proof.w4; - uint256 w4_omega = proof.w4_omega; - assembly { - delta := addmod( - w4_omega, - sub(p, mulmod(w4, 0x04, p)), - p - ) - } - } - uint256 w1 = proof.w1; - - assembly { - scalar_multiplier := w1 - scalar_multiplier := mulmod( - scalar_multiplier, - alpha_base, - p - ) - scalar_multiplier := mulmod(scalar_multiplier, q_arith, p) - - scaling_alpha := mulmod(scaling_alpha, alpha, p) - scaling_alpha := mulmod(scaling_alpha, alpha, p) - scaling_alpha := mulmod(scaling_alpha, alpha, p) - let t0 := mulmod(delta, delta, p) - t0 := mulmod(t0, q_ecc, p) - t0 := mulmod(t0, scaling_alpha, p) - - scalar_multiplier := addmod(scalar_multiplier, t0, p) - } - Types.G1Point memory Q1 = vk.Q1; - Q1.validateG1Point(); - bool success; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(Q1)) - mstore(add(mPtr, 0x20), mload(add(Q1, 0x20))) - mstore(add(mPtr, 0x40), scalar_multiplier) - success := staticcall( - gas(), - 7, - mPtr, - 0x60, - accumulator_ptr, - 0x40 - ) - } - require(success, "G1 point multiplication failed!"); - } - - // Q2 Selector - { - uint256 w2 = proof.w2; - assembly { - scalar_multiplier := w2 - scalar_multiplier := mulmod( - scalar_multiplier, - alpha_base, - p - ) - scalar_multiplier := mulmod(scalar_multiplier, q_arith, p) - - let t0 := mulmod(scaling_alpha, q_ecc, p) - scalar_multiplier := addmod(scalar_multiplier, t0, p) - } - - Types.G1Point memory Q2 = vk.Q2; - Q2.validateG1Point(); - bool success; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(Q2)) - mstore(add(mPtr, 0x20), mload(add(Q2, 0x20))) - mstore(add(mPtr, 0x40), scalar_multiplier) - - // write scalar mul output 0x40 bytes ahead of accumulator - success := staticcall( - gas(), - 7, - mPtr, - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - require(success, "G1 point multiplication failed!"); - } - - // Q3 Selector - { - { - uint256 w3 = proof.w3; - assembly { - scalar_multiplier := w3 - scalar_multiplier := mulmod( - scalar_multiplier, - alpha_base, - p - ) - scalar_multiplier := mulmod( - scalar_multiplier, - q_arith, - p - ) - } - } - { - uint256 t1; - { - uint256 w3_omega = proof.w3_omega; - assembly { - t1 := mulmod(delta, w3_omega, p) - } - } - { - uint256 w2 = proof.w2; - assembly { - scaling_alpha := mulmod(scaling_alpha, alpha, p) - - t1 := mulmod(t1, w2, p) - t1 := mulmod(t1, scaling_alpha, p) - t1 := addmod(t1, t1, p) - t1 := mulmod(t1, q_ecc, p) - - scalar_multiplier := addmod( - scalar_multiplier, - t1, - p - ) - } - } - } - uint256 t0 = proof.w1_omega; - { - uint256 w1 = proof.w1; - assembly { - scaling_alpha := mulmod(scaling_alpha, alpha, p) - t0 := addmod(t0, sub(p, w1), p) - t0 := mulmod(t0, delta, p) - } - } - uint256 w3_omega = proof.w3_omega; - assembly { - t0 := mulmod(t0, w3_omega, p) - t0 := mulmod(t0, scaling_alpha, p) - - t0 := mulmod(t0, q_ecc, p) - - scalar_multiplier := addmod(scalar_multiplier, t0, p) - } - } - - Types.G1Point memory Q3 = vk.Q3; - Q3.validateG1Point(); - bool success; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(Q3)) - mstore(add(mPtr, 0x20), mload(add(Q3, 0x20))) - mstore(add(mPtr, 0x40), scalar_multiplier) - - // write scalar mul output 0x40 bytes ahead of accumulator - success := staticcall( - gas(), - 7, - mPtr, - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - require(success, "G1 point multiplication failed!"); - } - - // Q4 Selector - { - uint256 w3 = proof.w3; - uint256 w4 = proof.w4; - uint256 q_c = proof.q_c; - assembly { - scalar_multiplier := w4 - scalar_multiplier := mulmod(scalar_multiplier, alpha_base, p) - scalar_multiplier := mulmod(scalar_multiplier, q_arith, p) - - scaling_alpha := mulmod( - scaling_alpha, - mulmod(alpha, alpha, p), - p - ) - let t0 := mulmod(w3, q_ecc, p) - t0 := mulmod(t0, q_c, p) - t0 := mulmod(t0, scaling_alpha, p) - - scalar_multiplier := addmod(scalar_multiplier, t0, p) - } - - Types.G1Point memory Q4 = vk.Q4; - Q4.validateG1Point(); - bool success; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(Q4)) - mstore(add(mPtr, 0x20), mload(add(Q4, 0x20))) - mstore(add(mPtr, 0x40), scalar_multiplier) - - // write scalar mul output 0x40 bytes ahead of accumulator - success := staticcall( - gas(), - 7, - mPtr, - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - require(success, "G1 point multiplication failed!"); - } - - // Q5 Selector - { - uint256 w4 = proof.w4; - uint256 q_c = proof.q_c; - assembly { - let neg_w4 := sub(p, w4) - scalar_multiplier := mulmod(w4, w4, p) - scalar_multiplier := addmod(scalar_multiplier, neg_w4, p) - scalar_multiplier := mulmod( - scalar_multiplier, - addmod(w4, sub(p, 2), p), - p - ) - scalar_multiplier := mulmod(scalar_multiplier, alpha_base, p) - scalar_multiplier := mulmod(scalar_multiplier, alpha, p) - scalar_multiplier := mulmod(scalar_multiplier, q_arith, p) - - let t0 := addmod(0x01, neg_w4, p) - t0 := mulmod(t0, q_ecc, p) - t0 := mulmod(t0, q_c, p) - t0 := mulmod(t0, scaling_alpha, p) - - scalar_multiplier := addmod(scalar_multiplier, t0, p) - } - - Types.G1Point memory Q5 = vk.Q5; - Q5.validateG1Point(); - bool success; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(Q5)) - mstore(add(mPtr, 0x20), mload(add(Q5, 0x20))) - mstore(add(mPtr, 0x40), scalar_multiplier) - - // write scalar mul output 0x40 bytes ahead of accumulator - success := staticcall( - gas(), - 7, - mPtr, - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - require(success, "G1 point multiplication failed!"); - } - - // QM Selector - { - { - uint256 w1 = proof.w1; - uint256 w2 = proof.w2; - - assembly { - scalar_multiplier := mulmod(w1, w2, p) - scalar_multiplier := mulmod( - scalar_multiplier, - alpha_base, - p - ) - scalar_multiplier := mulmod(scalar_multiplier, q_arith, p) - } - } - uint256 w3 = proof.w3; - uint256 q_c = proof.q_c; - assembly { - scaling_alpha := mulmod(scaling_alpha, alpha, p) - let t0 := mulmod(w3, q_ecc, p) - t0 := mulmod(t0, q_c, p) - t0 := mulmod(t0, scaling_alpha, p) - - scalar_multiplier := addmod(scalar_multiplier, t0, p) - } - - Types.G1Point memory QM = vk.QM; - QM.validateG1Point(); - bool success; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(QM)) - mstore(add(mPtr, 0x20), mload(add(QM, 0x20))) - mstore(add(mPtr, 0x40), scalar_multiplier) - - // write scalar mul output 0x40 bytes ahead of accumulator - success := staticcall( - gas(), - 7, - mPtr, - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - - // add scalar mul output into accumulator - success := and( - success, - staticcall( - gas(), - 6, - accumulator_ptr, - 0x80, - accumulator_ptr, - 0x40 - ) - ) - } - require(success, "G1 point multiplication failed!"); - } - - Types.G1Point memory output; - // QC Selector - { - uint256 q_c_challenge = challenges.v9; - assembly { - scalar_multiplier := alpha_base - scalar_multiplier := mulmod(scalar_multiplier, q_arith, p) - - // TurboPlonk requires an explicit evaluation of q_c - scalar_multiplier := addmod(scalar_multiplier, q_c_challenge, p) - - alpha_base := mulmod(scaling_alpha, alpha, p) - } - - Types.G1Point memory QC = vk.QC; - QC.validateG1Point(); - bool success; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(QC)) - mstore(add(mPtr, 0x20), mload(add(QC, 0x20))) - mstore(add(mPtr, 0x40), scalar_multiplier) - - // write scalar mul output 0x40 bytes ahead of accumulator - success := staticcall( - gas(), - 7, - mPtr, - 0x60, - add(accumulator_ptr, 0x40), - 0x40 - ) - - // add scalar mul output into output point - success := and( - success, - staticcall(gas(), 6, accumulator_ptr, 0x80, output, 0x40) - ) - } - require(success, "G1 point multiplication failed!"); - } - challenges.alpha_base = alpha_base; - - return output; - } - - // Compute kate opening scalar for logic gate opening scalars - // This method evalautes the polynomial identity used to evaluate either - // a 2-bit AND or XOR operation in a single constraint - function compute_logic_gate_opening_scalar( - Types.Proof memory proof, - Types.ChallengeTranscript memory challenges - ) internal pure returns (uint256) { - uint256 identity = 0; - uint256 p = Bn254Crypto.r_mod; - { - uint256 delta_sum = 0; - uint256 delta_squared_sum = 0; - uint256 t0 = 0; - uint256 t1 = 0; - uint256 t2 = 0; - uint256 t3 = 0; - { - uint256 wire1_omega = proof.w1_omega; - uint256 wire1 = proof.w1; - assembly { - t0 := addmod(wire1_omega, sub(p, mulmod(wire1, 0x04, p)), p) - } - } - - { - uint256 wire2_omega = proof.w2_omega; - uint256 wire2 = proof.w2; - assembly { - t1 := addmod(wire2_omega, sub(p, mulmod(wire2, 0x04, p)), p) - - delta_sum := addmod(t0, t1, p) - t2 := mulmod(t0, t0, p) - t3 := mulmod(t1, t1, p) - delta_squared_sum := addmod(t2, t3, p) - identity := mulmod(delta_sum, delta_sum, p) - identity := addmod(identity, sub(p, delta_squared_sum), p) - } - } - - uint256 t4 = 0; - uint256 alpha = challenges.alpha; - - { - uint256 wire3 = proof.w3; - assembly { - t4 := mulmod(wire3, 0x02, p) - identity := addmod(identity, sub(p, t4), p) - identity := mulmod(identity, alpha, p) - } - } - - assembly { - t4 := addmod(t4, t4, p) - t2 := addmod(t2, sub(p, t0), p) - t0 := mulmod(t0, 0x04, p) - t0 := addmod(t2, sub(p, t0), p) - t0 := addmod(t0, 0x06, p) - - t0 := mulmod(t0, t2, p) - identity := addmod(identity, t0, p) - identity := mulmod(identity, alpha, p) - - t3 := addmod(t3, sub(p, t1), p) - t1 := mulmod(t1, 0x04, p) - t1 := addmod(t3, sub(p, t1), p) - t1 := addmod(t1, 0x06, p) - - t1 := mulmod(t1, t3, p) - identity := addmod(identity, t1, p) - identity := mulmod(identity, alpha, p) - - t0 := mulmod(delta_sum, 0x03, p) - - t1 := mulmod(t0, 0x03, p) - - delta_sum := addmod(t1, t1, p) - - t2 := mulmod(delta_sum, 0x04, p) - t1 := addmod(t1, t2, p) - - t2 := mulmod(delta_squared_sum, 0x03, p) - - delta_squared_sum := mulmod(t2, 0x06, p) - - delta_sum := addmod(t4, sub(p, delta_sum), p) - delta_sum := addmod(delta_sum, 81, p) - - t1 := addmod(delta_squared_sum, sub(p, t1), p) - t1 := addmod(t1, 83, p) - } - - { - uint256 wire3 = proof.w3; - assembly { - delta_sum := mulmod(delta_sum, wire3, p) - - delta_sum := addmod(delta_sum, t1, p) - delta_sum := mulmod(delta_sum, wire3, p) - } - } - { - uint256 wire4 = proof.w4; - assembly { - t2 := mulmod(wire4, 0x04, p) - } - } - { - uint256 wire4_omega = proof.w4_omega; - assembly { - t2 := addmod(wire4_omega, sub(p, t2), p) - } - } - { - uint256 q_c = proof.q_c; - assembly { - t3 := addmod(t2, t2, p) - t2 := addmod(t2, t3, p) - - t3 := addmod(t2, t2, p) - t3 := addmod(t3, t2, p) - - t3 := addmod(t3, sub(p, t0), p) - t3 := mulmod(t3, q_c, p) - - t2 := addmod(t2, t0, p) - delta_sum := addmod(delta_sum, delta_sum, p) - t2 := addmod(t2, sub(p, delta_sum), p) - - t2 := addmod(t2, t3, p) - - identity := addmod(identity, t2, p) - } - } - uint256 alpha_base = challenges.alpha_base; - - assembly { - identity := mulmod(identity, alpha_base, p) - } - } - // update alpha - uint256 alpha_base = challenges.alpha_base; - uint256 alpha = challenges.alpha; - assembly { - alpha := mulmod(alpha, alpha, p) - alpha := mulmod(alpha, alpha, p) - alpha_base := mulmod(alpha_base, alpha, p) - } - challenges.alpha_base = alpha_base; - - return identity; - } - - // Compute kate opening scalar for arithmetic gate selectors - function compute_range_gate_opening_scalar( - Types.Proof memory proof, - Types.ChallengeTranscript memory challenges - ) internal pure returns (uint256) { - uint256 wire1 = proof.w1; - uint256 wire2 = proof.w2; - uint256 wire3 = proof.w3; - uint256 wire4 = proof.w4; - uint256 wire4_omega = proof.w4_omega; - uint256 alpha = challenges.alpha; - uint256 alpha_base = challenges.alpha_base; - uint256 range_acc; - uint256 p = Bn254Crypto.r_mod; - assembly { - let delta_1 := addmod(wire3, sub(p, mulmod(wire4, 0x04, p)), p) - let delta_2 := addmod(wire2, sub(p, mulmod(wire3, 0x04, p)), p) - let delta_3 := addmod(wire1, sub(p, mulmod(wire2, 0x04, p)), p) - let delta_4 := addmod( - wire4_omega, - sub(p, mulmod(wire1, 0x04, p)), - p - ) - - let t0 := mulmod(delta_1, delta_1, p) - t0 := addmod(t0, sub(p, delta_1), p) - let t1 := addmod(delta_1, sub(p, 2), p) - t0 := mulmod(t0, t1, p) - t1 := addmod(delta_1, sub(p, 3), p) - t0 := mulmod(t0, t1, p) - t0 := mulmod(t0, alpha_base, p) - - range_acc := t0 - alpha_base := mulmod(alpha_base, alpha, p) - - t0 := mulmod(delta_2, delta_2, p) - t0 := addmod(t0, sub(p, delta_2), p) - t1 := addmod(delta_2, sub(p, 2), p) - t0 := mulmod(t0, t1, p) - t1 := addmod(delta_2, sub(p, 3), p) - t0 := mulmod(t0, t1, p) - t0 := mulmod(t0, alpha_base, p) - range_acc := addmod(range_acc, t0, p) - alpha_base := mulmod(alpha_base, alpha, p) - - t0 := mulmod(delta_3, delta_3, p) - t0 := addmod(t0, sub(p, delta_3), p) - t1 := addmod(delta_3, sub(p, 2), p) - t0 := mulmod(t0, t1, p) - t1 := addmod(delta_3, sub(p, 3), p) - t0 := mulmod(t0, t1, p) - t0 := mulmod(t0, alpha_base, p) - range_acc := addmod(range_acc, t0, p) - alpha_base := mulmod(alpha_base, alpha, p) - - t0 := mulmod(delta_4, delta_4, p) - t0 := addmod(t0, sub(p, delta_4), p) - t1 := addmod(delta_4, sub(p, 2), p) - t0 := mulmod(t0, t1, p) - t1 := addmod(delta_4, sub(p, 3), p) - t0 := mulmod(t0, t1, p) - t0 := mulmod(t0, alpha_base, p) - range_acc := addmod(range_acc, t0, p) - alpha_base := mulmod(alpha_base, alpha, p) - } - - challenges.alpha_base = alpha_base; - return range_acc; - } - - // Compute grand product opening scalar and perform kate verification scalar multiplication - function compute_grand_product_opening_group_element( - Types.Proof memory proof, - Types.VerificationKey memory vk, - Types.ChallengeTranscript memory challenges, - uint256 L1_fr - ) internal view returns (Types.G1Point memory) { - uint256 beta = challenges.beta; - uint256 zeta = challenges.zeta; - uint256 gamma = challenges.gamma; - uint256 p = Bn254Crypto.r_mod; - - uint256 partial_grand_product; - uint256 sigma_multiplier; - - { - uint256 w1 = proof.w1; - uint256 sigma1 = proof.sigma1; - assembly { - let witness_term := addmod(w1, gamma, p) - partial_grand_product := addmod( - mulmod(beta, zeta, p), - witness_term, - p - ) - sigma_multiplier := addmod( - mulmod(sigma1, beta, p), - witness_term, - p - ) - } - } - { - uint256 w2 = proof.w2; - uint256 sigma2 = proof.sigma2; - assembly { - let witness_term := addmod(w2, gamma, p) - partial_grand_product := mulmod( - partial_grand_product, - addmod( - mulmod(mulmod(zeta, 0x05, p), beta, p), - witness_term, - p - ), - p - ) - sigma_multiplier := mulmod( - sigma_multiplier, - addmod(mulmod(sigma2, beta, p), witness_term, p), - p - ) - } - } - { - uint256 w3 = proof.w3; - uint256 sigma3 = proof.sigma3; - assembly { - let witness_term := addmod(w3, gamma, p) - partial_grand_product := mulmod( - partial_grand_product, - addmod( - mulmod(mulmod(zeta, 0x06, p), beta, p), - witness_term, - p - ), - p - ) - - sigma_multiplier := mulmod( - sigma_multiplier, - addmod(mulmod(sigma3, beta, p), witness_term, p), - p - ) - } - } - { - uint256 w4 = proof.w4; - assembly { - partial_grand_product := mulmod( - partial_grand_product, - addmod( - addmod( - mulmod(mulmod(zeta, 0x07, p), beta, p), - gamma, - p - ), - w4, - p - ), - p - ) - } - } - { - uint256 alpha_base = challenges.alpha_base; - uint256 alpha = challenges.alpha; - uint256 separator_challenge = challenges.u; - uint256 grand_product_at_z_omega = proof.grand_product_at_z_omega; - uint256 l_start = L1_fr; - assembly { - partial_grand_product := mulmod( - partial_grand_product, - alpha_base, - p - ) - - sigma_multiplier := mulmod( - sub( - p, - mulmod( - mulmod( - sigma_multiplier, - grand_product_at_z_omega, - p - ), - alpha_base, - p - ) - ), - beta, - p - ) - - alpha_base := mulmod(mulmod(alpha_base, alpha, p), alpha, p) - - partial_grand_product := addmod( - addmod( - partial_grand_product, - mulmod(l_start, alpha_base, p), - p - ), - separator_challenge, - p - ) - - alpha_base := mulmod(alpha_base, alpha, p) - } - challenges.alpha_base = alpha_base; - } - //Need to understand the below code: - Types.G1Point memory Z = proof.Z; - Types.G1Point memory SIGMA4 = vk.SIGMA4; - Types.G1Point memory accumulator; - Z.validateG1Point(); - SIGMA4.validateG1Point(); - bool success; - assembly { - let mPtr := mload(0x40) - mstore(mPtr, mload(Z)) - mstore(add(mPtr, 0x20), mload(add(Z, 0x20))) - mstore(add(mPtr, 0x40), partial_grand_product) - success := staticcall(gas(), 7, mPtr, 0x60, mPtr, 0x40) - - mstore(add(mPtr, 0x40), mload(SIGMA4)) - mstore(add(mPtr, 0x60), mload(add(SIGMA4, 0x20))) - mstore(add(mPtr, 0x80), sigma_multiplier) - success := and( - success, - staticcall( - gas(), - 7, - add(mPtr, 0x40), - 0x60, - add(mPtr, 0x40), - 0x40 - ) - ) - - // mload(mPtr) : (partial_grand_product * [Z]).x - // mload(mPtr + 32) : (partial_grand_product * [Z]).y - // mload(mPtr + 64) : (sigma_multiplier * [SIGMA_4]).x - // mload(mPtr + 96) : (sigma_multiplier * [SIGMA_4]).y - - success := and( - success, - staticcall(gas(), 6, mPtr, 0x80, accumulator, 0x40) - ) - } - - require( - success, - "compute_grand_product_opening_scalar group operations failure" - ); - return accumulator; - } -} - - - - - - -/** - * @title Transcript library - * @dev Generates Plonk random challenges - */ -library Transcript { - struct TranscriptData { - bytes32 current_challenge; - } - - /** - * Compute keccak256 hash of 2 4-byte variables (circuit_size, num_public_inputs) - */ - function generate_initial_challenge( - TranscriptData memory self, - uint256 circuit_size, - uint256 num_public_inputs - ) internal pure { - bytes32 challenge; - assembly { - let mPtr := mload(0x40) - mstore8(add(mPtr, 0x20), shr(24, circuit_size)) - mstore8(add(mPtr, 0x21), shr(16, circuit_size)) - mstore8(add(mPtr, 0x22), shr(8, circuit_size)) - mstore8(add(mPtr, 0x23), circuit_size) - mstore8(add(mPtr, 0x24), shr(24, num_public_inputs)) - mstore8(add(mPtr, 0x25), shr(16, num_public_inputs)) - mstore8(add(mPtr, 0x26), shr(8, num_public_inputs)) - mstore8(add(mPtr, 0x27), num_public_inputs) - challenge := keccak256(add(mPtr, 0x20), 0x08) - } - self.current_challenge = challenge; - } - - /** - * We treat the beta challenge as a special case, because it includes the public inputs. - * The number of public inputs can be extremely large for rollups and we want to minimize mem consumption. - * => we directly allocate memory to hash the public inputs, in order to prevent the global memory pointer from increasing - */ - function generate_beta_gamma_challenges( - TranscriptData memory self, - Types.ChallengeTranscript memory challenges, - uint256 num_public_inputs - ) internal pure { - bytes32 challenge; - bytes32 old_challenge = self.current_challenge; - uint256 p = Bn254Crypto.r_mod; - uint256 reduced_challenge; - assembly { - let m_ptr := mload(0x40) - // N.B. If the calldata ABI changes this code will need to change! - // We can copy all of the public inputs, followed by the wire commitments, into memory - // using calldatacopy - mstore(m_ptr, old_challenge) - m_ptr := add(m_ptr, 0x20) - let inputs_start := add(calldataload(0x04), 0x24) - // num_calldata_bytes = public input size + 256 bytes for the 4 wire commitments - let num_calldata_bytes := add(0x100, mul(num_public_inputs, 0x20)) - calldatacopy(m_ptr, inputs_start, num_calldata_bytes) - - let start := mload(0x40) - let length := add(num_calldata_bytes, 0x20) - - challenge := keccak256(start, length) - reduced_challenge := mod(challenge, p) - } - challenges.beta = reduced_challenge; - - // get gamma challenge by appending 1 to the beta challenge and hash - assembly { - mstore(0x00, challenge) - mstore8(0x20, 0x01) - challenge := keccak256(0, 0x21) - reduced_challenge := mod(challenge, p) - } - challenges.gamma = reduced_challenge; - self.current_challenge = challenge; - } - - function generate_alpha_challenge( - TranscriptData memory self, - Types.ChallengeTranscript memory challenges, - Types.G1Point memory Z - ) internal pure { - bytes32 challenge; - bytes32 old_challenge = self.current_challenge; - uint256 p = Bn254Crypto.r_mod; - uint256 reduced_challenge; - assembly { - let m_ptr := mload(0x40) - mstore(m_ptr, old_challenge) - mstore(add(m_ptr, 0x20), mload(add(Z, 0x20))) - mstore(add(m_ptr, 0x40), mload(Z)) - challenge := keccak256(m_ptr, 0x60) - reduced_challenge := mod(challenge, p) - } - challenges.alpha = reduced_challenge; - challenges.alpha_base = reduced_challenge; - self.current_challenge = challenge; - } - - function generate_zeta_challenge( - TranscriptData memory self, - Types.ChallengeTranscript memory challenges, - Types.G1Point memory T1, - Types.G1Point memory T2, - Types.G1Point memory T3, - Types.G1Point memory T4 - ) internal pure { - bytes32 challenge; - bytes32 old_challenge = self.current_challenge; - uint256 p = Bn254Crypto.r_mod; - uint256 reduced_challenge; - assembly { - let m_ptr := mload(0x40) - mstore(m_ptr, old_challenge) - mstore(add(m_ptr, 0x20), mload(add(T1, 0x20))) - mstore(add(m_ptr, 0x40), mload(T1)) - mstore(add(m_ptr, 0x60), mload(add(T2, 0x20))) - mstore(add(m_ptr, 0x80), mload(T2)) - mstore(add(m_ptr, 0xa0), mload(add(T3, 0x20))) - mstore(add(m_ptr, 0xc0), mload(T3)) - mstore(add(m_ptr, 0xe0), mload(add(T4, 0x20))) - mstore(add(m_ptr, 0x100), mload(T4)) - challenge := keccak256(m_ptr, 0x120) - reduced_challenge := mod(challenge, p) - } - challenges.zeta = reduced_challenge; - self.current_challenge = challenge; - } - - /** - * We compute our initial nu challenge by hashing the following proof elements (with the current challenge): - * - * w1, w2, w3, w4, sigma1, sigma2, sigma3, q_arith, q_ecc, q_c, linearization_poly, grand_product_at_z_omega, - * w1_omega, w2_omega, w3_omega, w4_omega - * - * These values are placed linearly in the proofData, we can extract them with a calldatacopy call - * - */ - function generate_nu_challenges( - TranscriptData memory self, - Types.ChallengeTranscript memory challenges, - // uint256 quotient_poly_eval, - uint256 num_public_inputs - ) internal pure { - uint256 p = Bn254Crypto.r_mod; - bytes32 current_challenge = self.current_challenge; - uint256 base_v_challenge; - uint256 updated_v; - - // We want to copy SIXTEEN field elements from calldata into memory to hash - // But we start by adding the quotient poly evaluation to the hash transcript - assembly { - // get a calldata pointer that points to the start of the data we want to copy - let calldata_ptr := add(calldataload(0x04), 0x24) - // skip over the public inputs - calldata_ptr := add(calldata_ptr, mul(num_public_inputs, 0x20)) - // There are NINE G1 group elements added into the transcript in the `beta` round, that we need to skip over - calldata_ptr := add(calldata_ptr, 0x240) // 9 * 0x40 = 0x240 - - let m_ptr := mload(0x40) - mstore(m_ptr, current_challenge) - // mstore(add(m_ptr, 0x20), quotient_poly_eval) - calldatacopy(add(m_ptr, 0x20), calldata_ptr, 0x1e0) // 15 * 0x20 = 0x1e0 - base_v_challenge := keccak256(m_ptr, 0x200) // hash length = 0x200, we include the previous challenge in the hash - updated_v := mod(base_v_challenge, p) - } - - // assign the first challenge value - challenges.v0 = updated_v; - - // for subsequent challenges we iterate 10 times. - // At each iteration i \in [1, 10] we compute challenges.vi = keccak256(base_v_challenge, byte(i)) - assembly { - mstore(0x00, base_v_challenge) - mstore8(0x20, 0x01) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v1 = updated_v; - assembly { - mstore8(0x20, 0x02) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v2 = updated_v; - assembly { - mstore8(0x20, 0x03) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v3 = updated_v; - assembly { - mstore8(0x20, 0x04) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v4 = updated_v; - assembly { - mstore8(0x20, 0x05) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v5 = updated_v; - assembly { - mstore8(0x20, 0x06) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v6 = updated_v; - assembly { - mstore8(0x20, 0x07) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v7 = updated_v; - assembly { - mstore8(0x20, 0x08) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v8 = updated_v; - assembly { - mstore8(0x20, 0x09) - updated_v := mod(keccak256(0x00, 0x21), p) - } - challenges.v9 = updated_v; - - // update the current challenge when computing the final nu challenge - bytes32 challenge; - assembly { - mstore8(0x20, 0x0a) - challenge := keccak256(0x00, 0x21) - updated_v := mod(challenge, p) - } - challenges.v10 = updated_v; - - self.current_challenge = challenge; - } - - function generate_separator_challenge( - TranscriptData memory self, - Types.ChallengeTranscript memory challenges, - Types.G1Point memory PI_Z, - Types.G1Point memory PI_Z_OMEGA - ) internal pure { - bytes32 challenge; - bytes32 old_challenge = self.current_challenge; - uint256 p = Bn254Crypto.r_mod; - uint256 reduced_challenge; - assembly { - let m_ptr := mload(0x40) - mstore(m_ptr, old_challenge) - mstore(add(m_ptr, 0x20), mload(add(PI_Z, 0x20))) - mstore(add(m_ptr, 0x40), mload(PI_Z)) - mstore(add(m_ptr, 0x60), mload(add(PI_Z_OMEGA, 0x20))) - mstore(add(m_ptr, 0x80), mload(PI_Z_OMEGA)) - challenge := keccak256(m_ptr, 0xa0) - reduced_challenge := mod(challenge, p) - } - challenges.u = reduced_challenge; - self.current_challenge = challenge; - } -} - - - - \ No newline at end of file diff --git a/contracts/mocks/Kevin.sol b/contracts/mocks/Kevin.sol deleted file mode 100644 index cca2308..0000000 --- a/contracts/mocks/Kevin.sol +++ /dev/null @@ -1,18 +0,0 @@ -pragma solidity ^0.8.15; - -import "../Verifier.sol"; - -contract Kevin is TurboVerifier { - - event Banana(uint256 x, uint256 y, uint256 result); - - uint256 public last; - - function set(bytes memory proof) public { - uint256[3] memory inputs = abi.decode(proof, (uint256[3])); - require(this.verify(proof)); - last = inputs[2]; - emit Banana(inputs[0], inputs[1], inputs[2]); - } - -} \ No newline at end of file diff --git a/foundry.toml b/foundry.toml index 913fd3e..3279188 100644 --- a/foundry.toml +++ b/foundry.toml @@ -10,8 +10,4 @@ optimizer_runs = 5_000 optimizer = true src = "contracts" libs = ["lib"] - -[profile.hardhat] -src = "contracts" -out = "artifacts" -libs = ["node_modules"] \ No newline at end of file +fs_permissions = [{ access = "read-write", path = "./"}] \ No newline at end of file diff --git a/hardhat.config.ts b/hardhat.config.ts deleted file mode 100644 index f3048b4..0000000 --- a/hardhat.config.ts +++ /dev/null @@ -1,22 +0,0 @@ - -import { HardhatUserConfig } from "hardhat/config"; -import "@nomicfoundation/hardhat-toolbox"; - -const config: HardhatUserConfig = { - solidity: { - version: '0.8.15', - settings: { - evmVersion: 'london', - optimizer: { enabled: true, runs: 5000 }, - }, - }, - networks: { - hardhat: { - blockGasLimit: 10000000, - gasPrice: 10, - hardfork: 'istanbul', - }, - 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"name": "nplate", - "version": "1.0.0", - "description": "A template for noir.", - "main": "index.js", - "scripts": { - "test": "echo \"Error: no test specified\" && exit 1" - }, - "author": "", - "license": "ISC", - "devDependencies": { - "@ethersproject/abi": "^5.4.7", - "@ethersproject/providers": "^5.4.7", - "@nomicfoundation/hardhat-chai-matchers": "^1.0.0", - "@nomicfoundation/hardhat-network-helpers": "^1.0.0", - "@nomicfoundation/hardhat-toolbox": "^1.0.1", - "@nomiclabs/hardhat-ethers": "^2.0.0", - "@nomiclabs/hardhat-etherscan": "^3.0.0", - "@typechain/ethers-v5": "^10.1.0", - "@typechain/hardhat": "^6.1.2", - "@types/chai": "^4.2.0", - "@types/mocha": "^9.1.0", - "@types/node": ">=12.0.0", - "chai": "^4.2.0", - "ethers": "^5.4.7", - "hardhat": "^2.11.1", - "hardhat-gas-reporter": "^1.0.8", - "solidity-coverage": "^0.7.21", - "ts-node": ">=8.0.0", - "typechain": "^8.1.0", - "typescript": ">=4.5.0" - }, - "dependencies": { - "@noir-lang/aztec_backend": "^0.12.0", - "@noir-lang/barretenberg": "^2.19.0", - "@noir-lang/noir_wasm": "^0.10.0" - } -} \ No newline at end of file diff --git a/scripts/generateContract.ts b/scripts/generateContract.ts deleted file mode 100644 index 59710a5..0000000 --- a/scripts/generateContract.ts +++ /dev/null @@ -1,36 +0,0 @@ -import { resolve, join } from 'path'; -import { compile, acir_from_bytes } from '@noir-lang/noir_wasm'; -import { setup_generic_prover_and_verifier } from '@noir-lang/barretenberg/dest/client_proofs'; -import { writeFileSync, readFileSync } from 'fs'; -import path from 'path'; - -function path_to_uint8array(path: string) { - let buffer = readFileSync(path); - return new Uint8Array(buffer); -} - -async function generateSolidityVerifier() { - let acir; - try { - let compiled_program = compile(resolve(__dirname, '../circuits/src/main.nr')); - acir = compiled_program.circuit; - } catch (e : any ) { - let acirByteArray = path_to_uint8array(path.resolve(__dirname, `../circuits/build/${process.argv[2]}.acir`)); - acir = acir_from_bytes(acirByteArray); - } - console.log("Setting up generic verifier..."); - let [_, verifier] = await setup_generic_prover_and_verifier(acir); - - const sc = verifier.SmartContract(); - syncWriteFile("../contracts/Verifier.sol", sc); - - console.log('Done writing Verifier contract.'); -} - -function syncWriteFile(filename: string, data: any) { - writeFileSync(join(__dirname, filename), data, { - flag: 'w', - }); -} - -generateSolidityVerifier().then(() => process.exit(0)).catch(console.log); diff --git a/scripts/generateProof.ts b/scripts/generateProof.ts deleted file mode 100644 index d8b7d9b..0000000 --- a/scripts/generateProof.ts +++ /dev/null @@ -1,33 +0,0 @@ - -import { compile, acir_from_bytes } from '@noir-lang/noir_wasm'; -import { setup_generic_prover_and_verifier, create_proof, verify_proof, create_proof_with_witness } from '@noir-lang/barretenberg/dest/client_proofs'; -import path from 'path'; -import { readFileSync } from 'fs'; - -function path_to_uint8array(path: string) { - let buffer = readFileSync(path); - return new Uint8Array(buffer); -} - -async function generateProof() { - let acirByteArray = path_to_uint8array(path.resolve(__dirname, `../circuits/build/${process.argv[2]}.acir`)); - let acir = acir_from_bytes(acirByteArray); - - let abi = { - x : 1, - y : 2, - return : 3 - } - - console.log("Setting up generic prover and verifier..."); - let [prover, verifier] = await setup_generic_prover_and_verifier(acir); - console.log("Creating proof..."); - const proof = await create_proof(prover, acir, abi); - console.log("Verifying proof..."); - const verified = await verify_proof(verifier, proof); - - console.log("Proof : ", proof.toString('hex')); - console.log("Is the proof valid : ", verified); -} - -generateProof().then(() => process.exit(0)).catch(console.log); \ No newline at end of file diff --git a/test/Kevin.t.sol b/test/Kevin.t.sol index 12ef144..dbde7ac 100644 --- a/test/Kevin.t.sol +++ b/test/Kevin.t.sol @@ -3,7 +3,7 @@ pragma solidity ^0.8.15; import "forge-std/Test.sol"; import "forge-std/console2.sol"; -import {Kevin} from "contracts/mocks/Kevin.sol"; +import { Kevin } from "contracts/Kevin.sol"; contract KevinTest is Test { @@ -13,23 +13,18 @@ contract KevinTest is Test { kevin = new Kevin(); } - function getBasicProofRequest() public pure returns (string[] memory) { - string[] memory inputs = new string[](7); - inputs[0] = "npx"; - inputs[1] = "ts-node"; - inputs[2] = "test/utils/ffiProof.ts"; - return inputs; + function _readProof(string memory fileName) internal returns (bytes memory) { + string memory file = vm.readFile(string.concat("circuits/proofs/", fileName, ".proof")); + return vm.parseBytes(file); } function testLabouji() external { - string[] memory inputs = getBasicProofRequest(); - inputs[3] = "p"; - inputs[4] = "1"; - inputs[5] = "2"; - inputs[6] = "3"; - bytes memory proof = vm.ffi(inputs); - console2.logBytes(proof); - kevin.set(proof); + bytes memory proof = _readProof("a"); + bytes32[] memory inputs = new bytes32[](3); + inputs[0] = bytes32(uint256(1)); + inputs[1] = bytes32(uint256(2)); + inputs[2] = bytes32(uint256(3)); + kevin.set(proof, inputs); assertEq(kevin.last(), 3); } } \ No newline at end of file diff --git a/test/test.ts b/test/test.ts deleted file mode 100644 index dc4d190..0000000 --- a/test/test.ts +++ /dev/null @@ -1,47 +0,0 @@ -import { compile, acir_from_bytes } from '@noir-lang/noir_wasm'; -import { setup_generic_prover_and_verifier, create_proof, verify_proof, create_proof_with_witness } from '@noir-lang/barretenberg/dest/client_proofs'; -import { packed_witness_to_witness, serialise_public_inputs, compute_witnesses } from '@noir-lang/aztec_backend'; -import path from 'path'; -import { readFileSync } from 'fs'; -import { expect } from 'chai'; -import { ethers } from "hardhat"; -import { Contract, ContractFactory, utils } from 'ethers'; - -const BUILD = "build1"; - -describe('Using the solidity verifier', function() { - let Verifier: ContractFactory; - let verifierContract: Contract; - - before(async () => { - Verifier = await ethers.getContractFactory("TurboVerifier"); - verifierContract = await Verifier.deploy(); - }); - - it("Should verify using proof generated by typescript wrapper", async () => { - let acirByteArray = path_to_uint8array(path.resolve(__dirname, `../circuits/build/${BUILD}.acir`)); - let acir = acir_from_bytes(acirByteArray); - - let abi = { - x: 1, - y: 2, - return: 3, - } - - let [prover, verifier] = await setup_generic_prover_and_verifier(acir); - - const proof = await create_proof(prover, acir, abi); - - const verified = await verify_proof(verifier, proof); - expect(verified).eq(true) - - const sc_verified = await verifierContract.verify(proof); - expect(sc_verified).eq(true) - }); - -}); - -function path_to_uint8array(path: string) { - let buffer = readFileSync(path); - return new Uint8Array(buffer); -} \ No newline at end of file diff --git a/test/utils/ffiProof.ts b/test/utils/ffiProof.ts deleted file mode 100644 index d934bb5..0000000 --- a/test/utils/ffiProof.ts +++ /dev/null @@ -1,27 +0,0 @@ -import { compile, acir_from_bytes } from '@noir-lang/noir_wasm'; -import { setup_generic_prover_and_verifier, create_proof, verify_proof, create_proof_with_witness } from '@noir-lang/barretenberg/dest/client_proofs'; -import path from 'path'; -import { readFileSync } from 'fs'; - -function path_to_uint8array(path: string) { - let buffer = readFileSync(path); - return new Uint8Array(buffer); -} - -async function generateProof() { - let acirByteArray = path_to_uint8array(path.resolve(__dirname, `../../circuits/build/${process.argv[2]}.acir`)); - let acir = acir_from_bytes(acirByteArray); - - let abi = { - x : parseInt(process.argv[3]), - y : parseInt(process.argv[4]), - return : parseInt(process.argv[5]) - } - - let [prover, verifier] = await setup_generic_prover_and_verifier(acir); - const proof = await create_proof(prover, acir, abi); - // simple output -> easy to use by ffi - console.log(proof.toString('hex')); -} - -generateProof().then(() => process.exit(0)).catch(console.log); \ No newline at end of file diff --git a/utils/safeGenerateContract.sh b/utils/safeGenerateContract.sh deleted file mode 100755 index 67815fb..0000000 --- a/utils/safeGenerateContract.sh +++ /dev/null @@ -1,21 +0,0 @@ -#!/usr/bin/env bash - -# -# Runs nargo build and compile before generating the Verifier contract. -# If Prover.toml is malformed, it will still generate the proof using the last valid build. -# - -printf "Name of your build : " -read name_build -printf "\n#################\n\n" - -cd circuits/ - -nargo build -printf "\n#################\n\n" - -nargo compile ${name_build} -printf "\n#################\n\n" -cd .. - -npx ts-node scripts/generateContract.ts ${name_build} \ No newline at end of file diff --git a/utils/safeGenerateProof.sh b/utils/safeGenerateProof.sh deleted file mode 100755 index d61c5ff..0000000 --- a/utils/safeGenerateProof.sh +++ /dev/null @@ -1,19 +0,0 @@ -#!/usr/bin/env bash - -# -# Runs nargo build and compile before generating a proof. -# If Prover.toml is malformed, it will still generate the proof using the last valid build. -# - -printf "Name of your build : " -read name_build - -cd circuits/ -printf "\n#################\n\n" -nargo build -printf "\n#################\n\n" -nargo compile ${name_build} -printf "\n#################\n\n" - -cd .. -npx ts-node scripts/generateProof.ts ${name_build} \ No newline at end of file