NOTES.md

Notes

OpenSSL (binding/wrapper) in ruby

• https://github.com/ruby/openssl
• https://ruby-doc.org/stdlib-2.5.1/libdoc/openssl/rdoc/OpenSSL.html

Tips & Tricks

big number (bn)

• opensll adds Integer#to_bn for easy conversion

999.to_bn    # same as   OpenSSL::BN.new( 999 )
-999.to_bn
2**107-1).to_bn
(-(2**107-1)).to_bn

Source: https://github.com/ruby/openssl/blob/master/test/openssl/test_bn.rb

use to_bn to construct Point too? why? why not?

assert_equal 0x040603.to_bn, point.to_bn
assert_equal 0x040603.to_bn, point.to_bn(:uncompressed)
assert_equal 0x0306.to_bn,   point.to_bn(:compressed)

Source: https://github.com/ruby/openssl/blob/master/test/openssl/test_pkey_ec.rb

More Elliptic Libraries

ruby

• https://github.com/starkbank/ecdsa-ruby
• https://github.com/DavidEGrayson/ruby_ecdsa
• https://github.com/cedarcode/openssl-signature_algorithm

python

• https://github.com/alexmgr/tinyec
• https://pypi.org/project/ecdsa/, https://github.com/tlsfuzzer/python-ecdsa

More Elliptic Articles

A (relatively easy to understand) primer on elliptic curve cryptography Everything you wanted to know about the next generation of public key crypto by Nick Sullivan, October 2013 - https://arstechnica.com/information-technology/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/

Elliptic Curve Cryptography: a gentle introduction by Andrea Corbellini, May 2015 - https://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction/

What is the math behind elliptic curve cryptography? by Hans Knutson, April 2018 - https://hackernoon.com/what-is-the-math-behind-elliptic-curve-cryptography-f61b25253da3

Elliptic Curve @ Wolfram Math World - https://mathworld.wolfram.com/EllipticCurve.html

Practical Cryptography for Developers by Svetlin Nakov:

• Elliptic Curve Cryptography (ECC) - https://cryptobook.nakov.com/asymmetric-key-ciphers/elliptic-curve-cryptography-ecc
• ECDSA: Elliptic Curve Signatures - https://cryptobook.nakov.com/digital-signatures/ecdsa-sign-verify-messages

sources: https://github.com/nakov/practical-cryptography-for-developers-book

Wikipedia:

• Elliptic curve - https://en.wikipedia.org/wiki/Elliptic_curve
• Elliptic Curve Cryptography (ECC) - https://en.wikipedia.org/wiki/Elliptic-curve_cryptography
• Elliptic Curve Digital Signature Algorithm (ECDSA) - https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm
• Elliptic curve point multiplication - https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication

More Articles

A Layman's Guide to a Subset of ASN.1, BER, and DER by Burton S. Kaliski Jr., An RSA Laboratories Technical Note, Revised November, 1993 - http://luca.ntop.org/Teaching/Appunti/asn1.html

• ASN.1 = Abstract Syntax Notation One
• BER = Basic Encoding Rules (for ASN.1)
• DER = Distinguished Encoding Rules (for ASN.1) - note: (strict/deterministic) subset of BER