crypto

Crypto algorithms from scratch. Academic purposes only; Cryptoanalysis work; Notes and research

Crypto systems implementations

The implementations of these crypto primitives are for academical purposes only. Highly inspired by @arnaucube cryptofun project

HMAC

• https://en.wikipedia.org/wiki/HMAC

• HMAC-SHA256

RSA cryptosystem & Blind signature & Homomorphic Multiplication

• https://en.wikipedia.org/wiki/RSA_(cryptosystem)#

• https://en.wikipedia.org/wiki/Blind_signature

• https://en.wikipedia.org/wiki/Homomorphic_encryption

• GenerateKeyPair

• Encrypt

• Decrypt

• Blind

• Blind Signature

• Unblind Signature- RSA- RSA

• Verify Signature

• Homomorphic Multiplication

Paillier cryptosystem & Homomorphic Addition

• https://en.wikipedia.org/wiki/Paillier_cryptosystem

• https://en.wikipedia.org/wiki/Homomorphic_encryption

• GenerateKeyPair

• Encrypt

• Decrypt

• Homomorphic Addition

Shamir Secret Sharing

• https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing

• create secret sharing from number of secrets needed, number of shares, random point p, secret to share

• Lagrange Interpolation to restore the secret from the shares

Diffie-Hellman

• https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange

• key exchange

ECC

• https://en.wikipedia.org/wiki/Elliptic-curve_cryptography

• define elliptic curve

• get point at X

• get order of a Point on the elliptic curve

• Add two points on the elliptic curve

• Multiply a point n times on the elliptic curve

ECC ElGamal

• https://en.wikipedia.org/wiki/ElGamal_encryption

• ECC ElGamal key generation

• ECC ElGamal Encrypton

• ECC ElGamal Decryption

ECC ECDSA

• https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm

• define ECDSA data structure

• ECDSA Sign

• ECDSA Verify signature

Schnorr signature

• https://en.wikipedia.org/wiki/Schnorr_signature

• Hash[M || R] (where M is the msg bytes and R is a Point on the ECC, using sha256 hash function)

• Generate Schnorr scheme

• Sign

• Verify signature

Bn128

This is implemented followng the implementations and info from:

• https://github.com/iden3/zksnark

• https://github.com/zcash/zcash/tree/master/src/snark

• Multiplication and Squaring on Pairing-Friendly Fields, Augusto Jun Devegili, Colm Ó hÉigeartaigh, Michael Scott, and Ricardo Dahab https://pdfs.semanticscholar.org/3e01/de88d7428076b2547b60072088507d881bf1.pdf

• Optimal Pairings, Frederik Vercauteren https://www.cosic.esat.kuleuven.be/bcrypt/optimal.pdf

• Double-and-Add with Relative Jacobian Coordinates, Björn Fay https://eprint.iacr.org/2014/1014.pdf

• Fast and Regular Algorithms for Scalar Multiplication over Elliptic Curves, Matthieu Rivain https://eprint.iacr.org/2011/338.pdf

• Fq, Fq2, Fq6, Fq12 operations

• G1, G2 operations