cryptofun

Crypto algorithms from scratch. Academic purposes only.

RSA

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

• GenerateKeyPair
• Encrypt
• Decrypt
• Blind
• Blind Signature
• Unblind Signature
• Verify Signature
• Homomorphic Multiplication

Paillier

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

• 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

[not finished]

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

• Fq, Fq2, Fq6, Fq12 operations

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To run all tests:

go test ./... -v