Cryptography Python

This is a tutorial project about cryptography in python. Follow the steps and you will fully understand the magic of elliptic curves from scratch.

• Each file can be run independently!
• There are detailed paper references in the comments of the code

Based on this project, I implemented the SDKs of three famous blockchain projects: BTC, ETH and CKB.

• https://github.com/mohanson/pybtc: Almost fully supported.
• https://github.com/mohanson/pyeth: Almost fully supported.
• https://github.com/mohanson/pyckb: Almost fully supported.

Secp256k1

Written according to this paper: https://www.cs.miami.edu/home/burt/learning/Csc609.142/ecdsa-cert.pdf

• secp256k1.py: implement finite field and secp256k1 curve.
• secp256k1_generate_public_key.py: calculate bitcoin public key from private key.
• secp256k1_sign.py: signature messages and verify it.
• secp256k1_extract_private_key.py: extract the private key by two signatures that use the same k.
• secp256k1_jacobian: jacobian projective space.

Polynomial arith

Polynomial manipulation in Python.

• polynomial_numpy.py: polynomial operation by numpy.
• polynomial.py: polynomial operation by hand writting python.

Bn128

• bn128.py: bn128 curve, implements eip-196, eip-197.
• bn128_ethereum_api.py: bn128 pairing testsuite.

Kzg

KZG polynomial commitment is a scheme for polynomial commitment proposed by Kate, Zaverucha, Goldberg and others in the paper Polynomial Commitments published in 2010.

• kzg.py: implement kzg proof based on bn128.
• kzg_arith_relation.py: a more complex proof.

Secp256r1

Similar to secp256k1, but with different parameters.

• secp256r1.py: implement finite field and secp256r1 curve.
• secp256r1_recovery_pubkey.py: recover pubkey from signature.

Ed25519

Implements the Ed25519 elliptic curve and eddsa signature algorithms.

• ed25519.py
• eddsa.py

Licences

MIT.