Fast elliptic curve point operations in Python

Python bindings for general purpose elliptic curve point operations.

Supported curves and implementations:

• secp256r1 (P-256/prime256v1) (OpenSSL)
• secp256r1 (P-256/prime256v1) (Python)
• secp256k1 (OpenSSL)
• secp256k1 (Python)
• secp256k1 (libsecp256k1)
• Ed25519 (ed25519-donna)
• Ed25519 (Python)

Example usage:

$ sh secp256k1_openssl.sh
$ python
>>> import secp256r1_openssl as curve
>>> curve.g
[48439561293906451759052585252797914202762949526041747995844080717082404635286L, 36134250956749795798585127919587881956611106672985015071877198253568414405109L]
>>> curve.mul(curve.g, 5)
[36794669340896883012101473439538929759152396476648692591795318194054580155373L, 101659946828913883886577915207667153874746613498030835602133042203824767462820L]
>>> curve.add(curve.g, curve.inv(curve.g))
[None, None]
>>> 
>>> curve.compress(curve.g).encode('hex')
'036b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296'
>>> curve.decompress('036b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296'.decode('hex'))
[48439561293906451759052585252797914202762949526041747995844080717082404635286L, 36134250956749795798585127919587881956611106672985015071877198253568414405109L]
>>> curve.valid(curve.g)
1
>>> curve.valid([123,123])
0

Available methods:

• mul(point, scalar) - returns point multiplied with a scalar
• add(point, point) - returns addition of two points
• inv(point) - returns inverse of point
• valid(point) - returns 1 if point on curve, 0 otherwise
• comress(point) - returns 33 bytes - sign of Y coordinate (0x02 or 0x03) and X coordinate (32 bytes)
• decompress(bytestring33) - returns unpacked point

Point at infinity is represented as value [Null, Null] or 33 zero bytes (in compressed form).

Ed25519 does not have point at infinity. Neutral point is [0,1].