This a pure Python implementation of a generic multiplication and addition operations used key generation, document signing, and Diffie–Hellman key exchange.
This code would be imposable without Understanding Cryptography by Christof Paar and Jan Pelzl. The validity of the generic implementation would be hard to prove without NIST test vectors.
x3, y3 = point_add(x1, y1, x2, y2, prime, a)
x2, y2 = point_multiply(x1, y1, multiplicant, prime, a)Above the X and Y coordinates are assumed to be on the curve and the prime and a to belong to the curve domain parameters.
NIST domain parameters may be used ass follows:
from functional_ecc import domain_params
p_p21_dp = domain_params["P-521"]
x3, y3 = point_add(x1, y1, x2, y2, p_p21_dp.prime, p_p21_dp.a)New domain parameters and curves may be defined as follows.
from functional_ecc import domain_param
paar_17 = domain_param(prime=17, a=2, b=2, g_x=5, g_y=1)
This implementation should work for any prime field elliptic curve, however the following NIST curve domain parameters can be found in the domain_params dictionary:
- P-192
- P-224
- P-256
- P-384
- P-521
The code was intended for educational purposes.