Multiplication GF(2**8) using matrices

gf28.py

import numpy as np

def companion_matrix():
    C = np.zeros((8, 8), dtype=int)
    for i in range(7):
        C[i, i + 1] = 1
    C[7, [0, 1, 3, 4]] = 1
    return C

def matrix_mod2(mat):
    return np.mod(mat, 2)

def generate_multiplication_matrix(alpha):
    C = companion_matrix()
    M = np.zeros((8, 8), dtype=int)
    binary_representation = [(alpha >> i) & 1 for i in range(8)]
    for i, bit in enumerate(binary_representation):
        if bit:
            M += np.linalg.matrix_power(C, i)
    return (M)

def gf2_8_multiply(a, b):
    irreducible_poly = 0x11b
    result = 0
    for _ in range(8):
        if b & 1:
            result ^= a
        carry = a & 0x80
        a <<= 1
        if carry:
            a ^= irreducible_poly
        b >>= 1
    return result & 0xFF

for alpha in range(256):
    for beta in range(256):
        expected = gf2_8_multiply(alpha, beta)
        matrix = generate_multiplication_matrix(alpha)
        v = np.array([int(k) for k in '{:08b}'.format(beta)[::-1]])
        value = (v@matrix)%2
        aux = int("".join([str(k) for k in value])[::-1], 2)
        if aux != expected:
            print("deu ruim:", alpha, beta, aux, expected, value, '{:08b}'.format(expected))