如何在python中制作AES逆mix_column

Question

我目前正在使用此代码制作一个 AES 的小示例

mix_columns_matrix = [
    [0x2, 0x3, 0x1, 0x1],
    [0x1, 0x2, 0x3, 0x1],
    [0x1, 0x1, 0x2, 0x3],
    [0x3, 0x1, 0x1, 0x2]
]

def mix_columns(state):
    new_state = [[0 for _ in range(4)] for _ in range(4)]
    for i in range(4):
        for j in range(4):
            result = 0
            for k in range(4):
                result ^= state[k][j] * mix_columns_matrix[i][k]
            new_state[i][j] = result & 0xF  # Limit to 4 bits
    return new_state`

当我使用它时，我有：

Before MixColumns:
   
['0x3', '0x6', '0x5', '0xc']
['0xd', '0xe', '0x8', '0xa']
['0x1', '0xf', '0x4', '0x7']
['0x0', '0x2', '0xb', '0x9']

After MixColumns:
['0x0', '0xb', '0xd', '0x8']
['0xa', '0x5', '0x2', '0x4']
['0xc', '0x0', '0x4', '0x3']
['0x5', '0x7', '0x5', '0xb']

所以我尝试创建反向函数

def inv_mix_columns(state):
    inv_mix_columns_matrix = [
        [0xE, 0xB, 0xD, 0x9],
        [0x9, 0xE, 0xB, 0xD],
        [0xD, 0x9, 0xE, 0xB],
        [0xB, 0xD, 0x9, 0xE]
    ]

    new_state = [[0 for _ in range(4)] for _ in range(4)]
    for i in range(4):
        for j in range(4):
            result = 0
            for k in range(4):
                result ^= state[k][j] * inv_mix_columns_matrix[i][k]
            new_state[i][j] = result & 0xF  # Limit to 4 bits
    return new_state

根据之前的结果，我得到：

['0x3', '0x7', '0x7', '0xb']
['0x5', '0x3', '0xa', '0xd']
['0x1', '0x6', '0x6', '0x4']
['0xc', '0xb', '0x5', '0xe']

我不明白为什么我没有第一个输入结果以及如何修复它。

我尝试了几种形式的

inv_mix_columns

并多次检查我的矩阵，但我仍然不知道发生了什么.. 我想知道我是否很好地使用了 XOR 函数

当然，我不想使用库，因为它只是一个例子

感谢您的帮助

Answer 1

def mix_columns(state_matrix, mix_matrix):
    state_matrix = np.array(state_matrix)
    mix_matrix = np.array(mix_matrix)
    mixed_state = np.zeros_like(state_matrix, dtype=int)
    
    for col in range(4):
        for row in range(4):
            mixed_state[row][col] = gf_add_mul(state_matrix[:, col], mix_matrix[row, :])
    
    return mixed_state

def inv_mix_columns(state_matrix, inv_mix_matrix):
    state_matrix = np.array(state_matrix)
    inv_mix_matrix = np.array(inv_mix_matrix)
    mixed_state = np.zeros_like(state_matrix, dtype=int)
    
    for col in range(4):
        for row in range(4):
            mixed_state[row][col] = gf_add_mul(state_matrix[:, col], inv_mix_matrix[row, :])
    
    return mixed_state

def gf_add_mul(a, b):
    p = 0
    for i in range(4):
        p ^= gf_mul(a[i], b[i])
    return p

def gf_mul(a, b):
    p = 0
    for _ in range(4):
        if b & 1:
            p ^= a
        hi_bit_set = a & 0x8
        a <<= 1
        if hi_bit_set:
            a ^= 0x3
        b >>= 1
    return p & 0xF

我已经得到了解决方案，因为乘法和模运算必须使用字节上的有限域规则 GF(2^4) 来完成。这意味着加法和乘法必须在这个特定的上下文中执行。我用了numpy