深入理解AES加密算法：原理与Python实现
# S盒 (SubBytes 使用)
S_BOX = [
[0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76],
[0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0],
[0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15],
[0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75],
[0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84],
[0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf],
[0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8],
[0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2],
[0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73],
[0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb],
[0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79],
[0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08],
[0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a],
[0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e],
[0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf],
[0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16]
]
# 逆S盒 (InvSubBytes 使用)
INV_S_BOX = [
[0x52, 0x09, 0x6a, 0xd5, 0x30, 0x36, 0xa5, 0x38, 0xbf, 0x40, 0xa3, 0x9e, 0x81, 0xf3, 0xd7, 0xfb],
[0x7c, 0xe3, 0x39, 0x82, 0x9b, 0x2f, 0xff, 0x87, 0x34, 0x8e, 0x43, 0x44, 0xc4, 0xde, 0xe9, 0xcb],
[0x54, 0x7b, 0x94, 0x32, 0xa6, 0xc2, 0x23, 0x3d, 0xee, 0x4c, 0x95, 0x0b, 0x42, 0xfa, 0xc3, 0x4e],
[0x08, 0x2e, 0xa1, 0x66, 0x28, 0xd9, 0x24, 0xb2, 0x76, 0x5b, 0xa2, 0x49, 0x6d, 0x8b, 0xd1, 0x25],
[0x72, 0xf8, 0xf6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xd4, 0xa4, 0x5c, 0xcc, 0x5d, 0x65, 0xb6, 0x92],
[0x6c, 0x70, 0x48, 0x50, 0xfd, 0xed, 0xb9, 0xda, 0x5e, 0x15, 0x46, 0x57, 0xa7, 0x8d, 0x9d, 0x84],
[0x90, 0xd8, 0xab, 0x00, 0x8c, 0xbc, 0xd3, 0x0a, 0xf7, 0xe4, 0x58, 0x05, 0xb8, 0xb3, 0x45, 0x06],
[0xd0, 0x2c, 0x1e, 0x8f, 0xca, 0x3f, 0x0f, 0x02, 0xc1, 0xaf, 0xbd, 0x03, 0x01, 0x13, 0x8a, 0x6b],
[0x3a, 0x91, 0x11, 0x41, 0x4f, 0x67, 0xdc, 0xea, 0x97, 0xf2, 0xcf, 0xce, 0xf0, 0xb4, 0xe6, 0x73],
[0x96, 0xac, 0x74, 0x22, 0xe7, 0xad, 0x35, 0x85, 0xe2, 0xf9, 0x37, 0xe8, 0x1c, 0x75, 0xdf, 0x6e],
[0x47, 0xf1, 0x1a, 0x71, 0x1d, 0x29, 0xc5, 0x89, 0x6f, 0xb7, 0x62, 0x0e, 0xaa, 0x18, 0xbe, 0x1b],
[0xfc, 0x56, 0x3e, 0x4b, 0xc6, 0xd2, 0x79, 0x20, 0x9a, 0xdb, 0xc0, 0xfe, 0x78, 0xcd, 0x5a, 0xf4],
[0x1f, 0xdd, 0xa8, 0x33, 0x88, 0x07, 0xc7, 0x31, 0xb1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xec, 0x5f],
[0x60, 0x51, 0x7f, 0xa9, 0x19, 0xb5, 0x4a, 0x0d, 0x2d, 0xe5, 0x7a, 0x9f, 0x93, 0xc9, 0x9c, 0xef],
[0xa0, 0xe0, 0x3b, 0x4d, 0xae, 0x2a, 0xf5, 0xb0, 0xc8, 0xeb, 0xbb, 0x3c, 0x83, 0x53, 0x99, 0x61],
[0x17, 0x2b, 0x04, 0x7e, 0xba, 0x77, 0xd6, 0x26, 0xe1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0c, 0x7d]
]
# 密钥扩展需要的Rcon常量
RCON = [
[0x01, 0x00, 0x00, 0x00],
[0x02, 0x00, 0x00, 0x00],
[0x04, 0x00, 0x00, 0x00],
[0x08, 0x00, 0x00, 0x00],
[0x10, 0x00, 0x00, 0x00],
[0x20, 0x00, 0x00, 0x00],
[0x40, 0x00, 0x00, 0x00],
[0x80, 0x00, 0x00, 0x00],
[0x1b, 0x00, 0x00, 0x00],
[0x36, 0x00, 0x00, 0x00],
]
# 字节代换
def sub_bytes(state):
for i in range(4):
for j in range(4):
state[i][j] = S_BOX[state[i][j] >> 4][state[i][j] & 0x0f]
# 逆字节代换
def inv_sub_bytes(state):
for i in range(4):
for j in range(4):
state[i][j] = INV_S_BOX[state[i][j] >> 4][state[i][j] & 0x0f]
# 行移位
def shift_rows(state):
state[1][0], state[1][1], state[1][2], state[1][3] = state[1][1], state[1][2], state[1][3], state[1][0]
state[2][0], state[2][1], state[2][2], state[2][3] = state[2][2], state[2][3], state[2][0], state[2][1]
state[3][0], state[3][1], state[3][2], state[3][3] = state[3][3], state[3][0], state[3][1], state[3][2]
# 逆行移位
def inv_shift_rows(state):
state[1][0], state[1][1], state[1][2], state[1][3] = state[1][3], state[1][0], state[1][1], state[1][2]
state[2][0], state[2][1], state[2][2], state[2][3] = state[2][2], state[2][3], state[2][0], state[2][1]
state[3][0], state[3][1], state[3][2], state[3][3] = state[3][1], state[3][2], state[3][3], state[3][0]
# 列混合
def mix_columns(state):
for i in range(4):
t = state[0][i] ^ state[1][i] ^ state[2][i] ^ state[3][i]
u = state[0][i]
state[0][i] ^= t ^ xtime(state[0][i] ^ state[1][i])
state[1][i] ^= t ^ xtime(state[1][i] ^ state[2][i])
state[2][i] ^= t ^ xtime(state[2][i] ^ state[3][i])
state[3][i] ^= t ^ xtime(state[3][i] ^ u)
# 逆列混合
def inv_mix_columns(state):
for i in range(4):
u = xtime(xtime(state[0][i] ^ state[2][i]))
v = xtime(xtime(state[1][i] ^ state[3][i]))
state[0][i] ^= u
state[1][i] ^= v
state[2][i] ^= u
state[3][i] ^= v
mix_columns(state)
# 辅助函数xtime，用于Galois域GF(2^8)的乘法
def xtime(a):
return ((a << 1) ^ 0x1b) & 0xff if a & 0x80 else a << 1
# 轮密钥加
def add_round_key(state, key_schedule, round_idx):
for i in range(4):
for j in range(4):
state[i][j] ^= key_schedule[round_idx * 4 + j][i]
# 密钥扩展
def key_expansion(key):
key_symbols = [ord(symbol) for symbol in key]
if len(key_symbols) < 4 * 4:
for i in range(len(key_symbols), 4 * 4):
key_symbols.append(0x01)
key_schedule = []
for r in range(4):
key_schedule.append(key_symbols[r*4:(r+1)*4])
for col in range(4, 4 * (10 + 1)):
if col % 4 == 0:
tmp = [key_schedule[col-1][1], key_schedule[col-1][2],
key_schedule[col-1][3], key_schedule[col-1][0]]
tmp = [S_BOX[b >> 4][b & 0x0f] for b in tmp]
tmp[0] ^= RCON[col//4-1][0]
else:
tmp = key_schedule[col-1]
key_schedule.append([key_schedule[col-4][i] ^ tmp[i] for i in range(4)])
return key_schedule
# AES加密函数
def aes_encrypt(plaintext, key):
state = [[0] * 4 for _ in range(4)]
for i in range(4):
for j in range(4):
state[i][j] = plaintext[i + 4 * j]
key_schedule = key_expansion(key)
add_round_key(state, key_schedule, 0)
for round_idx in range(1, 10):
sub_bytes(state)
shift_rows(state)
mix_columns(state)
add_round_key(state, key_schedule, round_idx)
sub_bytes(state)
shift_rows(state)
add_round_key(state, key_schedule, 10)
ciphertext = []
for i in range(4):
for j in range(4):
ciphertext.append(state[i][j])
return ciphertext
# AES解密函数
def aes_decrypt(ciphertext, key):
state = [[0] * 4 for _ in range(4)]
for i in range(4):
for j in range(4):
state[i][j] = ciphertext[i + 4 * j]
key_schedule = key_expansion(key)
add_round_key(state, key_schedule, 10)
for round_idx in range(9, 0, -1):
inv_shift_rows(state)
inv_sub_bytes(state)
add_round_key(state, key_schedule, round_idx)
inv_mix_columns(state)
inv_shift_rows(state)
inv_sub_bytes(state)
add_round_key(state, key_schedule, 0)
plaintext = []
for i in range(4):
for j in range(4):
plaintext.append(state[i][j])
return plaintext
# 测试加密解密流程
key = "2b7e151628aed2a6abf7158809cf4f3c"
plaintext = [0x32, 0x43, 0xf6, 0xa8, 0x88, 0x5a, 0x30, 0x8d, 0x31, 0x31, 0x98, 0xa2, 0xe0, 0x37, 0x07, 0x34]
ciphertext = aes_encrypt(plaintext, key)
decrypted = aes_decrypt(ciphertext, key)
print("Ciphertext:", ciphertext)
print("Decrypted:", decrypted)