深入理解AES加密算法：原理与Python实现

深入理解AES加密算法：原理与Python实现

AES (Advanced Encryption Standard) 是目前最广泛使用的对称加密算法之一。它具有高效、安全和灵活的特点，被广泛应用于数据加密、通信加密以及各种安全协议中。本文将详细介绍AES算法的加密和解密流程，并通过Python从头实现AES的加密与解密，而不依赖任何加密算法第三方库。

1. AES算法简介

AES是一种分组加密算法，其主要特点如下：

• 分组长度：AES处理固定长度的分组，通常为128位（16字节）。
• 密钥长度：AES支持128位、192位和256位三种密钥长度。
• 轮数：加密过程中的轮数取决于密钥长度，分别为10轮（128位密钥）、12轮（192位密钥）和14轮（256位密钥）。

2. AES加密解密流程

AES的加密过程可以分为以下几个主要步骤：

1. 密钥扩展：将初始密钥扩展为多个子密钥。
2. 初始轮：初始轮中只执行AddRoundKey操作，即将明文与扩展后的第一个子密钥进行异或运算。
3. 主要轮：根据密钥长度执行10、12或14轮迭代。每轮包括四个步骤：
   • 字节代换 (SubBytes)：非线性替换操作，对数据的每个字节使用S盒进行替换。
   • 行移位 (ShiftRows)：行移位操作，对数据矩阵的行进行循环移位。
   • 列混合 (MixColumns)：线性变换操作，对数据矩阵的列进行混合运算。
   • 轮密钥加 (AddRoundKey)：将当前数据与当前轮的子密钥进行异或运算。
4. 最终轮：最后一轮中只执行SubBytes、ShiftRows和AddRoundKey操作，省略MixColumns操作。

解密过程是加密过程的逆过程，主要步骤如下：

1. 初始轮：执行AddRoundKey操作。
2. 主要轮：逆向执行AddRoundKey、逆MixColumns、逆ShiftRows、逆SubBytes操作。
3. 最终轮：执行逆ShiftRows、逆SubBytes和AddRoundKey操作。

3. Python实现AES加密解密

以下是Python代码的完整实现：

# 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] ^= ustate[1][i] ^= vstate[2][i] ^= ustate[3][i] ^= vmix_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)

4. 结论

通过以上实现，我们可以看到AES算法的复杂性和严谨性。尽管上述实现是简化版本，但它展示了AES加密和解密的核心思想。在实际应用中，使用经过验证的加密库来确保安全性更为妥当。然而，从头实现AES算法有助于深入理解加密过程的每个步骤及其安全性机制。

本文不仅阐明了AES算法的加密解密流程，还通过Python代码展示了如何实现AES加密和解密的核心功能，帮助读者对AES有更全面和深入的认识。