一、简介引入

密码学中的高级加密标准（Advanced Encryption Standard，AES），又称Rijndael加密法，是美国联邦政府采用的一种区块加密标准。

这个标准用来替代原先的DES（Data Encryption Standard），已经被多方分析且广为全世界所使用。经过五年的甄选流程，高级加密标准由美国国家标准与技术研究院 （NIST）于2001年11月26日发布于FIPS PUB 197，并在2002年5月26日成为有效的标准。2006年，高级加密标准已然成为对称密钥加密中最流行的算法之一 [1]  。

该算法为比利时密码学家Joan Daemen和Vincent Rijmen所设计，结合两位作者的名字，以Rijdael之名命之，投稿高级加密标准的甄选流程。（Rijdael的发音近于 "Rhine doll"。）

二、加密流程 

 密文通过密匙k进行加密，然后传输给接受方，接受方再用已知的密匙k对密文进行反向解密，从而解得发送方发送的明文P。（在加密和解密中密匙相同，都为K）

 

大致流程如上图所示；

在AES中，将需要加密的文件分为128个bit为一组的明文，由于8个为一个字符，所以每一组总共是由16个字符组成的。密钥的长度可以使用128位、192位或256位。密钥的长度不同，推荐加密轮数也不同，分别为10，12，14轮。

三、密匙 扩展（密匙的生成）

AES-128，也就是密钥的长度为128位，加密轮数为10轮。AES的加密公式为C = E(K,P)，在加密函数E中，会执行一个轮函数，并且执行10次这个轮函数，这个轮函数的前9次执行的操作是一样的，只有第10次有所不同。也就是说，一个明文分组会被加密10轮。AES的核心就是实现一轮中的所有操作。

AES的处理单位是字节，128位的输入明文分组P和输入密钥K都被分成16个字节，分别记为P = P0 P1 … P15 和 K = K0 K1 … K15。如，明文分组为P = abcdefghijklmnop,其中的字符a对应P0，p对应P15。

一般地，明文分组用字节为单位的正方形矩阵描述，称为状态矩阵。在算法的每一轮中，状态矩阵的内容不断发生变化，最后的结果作为密文输出。该矩阵中字节的排列顺序为从上到下、从左至右依次排列，如下图所示：

现在假设明文分组P为”abcdefghijklmnop”，则对应上面生成的状态矩阵图如下： 

类似地，128位密钥也是用字节为单位的矩阵表示，矩阵的每一列被称为1个32位比特字（一个单元格是8位，4个单元格32位）。

通过密钥编排函数该密钥矩阵被扩展成一个44个字组成的序列W[0],W[1], …

W[43],该序列的前4个元素W[0],W[1],W[2],W[3]是原始密钥，用于加密运算 中的 初始密钥加（下面介绍）;后面40个字分为10组，每组4个字（4*32=128比特）分别用于10轮加密运算中的轮密钥加。

128位即使扩展为（10+1）*4=44组，192同理为52组，256同理为60组。

四、AES实现

一、轮密匙加，就是取出密匙中的四位与明文进行简单的异或运算

 

二、字节代替

字节代替，既是aes中的混淆操作，将行列式进行一个S盒变换，把该字节的前四位作为行值，后四位作为列值，对应于S盒中的值输出。例如，十进制中{95}的行值为9，列值为5，对应于S盒中就是{2A}，所以{95}被映射为{2A} 

 

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
)

s_box1 = [
    [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],
]

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]
]

state = [
    [251, 64, 182, 81],
    [146, 168, 33, 80],
    [199, 159, 195, 24],
    [64, 80, 182, 255],
]


def remove_prefix(str, prefix='0x'):
    if str.startswith(prefix):
        return str[len(prefix):]
    else:
        return str


def remove_postfix(str, postfix="'"):
    if str.endswith(postfix):
        return str[:len(str)-len(postfix)]
    else:
        return str


def sub_bytes(s, sbox=s_box):
    for i in range(len(s)):
        for j in range(len(s[i])):
            stri = remove_prefix(str(hex(s[i][j])))
            if len(stri)>1:
                k = int('0x' + stri[0], 16)
                l = int('0x' + stri[1], 16)
                s[i][j] = sbox[k][l]
            else:
                k=0
                l = int('0x'+stri[0], 16)
            s[i][j] = sbox[k][l]
    return s


stri = ''
for i in sub_bytes(state, sbox=inv_s_box):
    stri += remove_postfix(remove_prefix(str(bytes(i)), "b'"))
print(stri)

三、行移位

将需要加密的四组进行简单的行方向变换。

收先，进行以列位方向的排列，然后，按照第一行不移动，第二行向左移动一位，第三行向左移动两位，第四行向做移动三位的方式进行行变换：

 

from Confusion_through_Substitution import remove_prefix, remove_postfix


def shift_rows(s):
    s[0][1], s[1][1], s[2][1], s[3][1] = s[1][1], s[2][1], s[3][1], s[0][1]
    s[0][2], s[1][2], s[2][2], s[3][2] = s[2][2], s[3][2], s[0][2], s[1][2]
    s[0][3], s[1][3], s[2][3], s[3][3] = s[3][3], s[0][3], s[1][3], s[2][3]


def inv_shift_rows(s):
    s[0][0], s[1][0], s[2][0], s[3][0] = s[0][0], s[1][0], s[2][0], s[3][0]
    s[0][1], s[1][1], s[2][1], s[3][1] = s[3][1], s[0][1], s[1][1], s[2][1]
    s[0][2], s[1][2], s[2][2], s[3][2] = s[2][2], s[3][2], s[0][2], s[1][2]
    s[0][3], s[1][3], s[2][3], s[3][3] = s[1][3], s[2][3], s[3][3], s[0][3]

# learned from http://cs.ucsb.edu/~koc/cs178/projects/JT/aes.c
xtime = lambda a: (((a << 1) ^ 0x1B) & 0xFF) if (a & 0x80) else (a << 1)


def mix_single_column(a):
    # see Sec 4.1.2 in The Design of Rijndael
    t = a[0] ^ a[1] ^ a[2] ^ a[3]
    u = a[0]
    a[0] ^= t ^ xtime(a[0] ^ a[1])
    a[1] ^= t ^ xtime(a[1] ^ a[2])
    a[2] ^= t ^ xtime(a[2] ^ a[3])
    a[3] ^= t ^ xtime(a[3] ^ u)


def mix_columns(s):
    for i in range(4):
        mix_single_column(s[i])


def inv_mix_columns(s):
    # see Sec 4.1.3 in The Design of Rijndael
    for i in range(4):
        u = xtime(xtime(s[i][0] ^ s[i][2]))
        v = xtime(xtime(s[i][1] ^ s[i][3]))
        s[i][0] ^= u
        s[i][1] ^= v
        s[i][2] ^= u
        s[i][3] ^= v

    mix_columns(s)


state = [
    [108, 106, 71, 86],
    [96, 62, 38, 72],
    [42, 184, 92, 209],
    [94, 79, 8, 54],
]


inv_mix_columns(state)
inv_shift_rows(state)
stri = ''
for i in state:
    stri += remove_postfix(remove_prefix(str(bytes(i)),"b'"))
print(stri)

 四、列变换

将State乘以一个固定的矩阵A，对State进行逐列进行变换，直到4列都变换完毕。

 

 进行十轮相同的操作后即可得到我们所需的密文；

三、反推导 

既是加密过程的相反方向进行，只是多了少许区别：

1、 逆向字节代替中使用逆S盒。

2、行位移中二三四行依旧移动1、2、3个数，但是是向右位移。

3、逆向列混淆

4、加轮密匙方式不变，依旧是简单的异或运算。

附带一个Bo Zhu's super simple Python AES implementation代码：

from Confusion_through_Substitution import s_box, sub_bytes, inv_s_box
from Diffusion_through_Permutation import inv_shift_rows, inv_mix_columns
from Round_Keys import add_round_key
from Structure_of_AES import bytes2matrix, matrix2bytes

N_ROUNDS = 10

key        = b'\xc3,\\\xa6\xb5\x80^\x0c\xdb\x8d\xa5z*\xb6\xfe\\'
ciphertext = b'\xd1O\x14j\xa4+O\xb6\xa1\xc4\x08B)\x8f\x12\xdd'



def expand_key(master_key):
    """
    Expands and returns a list of key matrices for the given master_key.
    """

    # Round constants https://en.wikipedia.org/wiki/AES_key_schedule#Round_constants
    r_con = (
        0x00, 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40,
        0x80, 0x1B, 0x36, 0x6C, 0xD8, 0xAB, 0x4D, 0x9A,
        0x2F, 0x5E, 0xBC, 0x63, 0xC6, 0x97, 0x35, 0x6A,
        0xD4, 0xB3, 0x7D, 0xFA, 0xEF, 0xC5, 0x91, 0x39,
    )

    # Initialize round keys with raw key material.
    key_columns = bytes2matrix(master_key)
    iteration_size = len(master_key) // 4

    # Each iteration has exactly as many columns as the key material.
    i = 1
    while len(key_columns) < (N_ROUNDS + 1) * 4:
        # Copy previous word.
        word = list(key_columns[-1])

        # Perform schedule_core once every "row".
        if len(key_columns) % iteration_size == 0:
            # Circular shift.
            word.append(word.pop(0))
            # Map to S-BOX.
            word = [s_box[b] for b in word]
            # XOR with first byte of R-CON, since the others bytes of R-CON are 0.
            word[0] ^= r_con[i]
            i += 1
        elif len(master_key) == 32 and len(key_columns) % iteration_size == 4:
            # Run word through S-box in the fourth iteration when using a
            # 256-bit key.
            word = [s_box[b] for b in word]

        # XOR with equivalent word from previous iteration.
        word = bytes(i^j for i, j in zip(word, key_columns[-iteration_size]))
        key_columns.append(word)

    # Group key words in 4x4 byte matrices.
    return [key_columns[4*i : 4*(i+1)] for i in range(len(key_columns) // 4)]


def decrypt(key, ciphertext):
    round_keys = expand_key(key) # Remember to start from the last round key and work backwards through them when decrypting

    # Convert ciphertext to state matrix
    state = bytes2matrix(ciphertext)
    # Initial add round key step
    state = add_round_key(state, round_keys[10])
    for i in range(N_ROUNDS - 1, 0, -1):
        # Do round
        inv_shift_rows(state)
        state = sub_bytes(state, inv_s_box)
        state = add_round_key(state, round_keys[i])
        inv_mix_columns(state)
    # Run final round (skips the InvMixColumns step)
    inv_shift_rows(state)
    state = sub_bytes(state, inv_s_box)
    state = add_round_key(state, round_keys[0])
    # Convert state matrix to plaintext
    plaintext = matrix2bytes(state)
    return plaintext


print(decrypt(key, ciphertext))