15 Jul 2019

AES从入门到放弃

AES从入门到放弃

  • 基本操作

    1

    解密算法的每一步分别对应加密算法的逆操作

    加解密所有操作的顺序是相反的

    算法中16字节的明文、密文和轮子密钥都以一个4x4的矩阵表示

    交 换逆向行移位和逆向字节代替不影响结果

    交换轮密钥加和逆向列混淆不影响结果

  • 轮密钥加

    每轮的输入与轮子密钥异或一次

  • 字节替代

    通过S盒完成一个字节到另外一个字节的映射,提供算法的混淆性

    S和S逆为16x16的矩阵,完成一个8比特输入到8比特输出的映射,输入的高4位对应的值作为行标,低4位对应的值作为列标

    • S盒

      2

    • 逆S盒

      3

    • 字节替换的数学规则

      9

      运算定义在$GF(2^8)$上

  • 行移位

    4x4的矩阵内部字节之间的置换,提供算法的扩散性

    • 正向行移位

      第一行保持不变,第二行循环左移8比特,第三行循环左移16比特,第四行循环左移24比特。

      5

    • 逆向行移位

      第一行保持不变,第二行循环右移8比特,第三行循环右移16比特,第四行循环右移24比特

  • 列混淆

    利用$GF(2^8)$域上算术特性的一个代替,用于提供算法的扩散性

    • 正向列混淆

      6

      1. 将某个字节所对应的值乘以2,其结果就是将该值的二进制位左移一位,如果原始值的最高位为1,则需要将移位后的结果异或0b00011011
      2. 乘法对加法满足分配率
      3. 各个值在相加时使用的是模$2^8$加法
    • 逆向列混淆

      7

      逆向列混淆与正向列混淆左乘矩阵互逆

      8

  • 密钥扩展

    4

    密钥按图(a)排列,k表示种子密钥的一个字节,排列后用4个双字表示,按照图中方式求解

    • g函数

      1. w循环左移8位

      2. 对每个字节做S盒置换

      3. 与32位常量异或

        RC = (
            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,)
               
        
  • AES的python实现

    s = (
    	[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 = (
    	[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])
      
    rc = (
    	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,)
      
    gfp2 = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 252, 254, 27, 25, 31, 29, 19, 17, 23, 21, 11, 9, 15, 13, 3, 1, 7, 5, 59, 57, 63, 61, 51, 49, 55, 53, 43, 41, 47, 45, 35, 33, 39, 37, 91, 89, 95, 93, 83, 81, 87, 85, 75, 73, 79, 77, 67, 65, 71, 69, 123, 121, 127, 125, 115, 113, 119, 117, 107, 105, 111, 109, 99, 97, 103, 101, 155, 153, 159, 157, 147, 145, 151, 149, 139, 137, 143, 141, 131, 129, 135, 133, 187, 185, 191, 189, 179, 177, 183, 181, 171, 169, 175, 173, 163, 161, 167, 165, 219, 217, 223, 221, 211, 209, 215, 213, 203, 201, 207, 205, 195, 193, 199, 197, 251, 249, 255, 253, 243, 241, 247, 245, 235, 233, 239, 237, 227, 225, 231, 229]
      
    gfp3 = [0, 3, 6, 5, 12, 15, 10, 9, 24, 27, 30, 29, 20, 23, 18, 17, 48, 51, 54, 53, 60, 63, 58, 57, 40, 43, 46, 45, 36, 39, 34, 33, 96, 99, 102, 101, 108, 111, 106, 105, 120, 123, 126, 125, 116, 119, 114, 113, 80, 83, 86, 85, 92, 95, 90, 89, 72, 75, 78, 77, 68, 71, 66, 65, 192, 195, 198, 197, 204, 207, 202, 201, 216, 219, 222, 221, 212, 215, 210, 209, 240, 243, 246, 245, 252, 255, 250, 249, 232, 235, 238, 237, 228, 231, 226, 225, 160, 163, 166, 165, 172, 175, 170, 169, 184, 187, 190, 189, 180, 183, 178, 177, 144, 147, 150, 149, 156, 159, 154, 153, 136, 139, 142, 141, 132, 135, 130, 129, 155, 152, 157, 158, 151, 148, 145, 146, 131, 128, 133, 134, 143, 140, 137, 138, 171, 168, 173, 174, 167, 164, 161, 162, 179, 176, 181, 182, 191, 188, 185, 186, 251, 248, 253, 254, 247, 244, 241, 242, 227, 224, 229, 230, 239, 236, 233, 234, 203, 200, 205, 206, 199, 196, 193, 194, 211, 208, 213, 214, 223, 220, 217, 218, 91, 88, 93, 94, 87, 84, 81, 82, 67, 64, 69, 70, 79, 76, 73, 74, 107, 104, 109, 110, 103, 100, 97, 98, 115, 112, 117, 118, 127, 124, 121, 122, 59, 56, 61, 62, 55, 52, 49, 50, 35, 32, 37, 38, 47, 44, 41, 42, 11, 8, 13, 14, 7, 4, 1, 2, 19, 16, 21, 22, 31, 28, 25, 26]
      
    gfp9 = [0, 9, 18, 27, 36, 45, 54, 63, 72, 65, 90, 83, 108, 101, 126, 119, 144, 153, 130, 139, 180, 189, 166, 175, 216, 209, 202, 195, 252, 245, 238, 231, 59, 50, 41, 32, 31, 22, 13, 4, 115, 122, 97, 104, 87, 94, 69, 76, 171, 162, 185, 176, 143, 134, 157, 148, 227, 234, 241, 248, 199, 206, 213, 220, 118, 127, 100, 109, 82, 91, 64, 73, 62, 55, 44, 37, 26, 19, 8, 1, 230, 239, 244, 253, 194, 203, 208, 217, 174, 167, 188, 181, 138, 131, 152, 145, 77, 68, 95, 86, 105, 96, 123, 114, 5, 12, 23, 30, 33, 40, 51, 58, 221, 212, 207, 198, 249, 240, 235, 226, 149, 156, 135, 142, 177, 184, 163, 170, 236, 229, 254, 247, 200, 193, 218, 211, 164, 173, 182, 191, 128, 137, 146, 155, 124, 117, 110, 103, 88, 81, 74, 67, 52, 61, 38, 47, 16, 25, 2, 11, 215, 222, 197, 204, 243, 250, 225, 232, 159, 150, 141, 132, 187, 178, 169, 160, 71, 78, 85, 92, 99, 106, 113, 120, 15, 6, 29, 20, 43, 34, 57, 48, 154, 147, 136, 129, 190, 183, 172, 165, 210, 219, 192, 201, 246, 255, 228, 237, 10, 3, 24, 17, 46, 39, 60, 53, 66, 75, 80, 89, 102, 111, 116, 125, 161, 168, 179, 186, 133, 140, 151, 158, 233, 224, 251, 242, 205, 196, 223, 214, 49, 56, 35, 42, 21, 28, 7, 14, 121, 112, 107, 98, 93, 84, 79, 70]
      
    gfp11 = [0, 11, 22, 29, 44, 39, 58, 49, 88, 83, 78, 69, 116, 127, 98, 105, 176, 187, 166, 173, 156, 151, 138, 129, 232, 227, 254, 245, 196, 207, 210, 217, 123, 112, 109, 102, 87, 92, 65, 74, 35, 40, 53, 62, 15, 4, 25, 18, 203, 192, 221, 214, 231, 236, 241, 250, 147, 152, 133, 142, 191, 180, 169, 162, 246, 253, 224, 235, 218, 209, 204, 199, 174, 165, 184, 179, 130, 137, 148, 159, 70, 77, 80, 91, 106, 97, 124, 119, 30, 21, 8, 3, 50, 57, 36, 47, 141, 134, 155, 144, 161, 170, 183, 188, 213, 222, 195, 200, 249, 242, 239, 228, 61, 54, 43, 32, 17, 26, 7, 12, 101, 110, 115, 120, 73, 66, 95, 84, 247, 252, 225, 234, 219, 208, 205, 198, 175, 164, 185, 178, 131, 136, 149, 158, 71, 76, 81, 90, 107, 96, 125, 118, 31, 20, 9, 2, 51, 56, 37, 46, 140, 135, 154, 145, 160, 171, 182, 189, 212, 223, 194, 201, 248, 243, 238, 229, 60, 55, 42, 33, 16, 27, 6, 13, 100, 111, 114, 121, 72, 67, 94, 85, 1, 10, 23, 28, 45, 38, 59, 48, 89, 82, 79, 68, 117, 126, 99, 104, 177, 186, 167, 172, 157, 150, 139, 128, 233, 226, 255, 244, 197, 206, 211, 216, 122, 113, 108, 103, 86, 93, 64, 75, 34, 41, 52, 63, 14, 5, 24, 19, 202, 193, 220, 215, 230, 237, 240, 251, 146, 153, 132, 143, 190, 181, 168, 163]
      
    gfp13 = [0, 13, 26, 23, 52, 57, 46, 35, 104, 101, 114, 127, 92, 81, 70, 75, 208, 221, 202, 199, 228, 233, 254, 243, 184, 181, 162, 175, 140, 129, 150, 155, 187, 182, 161, 172, 143, 130, 149, 152, 211, 222, 201, 196, 231, 234, 253, 240, 107, 102, 113, 124, 95, 82, 69, 72, 3, 14, 25, 20, 55, 58, 45, 32, 109, 96, 119, 122, 89, 84, 67, 78, 5, 8, 31, 18, 49, 60, 43, 38, 189, 176, 167, 170, 137, 132, 147, 158, 213, 216, 207, 194, 225, 236, 251, 246, 214, 219, 204, 193, 226, 239, 248, 245, 190, 179, 164, 169, 138, 135, 144, 157, 6, 11, 28, 17, 50, 63, 40, 37, 110, 99, 116, 121, 90, 87, 64, 77, 218, 215, 192, 205, 238, 227, 244, 249, 178, 191, 168, 165, 134, 139, 156, 145, 10, 7, 16, 29, 62, 51, 36, 41, 98, 111, 120, 117, 86, 91, 76, 65, 97, 108, 123, 118, 85, 88, 79, 66, 9, 4, 19, 30, 61, 48, 39, 42, 177, 188, 171, 166, 133, 136, 159, 146, 217, 212, 195, 206, 237, 224, 247, 250, 183, 186, 173, 160, 131, 142, 153, 148, 223, 210, 197, 200, 235, 230, 241, 252, 103, 106, 125, 112, 83, 94, 73, 68, 15, 2, 21, 24, 59, 54, 33, 44, 12, 1, 22, 27, 56, 53, 34, 47, 100, 105, 126, 115, 80, 93, 74, 71, 220, 209, 198, 203, 232, 229, 242, 255, 180, 185, 174, 163, 128, 141, 154, 151]
      
    gfp14 = [0, 14, 28, 18, 56, 54, 36, 42, 112, 126, 108, 98, 72, 70, 84, 90, 224, 238, 252, 242, 216, 214, 196, 202, 144, 158, 140, 130, 168, 166, 180, 186, 219, 213, 199, 201, 227, 237, 255, 241, 171, 165, 183, 185, 147, 157, 143, 129, 59, 53, 39, 41, 3, 13, 31, 17, 75, 69, 87, 89, 115, 125, 111, 97, 173, 163, 177, 191, 149, 155, 137, 135, 221, 211, 193, 207, 229, 235, 249, 247, 77, 67, 81, 95, 117, 123, 105, 103, 61, 51, 33, 47, 5, 11, 25, 23, 118, 120, 106, 100, 78, 64, 82, 92, 6, 8, 26, 20, 62, 48, 34, 44, 150, 152, 138, 132, 174, 160, 178, 188, 230, 232, 250, 244, 222, 208, 194, 204, 65, 79, 93, 83, 121, 119, 101, 107, 49, 63, 45, 35, 9, 7, 21, 27, 161, 175, 189, 179, 153, 151, 133, 139, 209, 223, 205, 195, 233, 231, 245, 251, 154, 148, 134, 136, 162, 172, 190, 176, 234, 228, 246, 248, 210, 220, 206, 192, 122, 116, 102, 104, 66, 76, 94, 80, 10, 4, 22, 24, 50, 60, 46, 32, 236, 226, 240, 254, 212, 218, 200, 198, 156, 146, 128, 142, 164, 170, 184, 182, 12, 2, 16, 30, 52, 58, 40, 38, 124, 114, 96, 110, 68, 74, 88, 86, 55, 57, 43, 37, 15, 1, 19, 29, 71, 73, 91, 85, 127, 113, 99, 109, 215, 217, 203, 197, 239, 225, 243, 253, 167, 169, 187, 181, 159, 145, 131, 141]
      
      
    def str2bin(str):
        res = ''
        for i in str:
            t = bin(ord(i))[2:].zfill(8)
            res += t
        return res
      
    def bin2str(bstr):
        res = ''
        for i in range(0, len(bstr), 8):
            t = chr(int(bstr[i:i+8], 2))
            res += t
        return res
      
    def bin2matrix(bstr):
        matrix = []
        for i in range(16):
            byte = int(bstr[i*8:i*8+8], 2)
            if i % 4 == 0:
                matrix.append([byte])
            else:
                matrix[i / 4].append(byte)
        return matrix
      
    def matrix2bin(matrix):
        bstr = ''
        for i in matrix:
            for j in i:
                bstr += bin(j)[2:].zfill(8)
        return bstr
      
    def dword_lshift(dword, n):
        return dword[n:] + dword[0:n]
      
    def dword_rshift(dword, n):
        return dword[-n:] + dword[0:-n]
      
    def s_change_byte(byte, box):
        col = (byte << 4 & 0b11110000) >> 4
        row = byte >> 4
        res = box[row][col]
        return res
      
      
    def s_change(matrix, box):
        res = []
        for i in range(len(matrix)):
            res.append([])
            for j in range(len(matrix)):
                byte = matrix[i][j]
                res[i].append(s_change_byte(byte, box))
        return res
      
    def dword2int(dword):
        str = ''
        for i in dword:
            str += hex(i)[2:].zfill(2)
        res = int(str, 16)
        return res
      
    def int2dword(val):
        res = []
        str = hex(val)[2:].zfill(8).decode('hex')
        for i in str:
            res.append(ord(i))
        return res
      
    def dword_xor(dword1, dword2):
        val1 = dword2int(dword1)
        val2 = dword2int(dword2)
        res = val1 ^ val2
        res = int2dword(res)
        return res
      
    def g_func(dword, round):
        res_dword = []
        rc_dword = [rc[round], 0, 0, 0]
        dword = dword_lshift(dword, 1)
        for i in range(4):
            res_dword.append(s_change_byte(dword[i], s))
        res_dword = dword_xor(res_dword, rc_dword)
        return res_dword
      
    def expand_key(dwords, round):
        g_res = g_func(dwords[3], round)
        dword_4 = dword_xor(dwords[0], g_res)
        dword_5 = dword_xor(dwords[1], dword_4)
        dword_6 = dword_xor(dwords[2], dword_5)
        dword_7 = dword_xor(dwords[3], dword_6)
        res = [dword_4, dword_5, dword_6, dword_7]
        return res
      
    def gen_key(matrix_key):
        round_keys = [matrix_key]
        for i in range(10):
            round_keys.append(expand_key(round_keys[i], i+1))
        return round_keys
      
      
    def add_round_keys(matrix_plain, round_key):
        res = []
        for i in range(4):
            res.append(dword_xor(matrix_plain[i], round_key[i]))
        return res
      
    def rows_shift(matrix):
        l = len(matrix)
        res = [[],[],[],[]]
        for i in range(l):
            for j in range(l):
                res[i].append(matrix[(i+j) % l][j])
        return res
      
    def inv_rows_shift(matrix):
        l = len(matrix)
        res = [[],[],[],[]]
        for i in range(l):
            for j in range(l):
                res[i].append(matrix[(i-j) % l][j])
        return res
      
    def cols_mix(matrix):
        res = [[],[],[],[]]
        for i in range(len(matrix)):
            res[i].append((gfp2[matrix[i][0]] ^ gfp3[matrix[i][1]] ^ matrix[i][2] ^ matrix[i][3]))
            res[i].append((matrix[i][0] ^ gfp2[matrix[i][1]] ^ gfp3[matrix[i][2]] ^ matrix[i][3]))
            res[i].append((matrix[i][0] ^ matrix[i][1] ^ gfp2[matrix[i][2]] ^ gfp3[matrix[i][3]]))
            res[i].append((gfp3[matrix[i][0]] ^ matrix[i][1] ^ matrix[i][2] ^ gfp2[matrix[i][3]]))
        return res
      
    def inv_cols_mix(matrix):
        res = [[],[],[],[]]
        for i in range(len(matrix)):
            res[i].append((gfp14[matrix[i][0]] ^ gfp11[matrix[i][1]] ^ gfp13[matrix[i][2]] ^ gfp9[matrix[i][3]]))
            res[i].append((gfp9[matrix[i][0]] ^ gfp14[matrix[i][1]] ^ gfp11[matrix[i][2]] ^ gfp13[matrix[i][3]]))
            res[i].append((gfp13[matrix[i][0]] ^ gfp9[matrix[i][1]] ^ gfp14[matrix[i][2]] ^ gfp11[matrix[i][3]]))
            res[i].append((gfp11[matrix[i][0]] ^ gfp13[matrix[i][1]] ^ gfp9[matrix[i][2]] ^ gfp14[matrix[i][3]]))
        return res
      
    def aes_enc(matrix_plain, round_keys):
        res = add_round_keys(matrix_plain, round_keys[0])
        for i in range(1, len(round_keys)-1):
            res = s_change(res, s)
            res = rows_shift(res)
            res = cols_mix(res)
            res = add_round_keys(res, round_keys[i])
        res = s_change(res, s)
        res = rows_shift(res)
        res = add_round_keys(res, round_keys[-1])
        return res
      
    def aes_dec(matrix_cipher, round_keys):
        res = add_round_keys(matrix_cipher, round_keys[-1])
        for i in range(2, len(round_keys)):
            res = inv_rows_shift(res)
            res = s_change(res, inv_s)
            res = add_round_keys(res, round_keys[-i])
            res = inv_cols_mix(res)
        res = inv_rows_shift(res)
        res = s_change(res, inv_s)
        res = add_round_keys(res, round_keys[0])
        return res
      
      
    def divide_enc(plaintext, key):
        bplain = str2bin(plaintext)
        bkey = str2bin(key)
        matrix_key = bin2matrix(bkey)
        round_keys = gen_key(matrix_key)
        bcipher = ''
        for i in range(0, len(bplain), 128):
            matrix_plain = bin2matrix(bplain[i:i+128])
            bcipher += matrix2bin(aes_enc(matrix_plain, round_keys))
        return bcipher
      
    def divide_dec(ciphertext, key):
        bcipher = str2bin(ciphertext)
        bkey = str2bin(key)
        matrix_key = bin2matrix(bkey)
        round_keys = gen_key(matrix_key)
        bplain = ''
        for i in range(0, len(bcipher), 128):
            matrix_cipher = bin2matrix(bcipher[i:i+128])
            bplain += matrix2bin(aes_dec(matrix_cipher, round_keys))
        return bplain
      
    def encrypt(plaintext, key):
        ciphertext = bin2str(divide_enc(plaintext, key)).encode('hex')
        return ciphertext
      
    def decrypt(ciphertext, key):
        plaintext = divide_dec(ciphertext.decode('hex'), key)
        return bin2str(plaintext)
      
    if __name__ == '__main__':
        a = encrypt('aaaaaaaaaaaaaaaa', '0000000000000000')
        print(a)
        b = decrypt(a,'0000000000000000')
        print(b)
      
    

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