AES加密的S盒和逆S盒的推导代码备份(C实现)

摘取自https://www.cnblogs.com/Junbo20141201/p/9369860.html，感谢原作者的详细解读。

#include <stdio.h>

static const int S[16][16] = {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
 */
static const int S2[16][16] = {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};

//S盒字节变换
uint8_t byteTransformation(uint8_t a, uint8_t x) {
    uint8_t tmp[8] = {0};

    for (uint8_t i = 0; i < 8; i++) {
        tmp[i] = (((a >> i) & 0x1) ^ ((a >> ((i + 4) % 8)) & 0x1) ^ ((a >> ((i + 5) % 8)) & 0x1) ^
                  ((a >> ((i + 6) % 8)) & 0x1) ^ ((a >> ((i + 7) % 8)) & 0x1) ^ ((x >> i) & 0x1)) << i;
    }
    tmp[0] = tmp[0] + tmp[1] + tmp[2] + tmp[3] + tmp[4] + tmp[5] + tmp[6] + tmp[7];
    return tmp[0];
}

//逆S盒字节变换
uint8_t invByteTransformation(uint8_t a, uint8_t x) {
    uint8_t tmp[8] = {0};

    for (uint8_t i = 0; i < 8; i++) {
        tmp[i] = (((a >> ((i + 2) % 8)) & 0x1) ^ ((a >> ((i + 5) % 8)) & 0x1) ^ ((a >> ((i + 7) % 8)) & 0x1) ^
                  ((x >> i) & 0x1)) << i;
    }
    tmp[0] = tmp[0] + tmp[1] + tmp[2] + tmp[3] + tmp[4] + tmp[5] + tmp[6] + tmp[7];
    return tmp[0];
}

//找到最高位
uint8_t findHigherBit(uint16_t val) {
    int i = 0;
    while (val) {
        i++;
        val = val >> 1;
    }
    return i;
}

//GF(2^8)的多项式除法
uint8_t gf28_div(uint16_t div_ed, uint16_t div, uint16_t *remainder) {
    uint16_t r0 = 0;
    uint8_t qn = 0;
    int bitCnt = 0;

    r0 = div_ed;

    bitCnt = findHigherBit(r0) - findHigherBit(div);
    while (bitCnt >= 0) {
        qn = qn | (1 << bitCnt);
        r0 = r0 ^ (div << bitCnt);
        bitCnt = findHigherBit(r0) - findHigherBit(div);
    }
    *remainder = r0;
    return qn;
}

//GF(2^8)的多项式乘法
uint16_t polynomialMutil(uint8_t a, uint8_t b) {
    uint16_t tmp[8] = {0};
    uint8_t i;
    for (i = 0; i < 8; i++) {
        tmp[i] = (a << i) * ((b >> i) & 0x1);
    }

    tmp[0] = tmp[0] ^ tmp[1] ^ tmp[2] ^ tmp[3] ^ tmp[4] ^ tmp[5] ^ tmp[6] ^ tmp[7];

    return tmp[0];
}

//GF(2^8)多项式的扩展欧几里得算法
uint8_t extEuclidPolynomial(uint8_t a, uint16_t m) {
    uint16_t r0, r1, r2;
    uint8_t qn, v0, v1, v2, w0, w1, w2;

    r0 = m;
    r1 = a;

    v0 = 1;
    v1 = 0;

    w0 = 0;
    w1 = 1;

    while (r1 != 1) {
        qn = gf28_div(r0, r1, &r2);

        v2 = v0 ^ polynomialMutil(qn, v1);
        w2 = w0 ^ polynomialMutil(qn, w1);

        r0 = r1;
        r1 = r2;

        v0 = v1;
        v1 = v2;

        w0 = w1;
        w1 = w2;
    }
    return w1;
}

//S盒产生
void s_box_gen(void) {
    uint8_t i, j;
    uint8_t s_box_ary[16][16] = {0};

//初始化S盒
    for (i = 0; i < 0x10; i++) {
        for (j = 0; j < 0x10; j++) {
            s_box_ary[i][j] = ((i << 4) & 0xF0) + (j & (0xF));
        }
    }

    printf("    0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F");
    for (i = 0; i < 0x10; i++) {
        printf("
%2x", i);
        for (j = 0; j < 0x10; j++) {
            printf(" %2x", s_box_ary[i][j]);
        }
    }
//求在GF(2^8)域上的逆，0映射到自身
    printf("
");
    for (i = 0; i < 0x10; i++) {
        for (j = 0; j < 0x10; j++) {
            if (s_box_ary[i][j] != 0) {
                s_box_ary[i][j] = extEuclidPolynomial(s_box_ary[i][j], 0x11B);
            }
        }
    }

    printf("

    0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F");
    for (i = 0; i < 0x10; i++) {
        printf("
%2x", i);
        for (j = 0; j < 0x10; j++) {
            printf(" %2x", s_box_ary[i][j]);
        }
    }
//对每个字节做变换
    for (i = 0; i < 0x10; i++) {
        for (j = 0; j < 0x10; j++) {
            s_box_ary[i][j] = byteTransformation(s_box_ary[i][j], 0x63);
        }
    }

    printf("

    0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F");
    for (i = 0; i < 0x10; i++) {
        printf("
%2x", i);
        for (j = 0; j < 0x10; j++) {
            printf(" %2x", s_box_ary[i][j]);
        }
    }
}

//逆S盒产生
void inv_s_box_gen(void) {
    uint8_t i, j;
    uint8_t s_box_ary[16][16] = {0};
    uint8_t b = 0, bb = 0;

//初始化S盒
    for (i = 0; i < 0x10; i++) {
        for (j = 0; j < 0x10; j++) {
            s_box_ary[i][j] = ((i << 4) & 0xF0) + (j & (0xF));
        }
    }

    printf("    0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F");
    for (i = 0; i < 0x10; i++) {
        printf("
%2x", i);
        for (j = 0; j < 0x10; j++) {
            printf(" %2x", s_box_ary[i][j]);
        }
    }
//对每个字节做变换
    for (i = 0; i < 0x10; i++) {
        for (j = 0; j < 0x10; j++) {
            s_box_ary[i][j] = invByteTransformation(s_box_ary[i][j], 0x05);
        }
    }

    printf("

    0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F");
    for (i = 0; i < 0x10; i++) {
        printf("
%2x", i);
        for (j = 0; j < 0x10; j++) {
            printf(" %2x", s_box_ary[i][j]);
        }
    }

//求在GF(2^8)域上的逆，0映射到自身
    printf("
");
    for (i = 0; i < 0x10; i++) {
        for (j = 0; j < 0x10; j++) {
            if (s_box_ary[i][j] != 0) {
                s_box_ary[i][j] = extEuclidPolynomial(s_box_ary[i][j], 0x11B);
            }
        }
    }

    printf("

    0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F");
    for (i = 0; i < 0x10; i++) {
        printf("
%2x", i);
        for (j = 0; j < 0x10; j++) {
            printf(" %2x", s_box_ary[i][j]);
        }
    }
}

int main(int argc, char const *argv[]) {
//    s_box_gen();
    inv_s_box_gen();
    return 0;
}