作者：FloatingGuy 转载请注明出处：https://floatingguy.github.io/

密码学

密码算法的本质： 替换 和 置换

攻击加密算法的方法

  • 差分攻击 Differential attack
  • 线性攻击 Linear attack

认识AES 算法

AES 加密算法 – Rijndael

Rijndael 的特性:

  • rijndael 加密不采用 算术运算。
  • 数据块长度 128bit, 192bit, 256bit
  • 密钥长度 128bit, 192bit, 256bit
  • 数据块和密钥长度相互独立
  • 运算的轮数可变
  • 因为不采用算数运算，所有处理器硬件的差异对其影响较小
  • 轮变换可以并行处理
  • 不使用替换盒
  • 子密钥生成速度快
  • 潜在的平行运算

应用到AES 时对数据块长度做出规定，必须是128bit.

AES加密过程是在一个4×4的字节矩阵上运作，这个矩阵又称为“体（state）”，其初值就是一个明文区块（矩阵中一个元素大小就是明文区块中的一个Byte）。（Rijndael加密法因支持更大的区块，其矩阵行数可视情况增加）加密时，各轮AES加密循环（除最后一轮外）均包含4个步骤：

  1. MixColumns—为了充分混合矩阵中各个直行的操作。这个步骤使用线性转换来混合每内联的四个字节。
  2. SubBytes—通过一个非线性的替换函数，用查找表的方式把每个字节替换成对应的字节。
  3. ShiftRows—将矩阵中的每个横列进行循环式移位。
  4. AddRoundKey—矩阵中的每一个字节都与该次回合密钥（round key）做XOR运算；每个子密钥由密钥生成方案产生。
    在第一轮前，whitening AK 操作被执行；最后一个加密循环中省略MixColumns步骤，而以另一个AddRoundKey取代。

每一个步骤具体的操作原理，请参考维基百科

实现AES 算法

这类代码网上很多了, 我随便搜到了这篇 密码算法详解——AES。 文章还没有细看只看了评论，方便后期学习 我这里贴下部分代码，完整代码

debug

如果实现完测试发现 解密结果不正确， 那么就要分别排除是 加密环节 还是解密环节出现了问题，我的方法是使用在线加解密网站对比我们代码得到的结果。

确定了bug的范围，剩下的工作就是参考算法原理重新撸流程了。

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/*
 *
 * Chinese Academy of Sciences
 * State Key Laboratory of Information Security
 * Institute of Information Engineering
 *
 * Copyright (C) 2016 Chinese Academy of Sciences
 *
 * LuoPeng, luopeng@iie.ac.cn
 * Updated in Oct 2016
 * Updated in Jan 2017, update muliple function on GF(2^8).
 *
 */
#include <stdint.h>
#include <stdio.h>
#include "aes.h"
/*
 * round constants
 */
static uint8_t RC[] = {0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1b, 0x36};
/*
 * Sbox
 */
static uint8_t SBOX[256] = {
    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};
/*
 * Inverse Sboxs
 */
static uint8_t INV_SBOX[256] = {
    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};
/**
 * https://en.wikipedia.org/wiki/Finite_field_arithmetic
 * Multiply two numbers in the GF(2^8) finite field defined
 * by the polynomial x^8 + x^4 + x^3 + x + 1 = 0
 * We do use mul2(int8_t a) but not mul(uint8_t a, uint8_t b)
 * just in order to get a higher speed.
 */
static inline uint8_t mul2(uint8_t a) {
    return (a&0x80) ? ((a<<1)^0x1b) : (a<<1);
}
/**
 * @purpose:    ShiftRows
 * @descrption:
 *  Row0: s0  s4  s8  s12   <<< 0 byte
 *  Row1: s1  s5  s9  s13   <<< 1 byte
 *  Row2: s2  s6  s10 s14   <<< 2 bytes
 *  Row3: s3  s7  s11 s15   <<< 3 bytes
 */
static void shift_rows(uint8_t *state) {
    uint8_t temp;
    // row1
    temp        = *(state+1);
    *(state+1)  = *(state+5);
    *(state+5)  = *(state+9);
    *(state+9)  = *(state+13);
    *(state+13) = temp;
    // row2
    temp        = *(state+2);
    *(state+2)  = *(state+10);
    *(state+10) = temp;
    temp        = *(state+6);
    *(state+6)  = *(state+14);
    *(state+14) = temp;
    // row3
    temp        = *(state+15);
    *(state+15) = *(state+11);
    *(state+11) = *(state+7);
    *(state+7)  = *(state+3);
    *(state+3)  = temp;
}
/**
 * @purpose:    Inverse ShiftRows
 * @description
 *  Row0: s0  s4  s8  s12   >>> 0 byte
 *  Row1: s1  s5  s9  s13   >>> 1 byte
 *  Row2: s2  s6  s10 s14   >>> 2 bytes
 *  Row3: s3  s7  s11 s15   >>> 3 bytes
 */
static void inv_shift_rows(uint8_t *state) {
    uint8_t temp;
    // row1
    temp        = *(state+13);
    *(state+13) = *(state+9);
    *(state+9)  = *(state+5);
    *(state+5)  = *(state+1);
    *(state+1)  = temp;
    // row2
    temp        = *(state+14);
    *(state+14) = *(state+6);
    *(state+6)  = temp;
    temp        = *(state+10);
    *(state+10) = *(state+2);
    *(state+2)  = temp;
    // row1
    temp        = *(state+3);
    *(state+3)  = *(state+7);
    *(state+7)  = *(state+11);
    *(state+11) = *(state+15);
    *(state+15) = temp;
}
void aes_key_schedule_128(const uint8_t *key, uint8_t *roundkeys) {
    uint8_t temp[4];
    uint8_t *last4bytes; // point to the last 4 bytes of one round
    uint8_t *lastround;
    uint8_t i;
    for (i = 0; i < 16; ++i) {
        *roundkeys++ = *key++;
    }
    last4bytes = roundkeys-4;
    for (i = 0; i < AES_ROUNDS; ++i) {
        // k0-k3 for next round
        temp[3] = SBOX[*last4bytes++];
        temp[0] = SBOX[*last4bytes++];
        temp[1] = SBOX[*last4bytes++];
        temp[2] = SBOX[*last4bytes++];
        temp[0] ^= RC[i];
        lastround = roundkeys-16;
        *roundkeys++ = temp[0] ^ *lastround++;
        *roundkeys++ = temp[1] ^ *lastround++;
        *roundkeys++ = temp[2] ^ *lastround++;
        *roundkeys++ = temp[3] ^ *lastround++;
        // k4-k7 for next round
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        // k8-k11 for next round
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        // k12-k15 for next round
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
        *roundkeys++ = *last4bytes++ ^ *lastround++;
    }
}
void aes_encrypt_128(const uint8_t *roundkeys, const uint8_t *plaintext, uint8_t *ciphertext) {
    uint8_t tmp[16], t;
    uint8_t i, j;
    // first AddRoundKey
    for ( i = 0; i < AES_BLOCK_SIZE; ++i ) {
        *(ciphertext+i) = *(plaintext+i) ^ *roundkeys++;
    }
    // 9 rounds
    for (j = 1; j < AES_ROUNDS; ++j) {
        // SubBytes
        for (i = 0; i < AES_BLOCK_SIZE; ++i) {
            *(tmp+i) = SBOX[*(ciphertext+i)];
        }
        shift_rows(tmp);
        /*
         * MixColumns
         * [02 03 01 01]   [s0  s4  s8  s12]
         * [01 02 03 01] . [s1  s5  s9  s13]
         * [01 01 02 03]   [s2  s6  s10 s14]
         * [03 01 01 02]   [s3  s7  s11 s15]
         */
        for (i = 0; i < AES_BLOCK_SIZE; i+=4)  {
            t = tmp[i] ^ tmp[i+1] ^ tmp[i+2] ^ tmp[i+3];
            ciphertext[i]   = mul2(tmp[i]   ^ tmp[i+1]) ^ tmp[i]   ^ t;
            ciphertext[i+1] = mul2(tmp[i+1] ^ tmp[i+2]) ^ tmp[i+1] ^ t;
            ciphertext[i+2] = mul2(tmp[i+2] ^ tmp[i+3]) ^ tmp[i+2] ^ t;
            ciphertext[i+3] = mul2(tmp[i+3] ^ tmp[i]  ) ^ tmp[i+3] ^ t;
        }
        // AddRoundKey
        for ( i = 0; i < AES_BLOCK_SIZE; ++i ) {
            *(ciphertext+i) ^= *roundkeys++;
        }
    }
    // last round
    for (i = 0; i < AES_BLOCK_SIZE; ++i) {
        *(ciphertext+i) = SBOX[*(ciphertext+i)];
    }
    shift_rows(ciphertext);
    for ( i = 0; i < AES_BLOCK_SIZE; ++i ) {
        *(ciphertext+i) ^= *roundkeys++;
    }
}
void aes_decrypt_128(const uint8_t *roundkeys, const uint8_t *ciphertext, uint8_t *plaintext) {
    uint8_t tmp[16];
    uint8_t t, u, v;
    uint8_t i, j;
    roundkeys += 160;
    // first round
    for ( i = 0; i < AES_BLOCK_SIZE; ++i ) {
        *(plaintext+i) = *(plaintext+i) ^ *(roundkeys+i);
    }
    roundkeys -= 16;
    inv_shift_rows(plaintext);
    for (i = 0; i < AES_BLOCK_SIZE; ++i) {
        *(plaintext+i) = INV_SBOX[*(plaintext+i)];
    }
    for (j = 1; j < AES_ROUNDS; ++j) {
        // Inverse AddRoundKey
        for ( i = 0; i < AES_BLOCK_SIZE; ++i ) {
            *(tmp+i) = *(plaintext+i) ^ *(roundkeys+i);
        }
        /*
         * Inverse MixColumns
         * [0e 0b 0d 09]   [s0  s4  s8  s12]
         * [09 0e 0b 0d] . [s1  s5  s9  s13]
         * [0d 09 0e 0b]   [s2  s6  s10 s14]
         * [0b 0d 09 0e]   [s3  s7  s11 s15]
         */
        for (i = 0; i < AES_BLOCK_SIZE; i+=4) {
            t = tmp[i] ^ tmp[i+1] ^ tmp[i+2] ^ tmp[i+3];
            plaintext[i]   = t ^ tmp[i]   ^ mul2(tmp[i]   ^ tmp[i+1]);
            plaintext[i+1] = t ^ tmp[i+1] ^ mul2(tmp[i+1] ^ tmp[i+2]);
            plaintext[i+2] = t ^ tmp[i+2] ^ mul2(tmp[i+2] ^ tmp[i+3]);
            plaintext[i+3] = t ^ tmp[i+3] ^ mul2(tmp[i+3] ^ tmp[i]);
            u = mul2(mul2(tmp[i]   ^ tmp[i+2]));
            v = mul2(mul2(tmp[i+1] ^ tmp[i+3]));
            t = mul2(u ^ v);
            plaintext[i]   ^= t ^ u;
            plaintext[i+1] ^= t ^ v;
            plaintext[i+2] ^= t ^ u;
            plaintext[i+3] ^= t ^ v;
        }
        // Inverse ShiftRows
        inv_shift_rows(plaintext);
        // Inverse SubBytes
        for (i = 0; i < AES_BLOCK_SIZE; ++i) {
            *(plaintext+i) = INV_SBOX[*(plaintext+i)];
        }
        roundkeys -= 16;
    }
    // last AddRoundKey
    for ( i = 0; i < AES_BLOCK_SIZE; ++i ) {
        *(plaintext+i) ^= *(roundkeys+i);
    }
}

最后再来2张当年的PPT

Todo

  • 测试代码，撸流程