从零实现一个加密库：AES与RSA

前言

你有没有想过：你输入的密码、发送的消息、存储的文件------是怎么变成一堆乱码，让黑客看不懂的？

加密是信息安全的基石。今天我们从零实现两种经典加密算法：

· AES（对称加密）：同一个密钥加密和解密，速度快

· RSA（非对称加密）：公钥加密、私钥解密，安全分发密钥

一、AES加密原理

AES核心操作

AES是分组加密算法，每次处理16字节（128位）：

```

┌─────────────────────────────────────────────────────────────┐

│ AES加密流程 │

│ 明文(16B) → AddRoundKey → SubBytes → ShiftRows → MixCols │

│ ↓ │

│ 重复9/11/13轮（取决于密钥长度） │

│ ↓ │

│ 密文(16B) │

└─────────────────────────────────────────────────────────────┘

```

操作说明

SubBytes 字节替换（S盒查表）

ShiftRows 行移位

MixColumns 列混合（GF(2⁸)乘法）

AddRoundKey 与轮密钥异或

二、完整代码实现

AES核心操作

```c

#include <stdio.h>

#include <stdlib.h>

#include <string.h>

#include <stdint.h>

#include <time.h>

#include <math.h>

// AES S盒

static const 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

};

// 逆S盒

static const 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

};

// 轮常数

static const uint8_t rcon $10$ = {0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1b, 0x36};

// SubBytes

void sub_bytes(uint8_t *state) {

for (int i = 0; i < 16; i++) {

state $i$ = sbox $state\[i$ ];

}

void inv_sub_bytes(uint8_t *state) {

for (int i = 0; i < 16; i++) {

state $i$ = inv_sbox $state\[i$ ];

}

// ShiftRows

void shift_rows(uint8_t *state) {

uint8_t tmp $16$ ;

for (int i = 0; i < 4; i++) {

for (int j = 0; j < 4; j++) {

tmp $i \* 4 + j$ = state $i \* 4 + ((j + i) % 4)$ ;

}

memcpy(state, tmp, 16);

}

void inv_shift_rows(uint8_t *state) {

uint8_t tmp $16$ ;

for (int i = 0; i < 4; i++) {

for (int j = 0; j < 4; j++) {

tmp $i \* 4 + j$ = state $i \* 4 + ((j - i + 4) % 4)$ ;

}

memcpy(state, tmp, 16);

}

// GF(2^8)乘法

uint8_t gf_mul(uint8_t a, uint8_t b) {

uint8_t result = 0;

for (int i = 0; i < 8; i++) {

if (b & 1) result ^= a;

b >>= 1;

a <<= 1;

if (a & 0x100) a ^= 0x1b;

}

return result;

}

// MixColumns

void mix_columns(uint8_t *state) {

uint8_t tmp $16$ ;

for (int i = 0; i < 4; i++) {

int idx = i * 4;

tmp $idx$ = gf_mul(state $idx$ , 2) ^ gf_mul(state $idx+1$ , 3) ^ state $idx+2$ ^ state $idx+3$ ;

tmp $idx+1$ = state $idx$ ^ gf_mul(state $idx+1$ , 2) ^ gf_mul(state $idx+2$ , 3) ^ state $idx+3$ ;

tmp $idx+2$ = state $idx$ ^ state $idx+1$ ^ gf_mul(state $idx+2$ , 2) ^ gf_mul(state $idx+3$ , 3);

tmp $idx+3$ = gf_mul(state $idx$ , 3) ^ state $idx+1$ ^ state $idx+2$ ^ gf_mul(state $idx+3$ , 2);

}

memcpy(state, tmp, 16);

}

void inv_mix_columns(uint8_t *state) {

uint8_t tmp $16$ ;

for (int i = 0; i < 4; i++) {

int idx = i * 4;

tmp $idx$ = gf_mul(state $idx$ , 0x0e) ^ gf_mul(state $idx+1$ , 0x0b) ^ gf_mul(state $idx+2$ , 0x0d) ^ gf_mul(state $idx+3$ , 0x09);

tmp $idx+1$ = gf_mul(state $idx$ , 0x09) ^ gf_mul(state $idx+1$ , 0x0e) ^ gf_mul(state $idx+2$ , 0x0b) ^ gf_mul(state $idx+3$ , 0x0d);

tmp $idx+2$ = gf_mul(state $idx$ , 0x0d) ^ gf_mul(state $idx+1$ , 0x09) ^ gf_mul(state $idx+2$ , 0x0e) ^ gf_mul(state $idx+3$ , 0x0b);

tmp $idx+3$ = gf_mul(state $idx$ , 0x0b) ^ gf_mul(state $idx+1$ , 0x0d) ^ gf_mul(state $idx+2$ , 0x09) ^ gf_mul(state $idx+3$ , 0x0e);

}

memcpy(state, tmp, 16);

}

// AddRoundKey

void add_round_key(uint8_t *state, uint8_t *key) {

for (int i = 0; i < 16; i++) {

state $i$ ^= key $i$ ;

}

```

AES密钥扩展

```c

// 密钥扩展

void key_expansion(uint8_t *key, uint8_t *round_keys, int rounds) {

int key_len = 16; // AES-128

int total_words = (rounds + 1) * 4;

uint32_t *w = (uint32_t*)round_keys;

// 前4个字是原始密钥

for (int i = 0; i < 4; i++) {

w $i$ = (key $i\*4$ << 24) | (key $i\*4+1$ << 16) |

(key $i\*4+2$ << 8) | key $i\*4+3$ ;

}

for (int i = 4; i < total_words; i++) {

uint32_t temp = w $i-1$ ;

if (i % 4 == 0) {

// RotWord + SubWord + Rcon

temp = (temp << 8) | (temp >> 24);

temp = (sbox $temp \>\> 24$ << 24) | (sbox $(temp \>\> 16) \& 0xff$ << 16) |

(sbox $(temp \>\> 8) \& 0xff$ << 8) | sbox $temp \& 0xff$ ;

temp ^= (rcon $i/4 - 1$ << 24);

}

w $i$ = w $i-4$ ^ temp;

}

```

AES加密/解密

```c

// AES加密（AES-128）

void aes_encrypt(uint8_t *input, uint8_t *output, uint8_t *key) {

uint8_t state $16$ ;

memcpy(state, input, 16);

int rounds = 10;

uint8_t round_keys $176$ ;

key_expansion(key, round_keys, rounds);

// 初始轮

add_round_key(state, round_keys);

// 9轮

for (int r = 1; r < rounds; r++) {

sub_bytes(state);

shift_rows(state);

mix_columns(state);

add_round_key(state, round_keys + r * 16);

}

// 最后一轮

sub_bytes(state);

shift_rows(state);

add_round_key(state, round_keys + rounds * 16);

memcpy(output, state, 16);

}

void aes_decrypt(uint8_t *input, uint8_t *output, uint8_t *key) {

uint8_t state $16$ ;

memcpy(state, input, 16);

int rounds = 10;

uint8_t round_keys $176$ ;

key_expansion(key, round_keys, rounds);

// 初始轮（逆）

add_round_key(state, round_keys + rounds * 16);

// 9轮（逆）

for (int r = rounds - 1; r > 0; r--) {

inv_shift_rows(state);

inv_sub_bytes(state);

add_round_key(state, round_keys + r * 16);

inv_mix_columns(state);

}

// 最后一轮（逆）

inv_shift_rows(state);

inv_sub_bytes(state);

add_round_key(state, round_keys);

memcpy(output, state, 16);

}

```

RSA加密

```c

// 大整数运算（简化版，仅演示原理）

typedef struct big_int {

uint32_t parts $32$ ;

int size;

} big_int_t;

// 快速幂模运算

uint64_t mod_pow(uint64_t base, uint64_t exp, uint64_t mod) {

uint64_t result = 1;

base %= mod;

while (exp > 0) {

if (exp & 1) result = (result * base) % mod;

base = (base * base) % mod;

exp >>= 1;

}

return result;

}

// 判断素数（简单试除）

int is_prime(uint64_t n) {

if (n < 2) return 0;

if (n == 2) return 1;

if (n % 2 == 0) return 0;

for (uint64_t i = 3; i * i <= n; i += 2) {

if (n % i == 0) return 0;

}

return 1;

}

// 生成随机素数

uint64_t random_prime(int bits) {

uint64_t start = 1ULL << (bits - 1);

uint64_t end = (1ULL << bits) - 1;

uint64_t n;

do {

n = start + rand() % (end - start);

if (n % 2 == 0) n++;

} while (!is_prime(n));

return n;

}

// 扩展欧几里得

uint64_t mod_inverse(uint64_t a, uint64_t m) {

uint64_t m0 = m, a0 = a;

uint64_t y = 0, x = 1;

if (m == 1) return 0;

while (a > 1) {

uint64_t q = a / m;

uint64_t t = m;

m = a % m;

a = t;

t = y;

y = x - q * y;

x = t;

}

if (x < 0) x += m0;

return x;

}

// RSA密钥对

typedef struct rsa_key {

uint64_t n; // 模数

uint64_t e; // 公钥指数

uint64_t d; // 私钥指数

} rsa_key_t;

// 生成RSA密钥对

rsa_key_t rsa_generate_keys(int bits) {

uint64_t p = random_prime(bits);

uint64_t q = random_prime(bits);

uint64_t n = p * q;

uint64_t phi = (p - 1) * (q - 1);

uint64_t e = 65537;

uint64_t d = mod_inverse(e, phi);

rsa_key_t keys;

keys.n = n;

keys.e = e;

keys.d = d;

return keys;

}

// RSA加密（公钥）

uint64_t rsa_encrypt(uint64_t msg, uint64_t e, uint64_t n) {

if (msg >= n) {

fprintf(stderr, "消息过大，需要分段加密\n");

return 0;

}

return mod_pow(msg, e, n);

}

// RSA解密（私钥）

uint64_t rsa_decrypt(uint64_t cipher, uint64_t d, uint64_t n) {

return mod_pow(cipher, d, n);

}

```

测试代码

```c

void test_aes() {

printf("=== AES加密测试 ===\n\n");

uint8_t key $16$ = {0x2b, 0x7e, 0x15, 0x16, 0x28, 0xae, 0xd2, 0xa6,

0xab, 0xf7, 0x15, 0x88, 0x09, 0xcf, 0x4f, 0x3c};

uint8_t plaintext $16$ = {0x32, 0x43, 0xf6, 0xa8, 0x88, 0x5a, 0x30, 0x8d,

0x31, 0x31, 0x98, 0xa2, 0xe0, 0x37, 0x07, 0x34};

printf("明文: ");

for (int i = 0; i < 16; i++) printf("%02x ", plaintext $i$ );

printf("\n");

uint8_t ciphertext $16$ ;

aes_encrypt(plaintext, ciphertext, key);

printf("密文: ");

for (int i = 0; i < 16; i++) printf("%02x ", ciphertext $i$ );

printf("\n");

uint8_t decrypted $16$ ;

aes_decrypt(ciphertext, decrypted, key);

printf("解密: ");

for (int i = 0; i < 16; i++) printf("%02x ", decrypted $i$ );

printf("\n");

printf("原始==解密: %s\n",

memcmp(plaintext, decrypted, 16) == 0 ? "✅ 成功" : "❌ 失败");

}

void test_rsa() {

printf("\n=== RSA加密测试 ===\n\n");

rsa_key_t keys = rsa_generate_keys(8);

printf("公钥: (n=%llu, e=%llu)\n", keys.n, keys.e);

printf("私钥: (n=%llu, d=%llu)\n", keys.n, keys.d);

uint64_t msg = 42;

printf("\n原文: %llu\n", msg);

uint64_t cipher = rsa_encrypt(msg, keys.e, keys.n);

printf("加密: %llu\n", cipher);

uint64_t decrypted = rsa_decrypt(cipher, keys.d, keys.n);

printf("解密: %llu\n", decrypted);

printf("原始==解密: %s\n", msg == decrypted ? "✅ 成功" : "❌ 失败");

}

int main() {

srand(time(NULL));

test_aes();

test_rsa();

return 0;

}

```

三、编译和运行

```bash

gcc -o encryption encryption.c -lm

./encryption

```

四、AES vs RSA

特性 AES RSA

类型对称加密非对称加密

密钥同一密钥公钥+私钥

速度快慢（慢1000倍）

密钥长度 128/192/256位 1024/2048/4096位

适用场景数据加密密钥分发、数字签名

五、总结

通过这篇文章，你学会了：

· AES加密核心操作（S盒、行移位、列混合、密钥扩展）

· RSA密钥生成和加解密

· 两种加密算法的完整实现

· 对称加密 vs 非对称加密的区别

加密是信息安全的基石。掌握它，你就理解了HTTPS、SSH、数字签名的底层原理。

下一篇预告：《从零实现一个网络防火墙：包过滤与状态检测》

评论区分享一下你对加密技术的理解～