rsa签名算法c语言实现,要求体制参数:选两个保密的大素数p和q,计算n = p * q,φ(n)=(p-1)(q-1)选一整数e,满足1<e<φ(n),且gcd{φ(n),e}=1;计算d,满足d·e ≡ 1modφ(n);以pk = {n,e}为公开钥sk = {d,n}为秘密钥。要求签名过程:设消息为M,对其签名为σ≡M的d次方modn。要求验证过程收方在收到消息M和签名σ后,验证M≡σ的e次方modn是否成立,若成立,则发方的签名有效。
时间: 2024-02-21 07:56:56 浏览: 20
RSA签名算法的C语言实现如下:
```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <gmp.h>
void generate_key(mpz_t p, mpz_t q, mpz_t n, mpz_t phi_n, mpz_t e, mpz_t d) {
// Generate two large primes
gmp_randstate_t state;
gmp_randinit_default(state);
gmp_randseed_ui(state, time(NULL));
mpz_urandomb(p, state, 1024);
mpz_nextprime(p, p);
mpz_urandomb(q, state, 1024);
mpz_nextprime(q, q);
// Calculate n and phi(n)
mpz_mul(n, p, q);
mpz_sub_ui(p, p, 1);
mpz_sub_ui(q, q, 1);
mpz_mul(phi_n, p, q);
// Generate a random number e that is coprime to phi(n)
do {
mpz_urandomm(e, state, phi_n);
} while (mpz_gcd(e, phi_n) != 1);
// Calculate d such that d * e ≡ 1 (mod phi(n))
mpz_invert(d, e, phi_n);
}
void sign_message(mpz_t signature, mpz_t message, mpz_t d, mpz_t n) {
// Signature = message^d (mod n)
mpz_powm(signature, message, d, n);
}
int verify_signature(mpz_t signature, mpz_t message, mpz_t e, mpz_t n) {
// Verify that signature^e ≡ message (mod n)
mpz_t decrypted_signature;
mpz_init(decrypted_signature);
mpz_powm(decrypted_signature, signature, e, n);
int result = mpz_cmp(decrypted_signature, message) == 0;
mpz_clear(decrypted_signature);
return result;
}
int main() {
// Generate public and private keys
mpz_t p, q, n, phi_n, e, d;
mpz_inits(p, q, n, phi_n, e, d, NULL);
generate_key(p, q, n, phi_n, e, d);
// Print public and private keys
gmp_printf("Public key: (%Zd, %Zd)\n", n, e);
gmp_printf("Private key: (%Zd, %Zd)\n", n, d);
// Sign a message
char message_str[] = "Hello, world!";
mpz_t message, signature;
mpz_inits(message, signature, NULL);
mpz_import(message, strlen(message_str), 1, sizeof(char), 0, 0, message_str);
sign_message(signature, message, d, n);
// Print message and signature
gmp_printf("Message: %Zd\n", message);
gmp_printf("Signature: %Zd\n", signature);
// Verify the signature
int result = verify_signature(signature, message, e, n);
printf("Signature is %s\n", result ? "valid" : "invalid");
// Clean up
mpz_clears(p, q, n, phi_n, e, d, message, signature, NULL);
return 0;
}
```
该实现使用GNU MP库来处理大数运算。函数`generate_key`用于生成公钥和私钥,函数`sign_message`用于对消息进行签名,函数`verify_signature`用于验证签名。主函数中,首先生成公钥和私钥,然后对一条消息进行签名,并验证签名的有效性。