c++实现DSA签名算法
时间: 2023-08-28 22:03:20 浏览: 232
DSA(Digital Signature Algorithm)数字签名算法是一种公钥密码学的签名算法,用于数字签名和身份验证。C++实现DSA签名算法需要用到大数运算库,可以使用GMP(GNU Multiple Precision Arithmetic Library)库。
以下是一个简单的代码示例,演示如何使用GMP库实现DSA签名算法:
```c++
#include <iostream>
#include <gmpxx.h>
#include <string.h>
// DSA signature struct
struct DSASignature {
mpz_class r;
mpz_class s;
};
// DSA parameters struct
struct DSAParams {
mpz_class p;
mpz_class q;
mpz_class g;
};
// Generate DSA parameters
void generateDSAParams(DSAParams& params, int n) {
mpz_class p, q, g, h;
mpz_class zero = 0;
// Generate prime number p
mpz_urandomb(p.get_mpz_t(), gmp_randstate_t(NULL), n);
mpz_nextprime(p.get_mpz_t(), p.get_mpz_t());
// Generate prime number q
mpz_ui_pow_ui(q.get_mpz_t(), 2, 160);
mpz_nextprime(q.get_mpz_t(), q.get_mpz_t());
// Calculate g
while (true) {
mpz_urandomm(h.get_mpz_t(), gmp_randstate_t(NULL), p.get_mpz_t());
mpz_powm(g.get_mpz_t(), h.get_mpz_t(), (p - 1) / q, p.get_mpz_t());
if (g != 1) {
break;
}
}
// Set parameters
params.p = p;
params.q = q;
params.g = g;
}
// Generate DSA key pair
void generateDSAKeyPair(mpz_class& privateKey, mpz_class& publicKey, DSAParams& params) {
mpz_class zero = 0;
// Generate private key
do {
mpz_urandomm(privateKey.get_mpz_t(), gmp_randstate_t(NULL), params.q.get_mpz_t());
} while (privateKey == zero);
// Generate public key
mpz_powm(publicKey.get_mpz_t(), params.g.get_mpz_t(), privateKey.get_mpz_t(), params.p.get_mpz_t());
}
// Calculate DSA signature
void calculateDSASignature(DSASignature& signature, const mpz_class& privateKey, const DSAParams& params, const unsigned char* message, size_t messageLength) {
mpz_class k, r, s, h, x;
mpz_class zero = 0;
mpz_class one = 1;
// Generate random number k
do {
mpz_urandomm(k.get_mpz_t(), gmp_randstate_t(NULL), params.q.get_mpz_t());
} while (k == zero);
// Calculate r
mpz_powm(r.get_mpz_t(), params.g.get_mpz_t(), k.get_mpz_t(), params.p.get_mpz_t());
r %= params.q;
// Calculate s
mpz_invert(x.get_mpz_t(), k.get_mpz_t(), params.q.get_mpz_t());
mpz_import(h.get_mpz_t(), messageLength, 1, sizeof(unsigned char), 0, 0, message);
s = (x * (h + privateKey * r)) % params.q;
// Set signature
signature.r = r;
signature.s = s;
}
// Verify DSA signature
bool verifyDSASignature(const DSASignature& signature, const mpz_class& publicKey, const DSAParams& params, const unsigned char* message, size_t messageLength) {
mpz_class w, u1, u2, v, h;
mpz_class zero = 0;
// Calculate w
mpz_invert(w.get_mpz_t(), signature.s.get_mpz_t(), params.q.get_mpz_t());
// Calculate u1
mpz_import(h.get_mpz_t(), messageLength, 1, sizeof(unsigned char), 0, 0, message);
u1 = (h * w) % params.q;
// Calculate u2
u2 = (signature.r * w) % params.q;
// Calculate v
mpz_powm(v.get_mpz_t(), params.g.get_mpz_t(), u1.get_mpz_t(), params.p.get_mpz_t());
mpz_powm(u2.get_mpz_t(), publicKey.get_mpz_t(), u2.get_mpz_t(), params.p.get_mpz_t());
v = ((v * u2) % params.p) % params.q;
// Verify signature
return v == signature.r;
}
int main() {
// Initialize GMP library
mpz_class zero = 0;
gmp_randstate_t randState;
gmp_randinit_default(randState);
gmp_randseed_ui(randState, time(NULL));
// Generate DSA parameters and key pair
DSAParams params;
generateDSAParams(params, 1024);
mpz_class privateKey, publicKey;
generateDSAKeyPair(privateKey, publicKey, params);
// Sign message
const char* message = "Hello, world!";
size_t messageLength = strlen(message);
DSASignature signature;
calculateDSASignature(signature, privateKey, params, (const unsigned char*)message, messageLength);
// Verify signature
bool verified = verifyDSASignature(signature, publicKey, params, (const unsigned char*)message, messageLength);
if (verified) {
std::cout << "Signature verified!" << std::endl;
} else {
std::cout << "Signature verification failed!" << std::endl;
}
// Clear GMP library
gmp_randclear(randState);
return 0;
}
```
在上面的代码中,我们使用了GMP库中的大数运算函数来计算DSA签名。我们首先生成DSA参数和密钥对,然后使用私钥对消息进行签名,并使用公钥来验证签名。如果签名成功,则输出“Signature verified!”,否则输出“Signature verification failed!”。
需要注意的是,在实际应用中,我们需要使用安全的随机数生成器来生成随机数,以增强DSA签名的安全性。此处我们使用了GMP库中的随机数生成函数,但在实际应用中,我们需要使用更为安全的随机数生成器来生成随机数。