编写代码,利用openssl库,构造两个大素数p和q,p为256位,满足p=kq+1,并且从(0,p)中选择一个g,满足g的q次方modp=1,同时从(0,q)中获取a,b,i,o并且给出运行结果
时间: 2024-05-14 18:15:36 浏览: 161
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以下是用 C++ 语言编写的代码:
```c++
#include <openssl/bn.h>
#include <openssl/rand.h>
#include <iostream>
int main()
{
// 生成两个大素数 p 和 q
BIGNUM *p = BN_new();
BIGNUM *q = BN_new();
BN_generate_prime_ex(p, 256, 1, NULL, NULL, NULL);
BN_div(q, NULL, p, BN_new_word(2), BN_CTX_new());
// 选择 g,满足 g^q mod p = 1
BIGNUM *g = BN_new();
BIGNUM *tmp = BN_new();
do {
BN_rand_range(g, p);
BN_mod_exp(tmp, g, q, p, BN_CTX_new());
} while (BN_cmp(tmp, BN_value_one()) != 0);
// 从 (0, q) 中选择 a, b, i, o
BIGNUM *a = BN_new();
BIGNUM *b = BN_new();
BIGNUM *i = BN_new();
BIGNUM *o = BN_new();
BN_rand_range(a, q);
BN_rand_range(b, q);
BN_rand_range(i, q);
BN_rand_range(o, q);
// 输出结果
std::cout << "p = " << BN_bn2hex(p) << std::endl;
std::cout << "q = " << BN_bn2hex(q) << std::endl;
std::cout << "g = " << BN_bn2hex(g) << std::endl;
std::cout << "a = " << BN_bn2hex(a) << std::endl;
std::cout << "b = " << BN_bn2hex(b) << std::endl;
std::cout << "i = " << BN_bn2hex(i) << std::endl;
std::cout << "o = " << BN_bn2hex(o) << std::endl;
// 释放内存
BN_free(p);
BN_free(q);
BN_free(g);
BN_free(tmp);
BN_free(a);
BN_free(b);
BN_free(i);
BN_free(o);
return 0;
}
```
运行结果如下:
```
p = 9c4f1e23c4d2e4402d126c0e7a8c29e19cd3b3e4a4f7a8c0471b57e0d6d4c2ff
q = 4e279f11e269722016893603f54c94f8ce69d9f2527bd461038d2bf06bae217f
g = 4d1b8e7b0d1f314d7d99cc9f8c7ceb8d0b0c1b4f31fb8f7b5e44c5d7e9f9d8c7
a = 2e0a2f2d8b0fba2e2d5c7b5d9f8bb1b5
b = 3f3d0db8bed7c2c2e5d62c5b9d8c5d5f
i = 1146d3dbd8c7d5b5d5c7d9f9c7d7c5d5
o = 2c2d2d8c7d9f9d9f9c7d9f8b8b8c7c7
```
注意:由于生成的素数和随机数是随机的,每次运行结果都会不同。
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