编写代码,利用openssl库,构造两个大素数,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: 2024-05-05 08:22:48 浏览: 9
以下是使用openssl库构造两个大素数p和q,并从(0, p)中选择g,使得g的q次方mod p等于1的C++代码:
```c++
#include <openssl/bn.h>
#include <openssl/rand.h>
#include <iostream>
int main()
{
// Generate two large prime numbers
BIGNUM *p = BN_new();
BIGNUM *q = BN_new();
BN_generate_prime_ex(p, 1024, 1, NULL, NULL, NULL);
BN_generate_prime_ex(q, 1024, 1, NULL, NULL, NULL);
// Compute k = (p-1)/q
BIGNUM *k = BN_new();
BN_sub(k, p, BN_value_one());
BN_div(k, NULL, k, q, NULL);
// Find g such that 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, NULL);
} while (BN_cmp(tmp, BN_value_one()) != 0);
// Choose some values from (0, q)
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);
// Print out the results
std::cout << "p = " << BN_bn2hex(p) << std::endl;
std::cout << "q = " << BN_bn2hex(q) << std::endl;
std::cout << "k = " << BN_bn2hex(k) << 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;
// Free memory
BN_free(p);
BN_free(q);
BN_free(k);
BN_free(g);
BN_free(tmp);
BN_free(a);
BN_free(b);
BN_free(i);
BN_free(o);
return 0;
}
```
这个程序将生成两个1024位的大素数p和q,并计算k=p-1/q。然后,它将从(0, p)中选择g,使得g的q次方mod p等于1。最后,它将从(0, q)中选择a、b、i、o,并输出所有这些值。