密码工程-大素数

密码工程-大素数

任务

0. 在openEuler(推荐)或Ubuntu或Windows(不推荐)中完成下面任务
1. 利大整数库(GMP或者OpenSSL)，参考《密码工程》p113伪代码实现GenerateLargePrime 函数（10‘）
2. 在测试代码中产生一个在范围l = 2^255至u = 2^256-1内的素数。（5‘）
3. 用OpenSSL验证你产生的素数是不是正确（5’）
4. 提交代码和运行结果截图

代码

• 利用大整数库(GMP或者OpenSSL)，实现 GenerateLargePrime 函数，输入：l（素数所在范围的下界）、u（素数所在范围的上界），输出：p（一个在l，…，u区间内的随机素数）

#include <gmp.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

// Generate a random large prime number between lower and upper bounds
void GenerateLargePrime(mpz_t p, mpz_t l, mpz_t u) {
	mpz_t temp;
	mpz_init(temp);

	gmp_randstate_t state;
	gmp_randinit_default(state);
	gmp_randseed_ui(state, time(NULL));

	do {
		mpz_urandomm(temp, state, u); // Generate a random number between 0 and u
		mpz_add(temp, temp, l);       // Add l to the random number to get a number between l and u
		mpz_nextprime(p, temp);       // Find the next prime number after temp
	} while (mpz_cmp(p, u) > 0);    // Repeat until the prime number is within the range [l, u]

	mpz_clear(temp);
	gmp_randclear(state);
}

int main() {
	mpz_t l, u, p;
	mpz_init(l);
	mpz_init(u);
	mpz_init(p);

	mpz_set_str(l, "57896044618658097711785492504343953926634992332820282019728792003956564819968", 10); // Set lower bound 2^255
	mpz_set_str(u, "115792089237316195423570985008687907853269984665640564039457584007913129639935", 10); // Set upper bound 2^256-1

	GenerateLargePrime(p, l, u);

	gmp_printf("Large prime: %Zd\n", p);

	mpz_clear(l);
	mpz_clear(u);
	mpz_clear(p);

	return 0;
}

• 2^255:

  57896044618658097711785492504343953926634992332820282019728792003956564819968

• 83124435449170871735329890786632912703260867023741059705552134041721470528513

• 84240690159250997246407786282298096921052910984281216584040636438021785203849

• 2^256-1:

  115792089237316195423570985008687907853269984665640564039457584007913129639935