密码工程-大素数

任务详情

0.在openEuler(推荐)或Ubuntu或Windows(不推荐)中完成下面任务
1.利用大整数库(GMP或者OpenSSL)，参考《密码工程》p113伪代码实现 2.GenerateLargePrime 函数（10‘）
3.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‘）
4.用OpenSSL验证你产生的素数是不是正确（5’）
提交代码和运行结果截图

  测试

echo "2^255" | bc
57896044618658097711785492504343953926634992332820282019728792003956\
564819968
echo "2^256-1" | bc
11579208923731619542357098500868790785326998466564056403945758400791\
3129639935

  代码

#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;
}

  运行

sudo apt-get update
sudo apt-get install libgmp-dev

rjx@rjx-VirtualBox:~/test/2024.6.7$ ./test
Large prime: 102245892909274590127127437346763990236079888116777219746583252655183600606079
rjx@rjx-VirtualBox:~/test/2024.6.7$ ./test
Large prime: 85599317078990932562422224999979696330958333053715948349991704892713360607561

  验证

• 57896044618658097711785492504343953926634992332820282019728792003956564819968（2^255）
• 102245892909274590127127437346763990236079888116777219746583252655183600606079（大素数1）
• 85599317078990932562422224999979696330958333053715948349991704892713360607561（大素数2）
• 115792089237316195423570985008687907853269984665640564039457584007913129639935（2^256-1）