密码工程-大素数
任务
- 在openEuler(推荐)或Ubuntu或Windows(不推荐)中完成下面任务
- 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‘）
- 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‘）
- 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
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