solovary-stassen素性检验算法C语言

Solovay-Strassen素性检验算法是一种基于欧拉准则的素性检验算法。下面是一个用 C 语言实现的 Solovay-Strassen 素性检验算法的示例代码：

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

int modular_exponentiation(int base, int exponent, int modulus)
{
    int result = 1;
    while (exponent > 0)
    {
        if (exponent % 2 == 1)
        {
            result = (result * base) % modulus;
        }
        base = (base * base) % modulus;
        exponent = exponent / 2;
    }
    return result;
}

int jacobi_symbol(int a, int n)
{
    if (n <= 0 || n % 2 == 0)
    {
        return 0;
    }
    int j = 1;
    if (a < 0)
    {
        a = -a;
        if (n % 4 == 3)
        {
            j = -j;
        }
    }
    while (a != 0)
    {
        while (a % 2 == 0)
        {
            a = a / 2;
            if (n % 8 == 3 || n % 8 == 5)
            {
                j = -j;
            }
        }
        int temp = a;
        a = n;
        n = temp;
        if (a % 4 == 3 && n % 4 == 3)
        {
            j = -j;
        }
        a = a % n;
    }
    if (n == 1)
    {
        return j;
    }
    return 0;
}

int is_prime(int n, int k)
{
    if (n <= 1 || n == 4)
    {
        return 0;
    }
    if (n <= 3)
    {
        return 1;
    }
    while (k > 0)
    {
        int a = 2 + rand() % (n - 3);
        int j = jacobi_symbol(a, n);
        int x = modular_exponentiation(a, (n - 1) / 2, n);
        if (j == 0 || x != j)
        {
            return 0;
        }
        k--;
    }
    return 1;
}

int main()
{
    srand(time(NULL));
    int n, k;
    printf("Enter a number to check if it is prime: ");
    scanf("%d", &n);
    printf("Enter the number of iterations for the test: ");
    scanf("%d", &k);
    if (is_prime(n, k))
    {
        printf("%d is probably prime.\n", n);
    }
    else
    {
        printf("%d is composite.\n", n);
    }
    return 0;
}

这个程序中，`modular_exponentiation` 函数用于计算模幂，`jacobi_symbol` 函数用于计算雅可比符号，`is_prime` 函数用于执行素性检验。在 `main` 函数中，用户输入要检验的数和测试的迭代次数，然后调用 `is_prime` 函数进行素性检验。最终输出结果。