RSA加密解密总结

简单的控制台程序　

#include"stdafx.h"
#include <math.h>
#include<string.h>
/*/求解密密钥d的函数(根据Euclid算法)96403770511368768000*/
unsigned long  rsa(unsigned long p, unsigned long q, unsigned long e)  /*/求解密密钥d的函数(根据Euclid算法)*/
{
	unsigned long g, k, r, n1, n2, t;
	unsigned long b1 = 0, b2 = 1;
	g = (p - 1)*(q - 1);
	n1 = g;
	n2 = e;
	while (1)
	{
		k = n1 / n2;
		r = n1 - k*n2;
		if (r != 0)
		{
			n1 = n2;
			n2 = r;
			t = b2;
			b2 = b1 - k*b2;
			b1 = t;
		}
		else
		{
			break;
		}
	}
	return (g + b2) % g;
}
/*/判断一个数是否为素数*/
bool is_prime(int p) {
	int end = sqrt(p);
	for (int i = 2; i <= end; i++)
		if (p%i == 0)
			return false;
	return true;
}
/*/利用利用倍增法实现x^p mod m */
long long expmod(int x, int p, int m) {
	//x^p mod m 
	const int N = 110;
	int a[N];
	long long s;
	//scanf("%d%d%d", &x, &p, &m);
	//将p转成二进制传入a数组
	int k = 0;
	while (p>0) {
		++k;
		a[k] = p % 2;
		p = p / 2;
	}

	//for (int i = k; i>0; --i) printf("%d", a[i]);
	//printf("\n");

	//初始化连续变量t和答案s
	long long t = x;
	if (a[1] == 0) s = 1;
	else s = x;

	//倍增
	for (int i = 2; i <= k; ++i) {
		t = t*t%m;
		if (a[i] == 1) s = s*t%m;
	}
	//printf("%I64d", s);
	return s;
}
int main() {
	int p, q, e;//素数p,q和随机数e
	printf("welcom come to the ESA program\n");
	printf("please input two prime unsigned number p,q  and a rand unsigned number e\n");
	printf(" p=");	scanf("%d", &p);
	printf(" q=");	scanf("%d", &q);
	printf(" e=");	scanf("%d", &e); 
	bool bp=false, bq=false;
	while (bp == false || bq == false) {
		if (p*q < 127||p<0||q<0) {
			if(p>0&&q>0)printf("please input two more big prime unsigned number p,q\n");
			else if (p<0 || q<0)printf("please input two  prime unsigned number p,q(p>1,q>1)\n");
			printf(" p=");	scanf("%d", &p);
			printf(" q=");	scanf("%d", &q);
			bp = bq = false;
		}
		else {
			bp = is_prime(p);
			if (p <= 1)
				bp = false;
			bq = is_prime(q);
			if (q <= 1)
				bq = false;
			if (bp == false)
			{
				if (p == 1)
					printf("input a more big prime  number p=");
				else
					printf("input a prime unsigned number p=");
				scanf("%ud", &p); printf("\n");
			}
			if (bq == false) {
				if (q == 1)
					printf("input a more big prime  number q=");
				else
					printf("input a prime unsigned number q=");
				scanf("%ud", &q); printf("\n");
			}
		}
	}
	//计算公钥与私钥
	int n = p*q;
	int fn = (p - 1)*(q - 1);
	int d = rsa(p, q, e);
	printf("公钥：（e,n）为（%d,%d)\n",e,n);
	printf("私钥：（d,n）为（%d,%d)\n",d,n);
	printf("---------加密/解密---------\n");
	char ch = 'a';
	while (ch != 'd' && ch != 'D' && ch != 'e' && ch != 'E') {
		printf("加密输入e或E,解密输入d或D,请选择：\n");
		getchar();
		scanf("%c",&ch);
	}
	char* str = new char[1024];
	int i, len;
	//encryption加密
	if (ch == 'e' || ch == 'E') {
		printf("---------加密--------\n");
		printf("please input what you want to encryption(String):\n");
		scanf("%s", str);
		i = 0, len = strlen(str);
		int mingwen;
		while (i < 1024 && i < len) {
			mingwen = (int)str[i];
			int pr = expmod(mingwen, e, n);
			if (i != 0)
				printf(",");
			printf("%d", pr);
			i++;
		}
		printf("\n");
	}
	//decryption解密
	else if (ch == 'd' || ch == 'D') {
		printf("---------解密--------\n");
		printf("please input what you want to decryption(String)\n");
		printf("you should input just as XXX,XXX,XXX,XXX,XXX\n");
		scanf("%s", str);
		i = 0, len = strlen(str);
		long long im = 0;
		while (i < 1024 && i < len) {
			if (str[i] != ',')
				im = im * 10 + (int)str[i] - 48;
			else {
				im = expmod(im, d, n);
				printf("%c", (char)im);
				im = 0;
			}
			if (i == 1023 || i == len - 1) {
				im = expmod(im, d, n);
				printf("%c", (char)im);
				im = 0;
			}
			i++;
		}
		printf("\n");
	}
	getchar();
	getchar();
	return 0;
}