RSA3072的C++实现
时间: 2023-07-11 16:43:51 浏览: 97
RSA3072是一种非常强大的加密算法,其C++实现如下:
```cpp
#include <iostream>
#include <string>
#include <sstream>
#include <fstream>
#include <cmath>
#include <cstdlib>
#include <ctime>
using namespace std;
// Miller-Rabin素性测试
bool Miller_Rabin(long long n, int times)
{
if (n <= 2) return n == 2;
if (n % 2 == 0) return false;
long long m = n - 1;
int k = 0;
while ((m & 1) == 0) {
k++;
m >>= 1;
}
for (int i = 0; i < times; i++) {
long long a = rand() % (n - 2) + 2;
long long x = pow(a, m);
long long y = 0;
for (int j = 0; j < k; j++) {
y = x * x % n;
if (y == 1 && x != 1 && x != n - 1) return false;
x = y;
}
if (y != 1) return false;
}
return true;
}
// 生成大素数
long long Get_Prime(int bit)
{
long long n = rand() % (1LL << (bit - 1)) + (1LL << (bit - 1));
while (!Miller_Rabin(n, 20)) {
n += 2;
}
return n;
}
// 欧几里得算法
long long gcd(long long a, long long b)
{
if (b == 0) return a;
return gcd(b, a % b);
}
// 扩展欧几里得算法
long long exgcd(long long a, long long b, long long &x, long long &y)
{
if (b == 0) {
x = 1;
y = 0;
return a;
}
long long d = exgcd(b, a % b, y, x);
y -= a / b * x;
return d;
}
// 求逆元
long long Get_Inverse(long long a, long long mod)
{
long long x, y;
exgcd(a, mod, x, y);
return (x % mod + mod) % mod;
}
// 生成公钥和私钥
void Get_Key(long long &n, long long &e, long long &d)
{
srand(time(NULL));
long long p = Get_Prime(1536);
long long q = Get_Prime(1536);
n = p * q;
long long fn = (p - 1) * (q - 1);
e = 65537;
d = Get_Inverse(e, fn);
}
// 加密
string Encrypt(string plain, long long n, long long e)
{
stringstream ss;
for (int i = 0; i < plain.length(); i++) {
ss << hex << int(plain[i]);
}
long long m;
ss >> m;
long long c = 1;
while (e > 0) {
if (e & 1) c = c * m % n;
m = m * m % n;
e >>= 1;
}
stringstream res;
res << hex << c;
return res.str();
}
// 解密
string Decrypt(string cipher, long long n, long long d)
{
long long c;
stringstream ss;
ss << hex << cipher;
ss >> c;
long long m = 1;
while (d > 0) {
if (d & 1) m = m * c % n;
c = c * c % n;
d >>= 1;
}
stringstream res;
res << hex << m;
string plain = res.str();
if (plain.length() % 2 == 1) plain = "0" + plain;
string res_str = "";
for (int i = 0; i < plain.length(); i += 2) {
int tmp;
stringstream ss;
ss << hex << plain.substr(i, 2);
ss >> tmp;
res_str += char(tmp);
}
return res_str;
}
int main()
{
long long n, e, d;
Get_Key(n, e, d);
string plain = "Hello, RSA3072!";
cout << "Plain text: " << plain << endl;
string cipher = Encrypt(plain, n, e);
cout << "Cipher text: " << cipher << endl;
string dec_plain = Decrypt(cipher, n, d);
cout << "Decrypted plain text: " << dec_plain << endl;
return 0;
}
```
这个实现使用了Miller-Rabin素性测试、欧几里得算法、扩展欧几里得算法等算法。需要注意的是,这里的实现只是为了展示RSA3072的原理,实际上RSA3072的安全性要求更高,需要使用更多的技巧和算法来保证其安全性。
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