rsa-3072 算法c++
时间: 2023-06-15 16:08:34 浏览: 68
以下是 C++ 实现的 RSA-3072 算法示例代码:
```c++
#include <iostream>
#include <string>
#include <cstdlib>
#include <ctime>
#include <cmath>
using namespace std;
string decimalToBinary(long long decimal) {
string binary = "";
while(decimal != 0) {
binary = to_string(decimal % 2) + binary;
decimal /= 2;
}
return binary;
}
long long binaryToDecimal(string binary) {
long long decimal = 0;
for(int i = binary.length() - 1; i >= 0; i--) {
if(binary[i] == '1') {
decimal += pow(2, binary.length() - 1 - i);
}
}
return decimal;
}
long long fastPower(long long base, long long exponent, long long mod) {
long long result = 1;
while(exponent != 0) {
if(exponent % 2 == 1) {
result = (result * base) % mod;
}
base = (base * base) % mod;
exponent /= 2;
}
return result;
}
bool isPrime(long long n, int k) {
if(n == 2 || n == 3) {
return true;
}
if(n == 1 || n % 2 == 0) {
return false;
}
long long d = n - 1;
int s = 0;
while(d % 2 == 0) {
s++;
d /= 2;
}
for(int i = 0; i < k; i++) {
long long a = rand() % (n - 3) + 2;
long long x = fastPower(a, d, n);
if(x == 1 || x == n - 1) {
continue;
}
for(int j = 0; j < s - 1; j++) {
x = (x * x) % n;
if(x == 1) {
return false;
}
if(x == n - 1) {
break;
}
}
if(x != n - 1) {
return false;
}
}
return true;
}
long long generatePrimeNumber(int bits) {
long long min = pow(2, bits - 1);
long long max = pow(2, bits) - 1;
long long p;
do {
p = rand() % (max - min + 1) + min;
} while(!isPrime(p, 10));
return p;
}
long long gcd(long long a, long long b) {
while(b != 0) {
long long r = a % b;
a = b;
b = r;
}
return a;
}
void generateKeys(long long& p, long long& q, long long& n, long long& e, long long& d) {
srand(time(NULL));
p = generatePrimeNumber(1536);
q = generatePrimeNumber(1536);
n = p * q;
long long phi = (p - 1) * (q - 1);
do {
e = rand() % (phi - 2) + 2;
} while(gcd(e, phi) != 1);
long long k = 1;
while((k * phi + 1) % e != 0) {
k++;
}
d = (k * phi + 1) / e;
}
string encrypt(string message, long long e, long long n) {
string binary = "";
for(int i = 0; i < message.length(); i++) {
binary += decimalToBinary((int) message[i]);
}
while(binary.length() % 3072 != 0) {
binary += "0";
}
string ciphertext = "";
for(int i = 0; i < binary.length(); i += 3072) {
string block = binary.substr(i, 3072);
long long x = binaryToDecimal(block);
long long y = fastPower(x, e, n);
string cypherblock = decimalToBinary(y);
while(cypherblock.length() < 6176) {
cypherblock = "0" + cypherblock;
}
ciphertext += cypherblock;
}
return ciphertext;
}
string decrypt(string ciphertext, long long d, long long n) {
string message = "";
for(int i = 0; i < ciphertext.length(); i += 6176) {
string block = ciphertext.substr(i, 6176);
long long y = binaryToDecimal(block);
long long x = fastPower(y, d, n);
string plaintextblock = "";
while(x != 0) {
plaintextblock = to_string(x % 256) + plaintextblock;
x /= 256;
}
while(plaintextblock.length() < 24) {
plaintextblock = "0" + plaintextblock;
}
message += plaintextblock;
}
return message;
}
int main() {
long long p, q, n, e, d;
generateKeys(p, q, n, e, d);
string message;
cout << "Enter the message to be encrypted: ";
getline(cin, message);
string ciphertext = encrypt(message, e, n);
cout << "Ciphertext: " << ciphertext << endl;
string plaintext = decrypt(ciphertext, d, n);
cout << "Plaintext: " << plaintext << endl;
return 0;
}
```
这个示例代码实现了 RSA-3072 算法的密钥生成、加密和解密,其中 `generatePrimeNumber` 函数生成指定位数的质数,`generateKeys` 函数生成公钥和私钥,`encrypt` 函数将明文转换为二进制并加密,`decrypt` 函数对密文解密并转换为明文。