已知明文,选择p=11,q=13,e=17,计算出秘钥d,并实现RSA加密流程,c++
时间: 2024-03-02 18:49:56 浏览: 123
RSA加密算法 C++ 实现
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根据RSA算法的原理,我们可以先计算出n = p*q = 143,然后计算出欧拉函数φ(n) = (p-1)*(q-1) = 120。
接下来,我们需要求出d,满足e*d ≡ 1 (mod φ(n)),即17*d ≡ 1 (mod 120)。通过扩展欧几里得算法可以求出d = 89。
现在我们就可以进行RSA加密的流程了,假设明文为m = 7。
首先,我们需要将明文m进行加密,加密后的密文为c = m^e (mod n) = 7^17 (mod 143) = 30。
然后,我们可以将密文c进行解密,解密后的明文为m' = c^d (mod n) = 30^89 (mod 143) = 7。
因此,我们成功地进行了RSA加密和解密的流程。
以下是C++代码实现:
```
#include <iostream>
#include <cmath>
using namespace std;
int gcd(int a, int b) {
if (b == 0)
return a;
return gcd(b, a % b);
}
int mod_inverse(int a, int m) {
int m0 = m, t, q;
int x0 = 0, x1 = 1;
if (m == 1)
return 0;
while (a > 1) {
q = a / m;
t = m;
m = a % m, a = t;
t = x0;
x0 = x1 - q * x0;
x1 = t;
}
if (x1 < 0)
x1 += m0;
return x1;
}
int power_mod(int a, int b, int m) {
int res = 1;
while (b > 0) {
if (b & 1)
res = (res * a) % m;
a = (a * a) % m;
b >>= 1;
}
return res;
}
int main() {
int p = 11, q = 13, n = p * q, phi = (p - 1) * (q - 1), e = 17, d;
d = mod_inverse(e, phi);
int m = 7;
int c = power_mod(m, e, n);
int m_prime = power_mod(c, d, n);
cout << "Public key: (" << e << ", " << n << ")" << endl;
cout << "Private key: (" << d << ", " << n << ")" << endl;
cout << "Plaintext: " << m << endl;
cout << "Ciphertext: " << c << endl;
cout << "Decrypted plaintext: " << m_prime << endl;
return 0;
}
```
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