实现 RSA 算法的Java程序

RSA或Rivest–Shamir–Adleman是现代计算机用来加密和解密消息的算法。它是一种非对称密码算法。非对称意味着有两个不同的密钥。这也称为公钥 密码学，因为其中一个密钥通常会提供给任何人。另一个是保密的私钥。该算法基于这样一个事实，即寻找超大数的因数是困难的：当因数是素数时，这件事被称为素数分解。它也是一个密钥对（公钥和个人密钥）生成器。

例子：

Generating Public Key

1. Select two prime no's. Suppose P = 53 and Q = 59.
Now First part of the Public key  : n = P*Q = 3127.

2. We also need a small exponent say e : 
   But e Must be 

    -An integer.

    -Not be a factor of n.
 
    -1 < e < Φ(n) [Φ(n) is discussed below], 
     Let us now consider it to be equal to 3.
     
The public key has been made of n and e

Generating Private Key

1. We need to calculate Φ(n) :
   Such that Φ(n) = (P-1)(Q-1)     
      so,  Φ(n) = 3016

    
2. Now calculate Private Key, d : 
   d = (k*Φ(n) + 1) / e for some integer k
3. For k = 2, value of d is 2011.

The private key has been made of d

RSA算法的实现：

1. 考虑两个素数 p 和 q。
2. 计算 n = p*q
3. 计算 ϕ(n) = (p – 1) * (q – 1)
4. 选择 e 这样的 gcd(e , ϕ(n) ) = 1
5. 计算 d 这样的 e*d mod ϕ(n) = 1
6. 公钥 {e,n} 私钥 {d,n}
7. 密文 C = Pe mod n 其中 P = 明文
8. 对于解密 D = Dd mod n，其中 D 将退还明文。

下面是上述方法的实现：

Java

// Java Program to Implement the RSA Algorithm
import java.math.*;
import java.util.*;
 
class RSA {
    public static void main(String args[])
    {
        int p, q, n, z, d = 0, e, i;
 
        // The number to be encrypted and decrypted
        int msg = 12;
        double c;
        BigInteger msgback;
 
        // 1st prime number p
        p = 3;
 
        // 2nd prime number q
        q = 11;
        n = p * q;
        z = (p - 1) * (q - 1);
        System.out.println("the value of z = " + z);
 
        for (e = 2; e < z; e++) {
 
            // e is for public key exponent
            if (gcd(e, z) == 1) {
                break;
            }
        }
        System.out.println("the value of e = " + e);
        for (i = 0; i <= 9; i++) {
            int x = 1 + (i * z);
 
            // d is for private key exponent
            if (x % e == 0) {
                d = x / e;
                break;
            }
        }
        System.out.println("the value of d = " + d);
        c = (Math.pow(msg, e)) % n;
        System.out.println("Encrypted message is : " + c);
 
        // converting int value of n to BigInteger
        BigInteger N = BigInteger.valueOf(n);
 
        // converting float value of c to BigInteger
        BigInteger C = BigDecimal.valueOf(c).toBigInteger();
        msgback = (C.pow(d)).mod(N);
        System.out.println("Decrypted message is : "
                           + msgback);
    }
 
    static int gcd(int e, int z)
    {
        if (e == 0)
            return z;
        else
            return gcd(z % e, e);
    }
}