import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
import java.util.Scanner;
class ProducePrime {
/*
* 獲取第一個素數的方法
*/
public Integer Prime1() {
List<Integer> list = new ArrayList<Integer>();// 存儲素數的集合
for (int i = (int) Math.pow(2, 16) + 1; i <= Math.pow(2, 17); i+=2) {// 判斷奇數
boolean num2 = true;// 防止被false覆蓋
for (int m = 2; m <= Math.sqrt(i); m++) {// 提高試除效率
if (i % m == 0) {
num2 = false;// 不是素數
break;
} else if (num2) {
list.add(i);// 存儲素數到集合中
}
}
}
Random random = new Random();
int n = random.nextInt(list.size());
return list.get(n);
}
/*
* 獲取第二個素數的方法
*/
public int Prime2() {
int max = (int) Math.pow(2, 22);
int min = (int) Math.pow(2, 21);
int temp = 0;
int num = new Random().nextInt(max - min + 1) + min;// 隨機獲取指定范圍內的數字
if (Odd(num)) {
boolean flag = true;
for (int m = 2; m <= Math.sqrt(num); m++) {// 提高試除效率
if (num % m == 0) {
flag = false;// 不是素數
num = num + 2;
continue;
}
else if(flag) {
temp = num;
}
}
}
else {
num = num + 1;
boolean flag = true;
for (int m = 2; m <= Math.sqrt(num); m++) {// 提高試除效率
if (num % m == 0) {
flag = false;// 不是素數
num = num + 2;
continue;
}
else if(flag) {
temp = num;
}
}
}
return temp;
}
public boolean Odd(int n) {
boolean flag = true;
if (n % 2 == 0) {
flag = false;
return flag;
} else {
return flag;
}
}
}
class Division {
public void divison(int m) {
int temp = 1;
int c = 1;
int[] arr = new int[1000];
arr[0] = 2;
for (int i = 3; i < 1000; i+=2) {// 判斷奇數即可
boolean flag = true;
for (int q = 2; q <= Math.sqrt(i); q++) {
if (i % q == 0) {
flag = false;// 該數不是素數
break;
}
}
if (flag) {
arr[temp] = i;// 存儲1000以內素數，用于試除
temp++;
}
}
System.out.println("1000以內素數試除開始:");
System.out.println();
for (int a = 0; a < temp; a++) {
int b = m % arr[a];// 試除1000以內的素數,保存余數
System.out.println("試除第" + c + "次:" + m + " % " + arr[a] + "=" + b);
c++;
System.out.println("得到的余數為:" + b);
System.out.println();
}
System.out.println("1000以內素數試除結束");
}
}
class MillerRabin {
/*
* Miller-Rabin檢測算法，n為檢測數據
*/
public boolean MillerRabin2(int n) {
int a = new Random().nextInt(n) + 1;
long s = 1;
long n2 = n - 1;
long n3 = n - 1;
int t = 0, temp = 0;
boolean flag = true;
out :
for(;;) {
if (n2 % 2 != 0) {
s = temp;
break out;
}else {
n2 = n2 / 2;
temp++;
}
}
t = (int) (n3 / Math.pow(2, s));
int b = (int) Math.pow(a, t);
for(long i = (long) Math.pow(2,s - 1); i >= 1; i--){
if((Math.pow(b, i) + 1) % n == 0){
break;
}
if(i == 1){
if((Math.pow(b, i) - 1) % n == 0){
break;
}
else{
flag = false;
}
}
}
return flag;
}
}
class EuclideanAlgorithm {
/*
* 獲取私鑰d的方法
* 歐幾里得擴展算法
* 公鑰e = 17
*/
BigInteger x, y, a, b, t, r;
public BigInteger exgcd(BigInteger a, BigInteger b) {
if (b == BigInteger.valueOf(0)) {
x = BigInteger.valueOf(1);
y = BigInteger.valueOf(0);
return a;
}
r = exgcd(b, a.mod(b));
t = x;
x = y;
y = t.subtract((a.divide(b)).multiply(y));
return r;
}
public void XY(BigInteger fn, BigInteger e) {
System.out.println("解得x為:" + x);
System.out.println("解得y為:" + y);
if (y.compareTo(BigInteger.valueOf(0)) < 0) {
System.out.println("所以密鑰d為:" + (y.add(fn)));
}else {
System.out.println("所以密鑰d為:" + y);
}
}
}
class MoChongFuPingFang {
/*
* 模重復平方算法加密
* 輸入加密明文m = 32655，公鑰e = 17，模數為n
*/
String binary;
long a = 1;
BigInteger a2 = BigInteger.valueOf(a);
public BigInteger Encryption(long m, long e2, long n) {
binary = Long.toBinaryString(e2);
BigInteger a3 = a2;
BigInteger m2 = BigInteger.valueOf(m);
BigInteger m3 = m2;
BigInteger n2 = BigInteger.valueOf(n);
for (int i = binary.length() - 1; i >= 0; i--) {
if (binary.charAt(i) == '1') {
a3 = a2.multiply(m2).mod(n2);
a2 = a3;
m3 = m2.multiply(m2).mod(n2);
m2 = m3;
}else {
m3 = m2.multiply(m2).mod(n2);
m2 = m3;
}
}
return a3;
}
}
class PingFangCheng {
/*
* 平方乘算法解密
* 密文m，私鑰d，模數n
*/
String binary;
long x = 0, y = 1;
BigInteger x2 = BigInteger.valueOf(x);
BigInteger y2 = BigInteger.valueOf(y);
public BigInteger Decryption(long m, long d, long n) {
binary = Long.toBinaryString(d);
BigInteger x3 = x2;
BigInteger m2 = BigInteger.valueOf(m);
BigInteger n2 = BigInteger.valueOf(n);
BigInteger y3 = y2;
BigInteger c = BigInteger.valueOf(2);
BigInteger c2 = BigInteger.valueOf(1);
for(int i = 0; i < binary.length(); i++) {
x3 = x2.multiply(c);
x2 = x3;
y3 = y2.multiply(y2).mod(n2);
y2 = y3;
if (binary.charAt(i) == '1') {
x3 = x2.add(c2);
x2 = x3;
y3 = y2.multiply(m2).mod(n2);
y2 = y3;
}
}
return y3;
}
}
public class RSADemo {
public static void main(String[] args) {
ProducePrime ProducePrime = new ProducePrime();
Division Division = new Division();
EuclideanAlgorithm euclideanAlgorithm = new EuclideanAlgorithm();
MoChongFuPingFang moChongFuPingFang = new MoChongFuPingFang();
PingFangCheng pingFangCheng = new PingFangCheng();
MillerRabin MillerRabin = new MillerRabin();
Scanner scanner = new Scanner(System.in);
System.out.println("/****************/");
System.out.println("RSA算法加密解密實現");
System.out.println("/****************/");
int p = 1009;//ProducePrime.Prime1();
//int p = ProducePrime.Prime1();
System.out.println("輸出滿足要求的第一個素數p:" + p);
int q = 997;//ProducePrime.Prime2();
//int q = ProducePrime.Prime2();
System.out.println("輸出滿足要求的第二個素數q:" + q);
System.out.println("/****************/");
long n = (long)p * q;//避免越界，強制轉型
long fn = (long)(p - 1) * (q - 1);
System.out.println("n=p*q=" + n);
System.out.println("f(n)=(p-1)*(q-1)=" + fn);
System.out.println("/****************/");
Division.divison(p);
System.out.println("/****************/");
int p2 = (int)p;
boolean flag = MillerRabin.MillerRabin2(p2);
System.out.println("Miller-Rabin算法檢測標志符為:" + flag);
System.out.println("/****************/");
System.out.println("請輸入公鑰e:");
long e = scanner.nextLong();
BigInteger e3 = BigInteger.valueOf(e);
BigInteger fn2 = BigInteger.valueOf(fn);
System.out.println("公鑰e與fn的最大公約數為:" + euclideanAlgorithm.exgcd(fn2, e3));//最大公約數
euclideanAlgorithm.XY(fn2, e3);
System.out.println("/****************/");
//加密明文
System.out.println("加密開始:");
System.out.println("請輸入明文m:");
long m = scanner.nextLong();
System.out.println("請輸入公鑰e:");
long e2 = scanner.nextLong();
System.out.println("加密后的密文m2為:" + moChongFuPingFang.Encryption(m, e2, n));
System.out.println("/****************/");
//解密密文
System.out.println("解密開始:");
System.out.println("請輸入密文m2:");
long m2 = scanner.nextLong();
System.out.println("請輸入密鑰d:");
long d2 = scanner.nextLong();
System.out.println("解密后的明文為:" + pingFangCheng.Decryption(m2, d2, n));
}
}
- 大素數的運算使用BigInteger類解決數據長度溢出的問題。
- 自動獲取的大素數用來加解密會失敗，多番檢查也沒找到問題所在。
- 自定義的素數p = 1009，q = 997，公鑰e = 17可以加解密成功。
- 如果您有興趣，不妨試試解決這個問題，手動狗頭。
