RSA 公钥加密算法

Posted 2020-09-08 郑兴鹏

RSA公钥加密算法是1977年由Ron Rivest、Adi Shamirh和LenAdleman在（美国麻省理工学院）开发的。

    这个算法的名字也是他们三个人名字首字母，RSA算法基于一个十分简单的数论事实：

    将两个大素数相乘十分容易，但想要对其乘积进行因式分解却极其困难，因此可以将乘积公开作为加密密钥。

package rsa; 
import java.math.BigInteger; 

public class RSA { 
 private long p,q,e,d,n; 
 public RSA(){ 
  int pIndex = (int)(Math.random()*10); 
  int qIndex; 
  int eIndex; 
  do{ 
   qIndex = (int)(Math.random()*10); 
  } 
  while(qIndex==pIndex); 
  do{ 
   eIndex = (int)(Math.random()*10); 
  } 
  while(eIndex==pIndex||eIndex==pIndex); 
  p = 1033; 
  q = 2017; 
  e = 29437; 
  n = p*q; 
  d = calculateD(); 
 } 
 private long calculateD(){ 
  long t0 = 0,t1 = 1,t2 = -1; 
  long r0 = (p-1)*(q-1), m = r0,r1 = e ,r2 = -1; 
  do{ 
   long q = r0/r1; 
   r2 = r0-r1*q; 
   if(r2==0)break; 
   t2 = t0 - t1*q; 
   while(t2<0){ 
    t2+=m; 
   } 
   if(t2>=m){ 
    t2 %= m; 
   }     
   r0 = r1; 
   r1 = r2; 
   t0 = t1; 
   t1 = t2; 
  }while(r2!=0); 
  if(r1!=1){ 
   return 0; 
  } 
  else{ 
   return t2; 
  } 
 } 
  
 public long getE() { 
  return e; 
 } 
 public long getN() { 
  return n; 
 } 
 public long getD() { 
  return d; 
 } 
 public BigInteger encode(BigInteger data){ 
  return pow(data,d).mod(new BigInteger(n+"")); 
 } 
 public BigInteger decode(BigInteger code){ 
  return pow(code,e).mod(new BigInteger(n+"")); 
 } 
 public BigInteger pow(BigInteger data,long p){ 
  data = data.pow((int)p); 
  return data; 
 } 
 public static void main(String args[]){ 
  RSA rsa = new RSA(); 
   
  BigInteger data = new BigInteger("222222"); 
  long oldtime = System.currentTimeMillis(); 
  BigInteger code = rsa.encode(data); 
  long newtime = System.currentTimeMillis(); 
  double codetime = ((double)(newtime-oldtime))/1000; 
  oldtime = System.currentTimeMillis(); 
  BigInteger decode = rsa.decode(code); 
  newtime = System.currentTimeMillis(); 
  double decodetime = ((double)(newtime-oldtime))/1000; 
  System.out.println("privateKey:"+rsa.d); 
  System.out.println("publickKey:"+rsa.e); 
  System.out.println("N:"+rsa.n); 
  System.out.println("data:"+data); 
  System.out.println("code:"+code+" time:"+codetime); 
  System.out.println("decode:"+decode+" time:"+decodetime); 

 } 

}