关于Web登录使用RSA对密码进行加密解密过程

公司需求，需要安全的通信，md5以及AES加密相对于RSA的加密性还是稍差了，所以首选了RSA这种加密方式。

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，但那时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。首先简单说一下RSA加密方式（借用知乎上面的理解，通俗易懂）：

A要发消息给B

B有一个盒子（公钥）一把锁（私钥）

A拿到盒子放消息进去，上锁。

快递给B，只有B能打开盒子。

即使中途被劫也无法打开盒子。

本文demo的实现逻辑如下：

1、在后台服务端构造一个产生特定的密钥对方法；

2、在jsp页面里通过调用后台服务端方法，产生密钥对，并将私钥以及公钥中获取到的publicExponent,Modulus保存session中；

3、在js中使用公钥中获取到的publicExponent,Modulus,重新生成一个key;

4、使用key来加密密码信息；

5、提交信息到后台，后台获取到加密信息，通过本地存储的私钥进行解密，安全地获得需要的信息。

下面直接贴代码了：

首先我创建的是一个maven项目，所以要添加一些依赖库，pom.xml配置如下

RSA工具类（主要构建rsa密钥对的工具类）：

package com.vernon.utils;

import java.math.BigInteger;
import java.security.KeyFactory;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import java.security.NoSuchAlgorithmException;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;
import java.security.spec.RSAPrivateKeySpec;
import java.security.spec.RSAPublicKeySpec;
import java.util.HashMap;
import javax.crypto.Cipher;

public class RSAUtils {
    /**
     * 生成公钥和私钥
     * @throws NoSuchAlgorithmException
     *
     */
    public static HashMap, Object> getKeys() throws NoSuchAlgorithmException{
        HashMap, Object> map = new HashMap, Object>();
        KeyPairGenerator keyPairGen = KeyPairGenerator.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
        keyPairGen.initialize(1024);
        KeyPair keyPair = keyPairGen.generateKeyPair();
        RSAPublicKey publicKey = (RSAPublicKey) keyPair.getPublic();
        RSAPrivateKey privateKey = (RSAPrivateKey) keyPair.getPrivate();
        map.put("public", publicKey);
        map.put("private", privateKey);
        return map;
    }
    /**
     * 使用模和指数生成RSA公钥
     *
     *
     * @param modulus
     *            模
     * @param exponent
     *            指数
     * @return
     */
    public static RSAPublicKey getPublicKey(String modulus, String exponent) {
        try {
            BigInteger b1 = new BigInteger(modulus);
            BigInteger b2 = new BigInteger(exponent);
            KeyFactory keyFactory = KeyFactory.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
            RSAPublicKeySpec keySpec = new RSAPublicKeySpec(b1, b2);
            return (RSAPublicKey) keyFactory.generatePublic(keySpec);
        } catch (Exception e) {
            e.printStackTrace();
            return null;
        }
    }

    /**
     * 使用模和指数生成RSA私钥

     * /None/NoPadding】
     *
     * @param modulus
     *            模
     * @param exponent
     *            指数
     * @return
     */
    public static RSAPrivateKey getPrivateKey(String modulus, String exponent) {
        try {
            BigInteger b1 = new BigInteger(modulus);
            BigInteger b2 = new BigInteger(exponent);
            KeyFactory keyFactory = KeyFactory.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
            RSAPrivateKeySpec keySpec = new RSAPrivateKeySpec(b1, b2);
            return (RSAPrivateKey) keyFactory.generatePrivate(keySpec);
        } catch (Exception e) {
            e.printStackTrace();
            return null;
        }
    }

    /**
     * 公钥加密
     *
     * @param data
     * @param publicKey
     * @return
     * @throws Exception
     */
    public static String encryptByPublicKey(String data, RSAPublicKey publicKey)
            throws Exception {
        Cipher cipher = Cipher.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
        cipher.init(Cipher.ENCRYPT_MODE, publicKey);
        // 模长
        int key_len = publicKey.getModulus().bitLength() / 8;
        // 加密数据长度 <= 模长-11
        String[] datas = splitString(data, key_len - 11);
        String mi = "";
        //如果明文长度大于模长-11则要分组加密
        for (String s : datas) {
            mi += bcd2Str(cipher.doFinal(s.getBytes()));
        }
        return mi;
    }

    /**
     * 私钥解密
     *
     * @param data
     * @param privateKey
     * @return
     * @throws Exception
     */
    public static String decryptByPrivateKey(String data, RSAPrivateKey privateKey)
            throws Exception {
        Cipher cipher = Cipher.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
        cipher.init(Cipher.DECRYPT_MODE, privateKey);
        //模长
        int key_len = privateKey.getModulus().bitLength() / 8;
        byte[] bytes = data.getBytes();
        byte[] bcd = ASCII_To_BCD(bytes, bytes.length);
        //System.err.println(bcd.length);
        //如果密文长度大于模长则要分组解密
        String ming = "";
        byte[][] arrays = splitArray(bcd, key_len);
        for(byte[] arr : arrays){
            ming += new String(cipher.doFinal(arr));
        }

        return new  StringBuilder(ming).reverse().toString();
    }
    /**
     * ASCII码转BCD码
     *
     */
    public static byte[] ASCII_To_BCD(byte[] ascii, int asc_len) {
        byte[] bcd = new byte[asc_len / 2];
        int j = 0;
        for (int i = 0; i < (asc_len + 1) / 2; i++) {
            bcd[i] = asc_to_bcd(ascii[j++]);
            bcd[i] = (byte) (((j >= asc_len) ? 0x00 : asc_to_bcd(ascii[j++])) + (bcd[i] << 4));
        }
        return bcd;
    }
    public static byte asc_to_bcd(byte asc) {
        byte bcd;

        if ((asc >= '0') && (asc <= '9'))
            bcd = (byte) (asc - '0');
        else if ((asc >= 'A') && (asc <= 'F'))
            bcd = (byte) (asc - 'A' + 10);
        else if ((asc >= 'a') && (asc <= 'f'))
            bcd = (byte) (asc - 'a' + 10);
        else
            bcd = (byte) (asc - 48);
        return bcd;
    }
    /**
     * BCD转字符串
     */
    public static String bcd2Str(byte[] bytes) {
        char temp[] = new char[bytes.length * 2], val;

        for (int i = 0; i < bytes.length; i++) {
            val = (char) (((bytes[i] & 0xf0) >> 4) & 0x0f);
            temp[i * 2] = (char) (val > 9 ? val + 'A' - 10 : val + '0');

            val = (char) (bytes[i] & 0x0f);
            temp[i * 2 + 1] = (char) (val > 9 ? val + 'A' - 10 : val + '0');
        }
        return new String(temp);
    }
    /**
     * 拆分字符串
     */
    public static String[] splitString(String string, int len) {
        int x = string.length() / len;
        int y = string.length() % len;
        int z = 0;
        if (y != 0) {
            z = 1;
        }
        String[] strings = new String[x + z];
        String str = "";
        for (int i=0; i; i++) {
            if (i==x+z-1 && y!=0) {
                str = string.substring(i*len, i*len+y);
            }else{
                str = string.substring(i*len, i*len+len);
            }
            strings[i] = str;
        }
        return strings;
    }
    /**
     *拆分数组
     */
    public static byte[][] splitArray(byte[] data,int len){
        int x = data.length / len;
        int y = data.length % len;
        int z = 0;
        if(y!=0){
            z = 1;
        }
        byte[][] arrays = new byte[x+z][];
        byte[] arr;
        for(int i=0; i; i++){
            arr = new byte[len];
            if(i==x+z-1 && y!=0){
                System.arraycopy(data, i*len, arr, 0, y);
            }else{
                System.arraycopy(data, i*len, arr, 0, len);
            }
            arrays[i] = arr;
        }
        return arrays;
    }
    public static void main(String[] args) throws Exception{
        HashMap, Object> map = getKeys();
        //生成公钥和私钥
        RSAPublicKey publicKey = (RSAPublicKey) map.get("public");
        RSAPrivateKey privateKey = (RSAPrivateKey) map.get("private");

        //模
        String modulus = publicKey.getModulus().toString();
        System.out.println("pubkey modulus="+modulus);
        //公钥指数
        String public_exponent = publicKey.getPublicExponent().toString();
        System.out.println("pubkey exponent="+public_exponent);
        //私钥指数
        String private_exponent = privateKey.getPrivateExponent().toString();
        System.out.println("private exponent="+private_exponent);
        //明文
        String ming = "111";
        //使用模和指数生成公钥和私钥
        RSAPublicKey pubKey = RSAUtils.getPublicKey(modulus, public_exponent);
        RSAPrivateKey priKey = RSAUtils.getPrivateKey(modulus, private_exponent);
        //加密后的密文
        String mi = RSAUtils.encryptByPublicKey(ming, pubKey);
        System.err.println("mi="+mi);
        //解密后的明文
        String ming2 = RSAUtils.decryptByPrivateKey(mi, priKey);
        System.err.println("ming2="+ming2);
    }
}

然后是Java后台处理的Servlet代码，LoginAction：

package com.vernon.servlet;


import com.vernon.utils.RSAUtils;

import java.io.IOException;

import java.security.interfaces.RSAPrivateKey;


import javax.servlet.ServletException;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;



/**
 * MyEclipse Struts Creation date: 06-28-2008
 *
 * XDoclet definition:
 *
 * @struts.action path="/login" name="loginForm" input="/login.jsp"
 *                scope="request" validate="true"
 * @struts.action-forward name="error" path="/error.jsp"
 * @struts.action-forward name="success" path="/success.jsp"
 */
public class LoginAction extends HttpServlet {
    /*
     * Generated Methods
     */


    @Override
    protected void doGet(HttpServletRequest req, HttpServletResponse resp) {

        try {
            execute(req,resp);

        } catch (Exception e) {
            e.printStackTrace();
        }

    }

    @Override
    protected void doPost(HttpServletRequest req, HttpServletResponse resp) throws ServletException, IOException {
        doGet(req,resp);
    }

    /**
     * Method execute
     *
     * @param request
     * @param response
     * @return ActionForward
     */



    public boolean execute(HttpServletRequest request,
                           HttpServletResponse response) throws Exception {
        String password = request.getParameter("password");
        RSAPrivateKey privateKey = (RSAPrivateKey)request.getSession().getAttribute("privateKey");
        String descrypedPwd = RSAUtils.decryptByPrivateKey(password, privateKey); //解密后的密码,password是提交过来的密码

        System.out.println("======解码前："+password+"===========");
        System.out.println("======解码后："+descrypedPwd+"===========");


        return true;
    }


}

登录页（没做样式了，本文关键是如何实现rsa加密解密过程）：

<%@ page import="com.vernon.utils.RSAUtils" %>
<%@ page import="java.security.interfaces.RSAPublicKey" %>
<%@ page import="java.security.interfaces.RSAPrivateKey" %>
<%@ page import="java.util.HashMap" %>
<%@ page language="java" pageEncoding="UTF-8" contentType="text/html; charset=UTF-8"%>

HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html:html lang="true">
  
    
      
      
    
  

  
  
method="post" name="loginForm" target=_blank>
    border="0">

                            
                                                                                


          用户名:
        

          type='text' name="txtUsername" id="txtUsername" style='width:400px'/>
        



          密码:
        

          type='text' name="txtPassword" id="txtPassword" style='width:400px' value="my passwd"/>
        



          验证码:
        

          type='text' name="txtRandCode" id="txtRandCode" style='width:400px'/>
        


colspan="2" align="center">
          type="button" value="SUBMIT" οnclick="login();" />
        


  
  
html:html>

贴出js代码吧，网上找的

/*
 * RSA, a suite of routines for performing RSA public-key computations in JavaScript.
 * Copyright 1998-2005 David Shapiro.
 * Dave Shapiro
 * [email protected] 
 * changed by Fuchun, 2010-05-06
 * [email protected]
 */

(function($w) {

if(typeof $w.RSAUtils === 'undefined')
   var RSAUtils = $w.RSAUtils = {};

var biRadixBase = 2;
var biRadixBits = 16;
var bitsPerDigit = biRadixBits;
var biRadix = 1 << 16; // = 2^16 = 65536
var biHalfRadix = biRadix >>> 1;
var biRadixSquared = biRadix * biRadix;
var maxDigitVal = biRadix - 1;
var maxInteger = 9999999999999998;

//maxDigits:
//Change this to accommodate your largest number size. Use setMaxDigits()
//to change it!
//
//In general, if you're working with numbers of size N bits, you'll need 2*N
//bits of storage. Each digit holds 16 bits. So, a 1024-bit key will need
//
//1024 * 2 / 16 = 128 digits of storage.
//
var maxDigits;
var ZERO_ARRAY;
var bigZero, bigOne;

var BigInt = $w.BigInt = function(flag) {
   if (typeof flag == "boolean" && flag == true) {
      this.digits = null;
   } else {
      this.digits = ZERO_ARRAY.slice(0);
   }
   this.isNeg = false;
};

RSAUtils.setMaxDigits = function(value) {
   maxDigits = value;
   ZERO_ARRAY = new Array(maxDigits);
   for (var iza = 0; iza < ZERO_ARRAY.length; iza++) ZERO_ARRAY[iza] = 0;
   bigZero = new BigInt();
   bigOne = new BigInt();
   bigOne.digits[0] = 1;
};
RSAUtils.setMaxDigits(20);

//The maximum number of digits in base 10 you can convert to an
//integer without JavaScript throwing up on you.
var dpl10 = 15;

RSAUtils.biFromNumber = function(i) {
   var result = new BigInt();
   result.isNeg = i < 0;
   i = Math.abs(i);
   var j = 0;
   while (i > 0) {
      result.digits[j++] = i & maxDigitVal;
      i = Math.floor(i / biRadix);
   }
   return result;
};

//lr10 = 10 ^ dpl10
var lr10 = RSAUtils.biFromNumber(1000000000000000);

RSAUtils.biFromDecimal = function(s) {
   var isNeg = s.charAt(0) == '-';
   var i = isNeg ? 1 : 0;
   var result;
   // Skip leading zeros.
   while (i < s.length && s.charAt(i) == '0') ++i;
   if (i == s.length) {
      result = new BigInt();
   }
   else {
      var digitCount = s.length - i;
      var fgl = digitCount % dpl10;
      if (fgl == 0) fgl = dpl10;
      result = RSAUtils.biFromNumber(Number(s.substr(i, fgl)));
      i += fgl;
      while (i < s.length) {
         result = RSAUtils.biAdd(RSAUtils.biMultiply(result, lr10),
               RSAUtils.biFromNumber(Number(s.substr(i, dpl10))));
         i += dpl10;
      }
      result.isNeg = isNeg;
   }
   return result;
};

RSAUtils.biCopy = function(bi) {
   var result = new BigInt(true);
   result.digits = bi.digits.slice(0);
   result.isNeg = bi.isNeg;
   return result;
};

RSAUtils.reverseStr = function(s) {
   var result = "";
   for (var i = s.length - 1; i > -1; --i) {
      result += s.charAt(i);
   }
   return result;
};

var hexatrigesimalToChar = [
   '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
   'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j',
   'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't',
   'u', 'v', 'w', 'x', 'y', 'z'
];

RSAUtils.biToString = function(x, radix) { // 2 <= radix <= 36
   var b = new BigInt();
   b.digits[0] = radix;
   var qr = RSAUtils.biDivideModulo(x, b);
   var result = hexatrigesimalToChar[qr[1].digits[0]];
   while (RSAUtils.biCompare(qr[0], bigZero) == 1) {
      qr = RSAUtils.biDivideModulo(qr[0], b);
      digit = qr[1].digits[0];
      result += hexatrigesimalToChar[qr[1].digits[0]];
   }
   return (x.isNeg ? "-" : "") + RSAUtils.reverseStr(result);
};

RSAUtils.biToDecimal = function(x) {
   var b = new BigInt();
   b.digits[0] = 10;
   var qr = RSAUtils.biDivideModulo(x, b);
   var result = String(qr[1].digits[0]);
   while (RSAUtils.biCompare(qr[0], bigZero) == 1) {
      qr = RSAUtils.biDivideModulo(qr[0], b);
      result += String(qr[1].digits[0]);
   }
   return (x.isNeg ? "-" : "") + RSAUtils.reverseStr(result);
};

var hexToChar = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        'a', 'b', 'c', 'd', 'e', 'f'];

RSAUtils.digitToHex = function(n) {
   var mask = 0xf;
   var result = "";
   for (i = 0; i < 4; ++i) {
      result += hexToChar[n & mask];
      n >>>= 4;
   }
   return RSAUtils.reverseStr(result);
};

RSAUtils.biToHex = function(x) {
   var result = "";
   var n = RSAUtils.biHighIndex(x);
   for (var i = RSAUtils.biHighIndex(x); i > -1; --i) {
      result += RSAUtils.digitToHex(x.digits[i]);
   }
   return result;
};

RSAUtils.charToHex = function(c) {
   var ZERO = 48;
   var NINE = ZERO + 9;
   var littleA = 97;
   var littleZ = littleA + 25;
   var bigA = 65;
   var bigZ = 65 + 25;
   var result;

   if (c >= ZERO && c <= NINE) {
      result = c - ZERO;
   } else if (c >= bigA && c <= bigZ) {
      result = 10 + c - bigA;
   } else if (c >= littleA && c <= littleZ) {
      result = 10 + c - littleA;
   } else {
      result = 0;
   }
   return result;
};

RSAUtils.hexToDigit = function(s) {
   var result = 0;
   var sl = Math.min(s.length, 4);
   for (var i = 0; i < sl; ++i) {
      result <<= 4;
      result |= RSAUtils.charToHex(s.charCodeAt(i));
   }
   return result;
};

RSAUtils.biFromHex = function(s) {
   var result = new BigInt();
   var sl = s.length;
   for (var i = sl, j = 0; i > 0; i -= 4, ++j) {
      result.digits[j] = RSAUtils.hexToDigit(s.substr(Math.max(i - 4, 0), Math.min(i, 4)));
   }
   return result;
};

RSAUtils.biFromString = function(s, radix) {
   var isNeg = s.charAt(0) == '-';
   var istop = isNeg ? 1 : 0;
   var result = new BigInt();
   var place = new BigInt();
   place.digits[0] = 1; // radix^0
   for (var i = s.length - 1; i >= istop; i--) {
      var c = s.charCodeAt(i);
      var digit = RSAUtils.charToHex(c);
      var biDigit = RSAUtils.biMultiplyDigit(place, digit);
      result = RSAUtils.biAdd(result, biDigit);
      place = RSAUtils.biMultiplyDigit(place, radix);
   }
   result.isNeg = isNeg;
   return result;
};

RSAUtils.biDump = function(b) {
   return (b.isNeg ? "-" : "") + b.digits.join(" ");
};

RSAUtils.biAdd = function(x, y) {
   var result;

   if (x.isNeg != y.isNeg) {
      y.isNeg = !y.isNeg;
      result = RSAUtils.biSubtract(x, y);
      y.isNeg = !y.isNeg;
   }
   else {
      result = new BigInt();
      var c = 0;
      var n;
      for (var i = 0; i < x.digits.length; ++i) {
         n = x.digits[i] + y.digits[i] + c;
         result.digits[i] = n % biRadix;
         c = Number(n >= biRadix);
      }
      result.isNeg = x.isNeg;
   }
   return result;
};

RSAUtils.biSubtract = function(x, y) {
   var result;
   if (x.isNeg != y.isNeg) {
      y.isNeg = !y.isNeg;
      result = RSAUtils.biAdd(x, y);
      y.isNeg = !y.isNeg;
   } else {
      result = new BigInt();
      var n, c;
      c = 0;
      for (var i = 0; i < x.digits.length; ++i) {
         n = x.digits[i] - y.digits[i] + c;
         result.digits[i] = n % biRadix;
         // Stupid non-conforming modulus operation.
         if (result.digits[i] < 0) result.digits[i] += biRadix;
         c = 0 - Number(n < 0);
      }
      // Fix up the negative sign, if any.
      if (c == -1) {
         c = 0;
         for (var i = 0; i < x.digits.length; ++i) {
            n = 0 - result.digits[i] + c;
            result.digits[i] = n % biRadix;
            // Stupid non-conforming modulus operation.
            if (result.digits[i] < 0) result.digits[i] += biRadix;
            c = 0 - Number(n < 0);
         }
         // Result is opposite sign of arguments.
         result.isNeg = !x.isNeg;
      } else {
         // Result is same sign.
         result.isNeg = x.isNeg;
      }
   }
   return result;
};

RSAUtils.biHighIndex = function(x) {
   var result = x.digits.length - 1;
   while (result > 0 && x.digits[result] == 0) --result;
   return result;
};

RSAUtils.biNumBits = function(x) {
   var n = RSAUtils.biHighIndex(x);
   var d = x.digits[n];
   var m = (n + 1) * bitsPerDigit;
   var result;
   for (result = m; result > m - bitsPerDigit; --result) {
      if ((d & 0x8000) != 0) break;
      d <<= 1;
   }
   return result;
};

RSAUtils.biMultiply = function(x, y) {
   var result = new BigInt();
   var c;
   var n = RSAUtils.biHighIndex(x);
   var t = RSAUtils.biHighIndex(y);
   var u, uv, k;

   for (var i = 0; i <= t; ++i) {
      c = 0;
      k = i;
      for (j = 0; j <= n; ++j, ++k) {
         uv = result.digits[k] + x.digits[j] * y.digits[i] + c;
         result.digits[k] = uv & maxDigitVal;
         c = uv >>> biRadixBits;
         //c = Math.floor(uv / biRadix);
      }
      result.digits[i + n + 1] = c;
   }
   // Someone give me a logical xor, please.
   result.isNeg = x.isNeg != y.isNeg;
   return result;
};

RSAUtils.biMultiplyDigit = function(x, y) {
   var n, c, uv;

   result = new BigInt();
   n = RSAUtils.biHighIndex(x);
   c = 0;
   for (var j = 0; j <= n; ++j) {
      uv = result.digits[j] + x.digits[j] * y + c;
      result.digits[j] = uv & maxDigitVal;
      c = uv >>> biRadixBits;
      //c = Math.floor(uv / biRadix);
   }
   result.digits[1 + n] = c;
   return result;
};

RSAUtils.arrayCopy = function(src, srcStart, dest, destStart, n) {
   var m = Math.min(srcStart + n, src.length);
   for (var i = srcStart, j = destStart; i < m; ++i, ++j) {
      dest[j] = src[i];
   }
};

var highBitMasks = [0x0000, 0x8000, 0xC000, 0xE000, 0xF000, 0xF800,
        0xFC00, 0xFE00, 0xFF00, 0xFF80, 0xFFC0, 0xFFE0,
        0xFFF0, 0xFFF8, 0xFFFC, 0xFFFE, 0xFFFF];

RSAUtils.biShiftLeft = function(x, n) {
   var digitCount = Math.floor(n / bitsPerDigit);
   var result = new BigInt();
   RSAUtils.arrayCopy(x.digits, 0, result.digits, digitCount,
             result.digits.length - digitCount);
   var bits = n % bitsPerDigit;
   var rightBits = bitsPerDigit - bits;
   for (var i = result.digits.length - 1, i1 = i - 1; i > 0; --i, --i1) {
      result.digits[i] = ((result.digits[i] << bits) & maxDigitVal) |
                         ((result.digits[i1] & highBitMasks[bits]) >>>
                          (rightBits));
   }
   result.digits[0] = ((result.digits[i] << bits) & maxDigitVal);
   result.isNeg = x.isNeg;
   return result;
};

var lowBitMasks = [0x0000, 0x0001, 0x0003, 0x0007, 0x000F, 0x001F,
        0x003F, 0x007F, 0x00FF, 0x01FF, 0x03FF, 0x07FF,
        0x0FFF, 0x1FFF, 0x3FFF, 0x7FFF, 0xFFFF];

RSAUtils.biShiftRight = function(x, n) {
   var digitCount = Math.floor(n / bitsPerDigit);
   var result = new BigInt();
   RSAUtils.arrayCopy(x.digits, digitCount, result.digits, 0,
             x.digits.length - digitCount);
   var bits = n % bitsPerDigit;
   var leftBits = bitsPerDigit - bits;
   for (var i = 0, i1 = i + 1; i < result.digits.length - 1; ++i, ++i1) {
      result.digits[i] = (result.digits[i] >>> bits) |
                         ((result.digits[i1] & lowBitMasks[bits]) << leftBits);
   }
   result.digits[result.digits.length - 1] >>>= bits;
   result.isNeg = x.isNeg;
   return result;
};

RSAUtils.biMultiplyByRadixPower = function(x, n) {
   var result = new BigInt();
   RSAUtils.arrayCopy(x.digits, 0, result.digits, n, result.digits.length - n);
   return result;
};

RSAUtils.biDivideByRadixPower = function(x, n) {
   var result = new BigInt();
   RSAUtils.arrayCopy(x.digits, n, result.digits, 0, result.digits.length - n);
   return result;
};

RSAUtils.biModuloByRadixPower = function(x, n) {
   var result = new BigInt();
   RSAUtils.arrayCopy(x.digits, 0, result.digits, 0, n);
   return result;
};

RSAUtils.biCompare = function(x, y) {
   if (x.isNeg != y.isNeg) {
      return 1 - 2 * Number(x.isNeg);
   }
   for (var i = x.digits.length - 1; i >= 0; --i) {
      if (x.digits[i] != y.digits[i]) {
         if (x.isNeg) {
            return 1 - 2 * Number(x.digits[i] > y.digits[i]);
         } else {
            return 1 - 2 * Number(x.digits[i] < y.digits[i]);
         }
      }
   }
   return 0;
};

RSAUtils.biDivideModulo = function(x, y) {
   var nb = RSAUtils.biNumBits(x);
   var tb = RSAUtils.biNumBits(y);
   var origYIsNeg = y.isNeg;
   var q, r;
   if (nb < tb) {
      // |x| < |y|
      if (x.isNeg) {
         q = RSAUtils.biCopy(bigOne);
         q.isNeg = !y.isNeg;
         x.isNeg = false;
         y.isNeg = false;
         r = biSubtract(y, x);
         // Restore signs, 'cause they're references.
         x.isNeg = true;
         y.isNeg = origYIsNeg;
      } else {
         q = new BigInt();
         r = RSAUtils.biCopy(x);
      }
      return [q, r];
   }

   q = new BigInt();
   r = x;

   // Normalize Y.
   var t = Math.ceil(tb / bitsPerDigit) - 1;
   var lambda = 0;
   while (y.digits[t] < biHalfRadix) {
      y = RSAUtils.biShiftLeft(y, 1);
      ++lambda;
      ++tb;
      t = Math.ceil(tb / bitsPerDigit) - 1;
   }
   // Shift r over to keep the quotient constant. We'll shift the
   // remainder back at the end.
   r = RSAUtils.biShiftLeft(r, lambda);
   nb += lambda; // Update the bit count for x.
   var n = Math.ceil(nb / bitsPerDigit) - 1;

   var b = RSAUtils.biMultiplyByRadixPower(y, n - t);
   while (RSAUtils.biCompare(r, b) != -1) {
      ++q.digits[n - t];
      r = RSAUtils.biSubtract(r, b);
   }
   for (var i = n; i > t; --i) {
    var ri = (i >= r.digits.length) ? 0 : r.digits[i];
    var ri1 = (i - 1 >= r.digits.length) ? 0 : r.digits[i - 1];
    var ri2 = (i - 2 >= r.digits.length) ? 0 : r.digits[i - 2];
    var yt = (t >= y.digits.length) ? 0 : y.digits[t];
    var yt1 = (t - 1 >= y.digits.length) ? 0 : y.digits[t - 1];
      if (ri == yt) {
         q.digits[i - t - 1] = maxDigitVal;
      } else {
         q.digits[i - t - 1] = Math.floor((ri * biRadix + ri1) / yt);
      }

      var c1 = q.digits[i - t - 1] * ((yt * biRadix) + yt1);
      var c2 = (ri * biRadixSquared) + ((ri1 * biRadix) + ri2);
      while (c1 > c2) {
         --q.digits[i - t - 1];
         c1 = q.digits[i - t - 1] * ((yt * biRadix) | yt1);
         c2 = (ri * biRadix * biRadix) + ((ri1 * biRadix) + ri2);
      }

      b = RSAUtils.biMultiplyByRadixPower(y, i - t - 1);
      r = RSAUtils.biSubtract(r, RSAUtils.biMultiplyDigit(b, q.digits[i - t - 1]));
      if (r.isNeg) {
         r = RSAUtils.biAdd(r, b);
         --q.digits[i - t - 1];
      }
   }
   r = RSAUtils.biShiftRight(r, lambda);
   // Fiddle with the signs and stuff to make sure that 0 <= r < y.
   q.isNeg = x.isNeg != origYIsNeg;
   if (x.isNeg) {
      if (origYIsNeg) {
         q = RSAUtils.biAdd(q, bigOne);
      } else {
         q = RSAUtils.biSubtract(q, bigOne);
      }
      y = RSAUtils.biShiftRight(y, lambda);
      r = RSAUtils.biSubtract(y, r);
   }
   // Check for the unbelievably stupid degenerate case of r == -0.
   if (r.digits[0] == 0 && RSAUtils.biHighIndex(r) == 0) r.isNeg = false;

   return [q, r];
};

RSAUtils.biDivide = function(x, y) {
   return RSAUtils.biDivideModulo(x, y)[0];
};

RSAUtils.biModulo = function(x, y) {
   return RSAUtils.biDivideModulo(x, y)[1];
};

RSAUtils.biMultiplyMod = function(x, y, m) {
   return RSAUtils.biModulo(RSAUtils.biMultiply(x, y), m);
};

RSAUtils.biPow = function(x, y) {
   var result = bigOne;
   var a = x;
   while (true) {
      if ((y & 1) != 0) result = RSAUtils.biMultiply(result, a);
      y >>= 1;
      if (y == 0) break;
      a = RSAUtils.biMultiply(a, a);
   }
   return result;
};

RSAUtils.biPowMod = function(x, y, m) {
   var result = bigOne;
   var a = x;
   var k = y;
   while (true) {
      if ((k.digits[0] & 1) != 0) result = RSAUtils.biMultiplyMod(result, a, m);
      k = RSAUtils.biShiftRight(k, 1);
      if (k.digits[0] == 0 && RSAUtils.biHighIndex(k) == 0) break;
      a = RSAUtils.biMultiplyMod(a, a, m);
   }
   return result;
};


$w.BarrettMu = function(m) {
   this.modulus = RSAUtils.biCopy(m);
   this.k = RSAUtils.biHighIndex(this.modulus) + 1;
   var b2k = new BigInt();
   b2k.digits[2 * this.k] = 1; // b2k = b^(2k)
   this.mu = RSAUtils.biDivide(b2k, this.modulus);
   this.bkplus1 = new BigInt();
   this.bkplus1.digits[this.k + 1] = 1; // bkplus1 = b^(k+1)
   this.modulo = BarrettMu_modulo;
   this.multiplyMod = BarrettMu_multiplyMod;
   this.powMod = BarrettMu_powMod;
};

function BarrettMu_modulo(x) {
   var $dmath = RSAUtils;
   var q1 = $dmath.biDivideByRadixPower(x, this.k - 1);
   var q2 = $dmath.biMultiply(q1, this.mu);
   var q3 = $dmath.biDivideByRadixPower(q2, this.k + 1);
   var r1 = $dmath.biModuloByRadixPower(x, this.k + 1);
   var r2term = $dmath.biMultiply(q3, this.modulus);
   var r2 = $dmath.biModuloByRadixPower(r2term, this.k + 1);
   var r = $dmath.biSubtract(r1, r2);
   if (r.isNeg) {
      r = $dmath.biAdd(r, this.bkplus1);
   }
   var rgtem = $dmath.biCompare(r, this.modulus) >= 0;
   while (rgtem) {
      r = $dmath.biSubtract(r, this.modulus);
      rgtem = $dmath.biCompare(r, this.modulus) >= 0;
   }
   return r;
}

function BarrettMu_multiplyMod(x, y) {
   /*
   x = this.modulo(x);
   y = this.modulo(y);
   */
   var xy = RSAUtils.biMultiply(x, y);
   return this.modulo(xy);
}

function BarrettMu_powMod(x, y) {
   var result = new BigInt();
   result.digits[0] = 1;
   var a = x;
   var k = y;
   while (true) {
      if ((k.digits[0] & 1) != 0) result = this.multiplyMod(result, a);
      k = RSAUtils.biShiftRight(k, 1);
      if (k.digits[0] == 0 && RSAUtils.biHighIndex(k) == 0) break;
      a = this.multiplyMod(a, a);
   }
   return result;
}

var RSAKeyPair = function(encryptionExponent, decryptionExponent, modulus) {
   var $dmath = RSAUtils;
   this.e = $dmath.biFromHex(encryptionExponent);
   this.d = $dmath.biFromHex(decryptionExponent);
   this.m = $dmath.biFromHex(modulus);
   // We can do two bytes per digit, so
   // chunkSize = 2 * (number of digits in modulus - 1).
   // Since biHighIndex returns the high index, not the number of digits, 1 has
   // already been subtracted.
   this.chunkSize = 2 * $dmath.biHighIndex(this.m);
   this.radix = 16;
   this.barrett = new $w.BarrettMu(this.m);
};

RSAUtils.getKeyPair = function(encryptionExponent, decryptionExponent, modulus) {
   return new RSAKeyPair(encryptionExponent, decryptionExponent, modulus);
};

if(typeof $w.twoDigit === 'undefined') {
   $w.twoDigit = function(n) {
      return (n < 10 ? "0" : "") + String(n);
   };
}

// Altered by Rob Saunders ([email protected]). New routine pads the
// string after it has been converted to an array. This fixes an
// incompatibility with Flash MX's ActionScript.
RSAUtils.encryptedString = function(key, s) {
   var a = [];
   var sl = s.length;
   var i = 0;
   while (i < sl) {
      a[i] = s.charCodeAt(i);
      i++;
   }

   while (a.length % key.chunkSize != 0) {
      a[i++] = 0;
   }

   var al = a.length;
   var result = "";
   var j, k, block;
   for (i = 0; i < al; i += key.chunkSize) {
      block = new BigInt();
      j = 0;
      for (k = i; k < i + key.chunkSize; ++j) {
         block.digits[j] = a[k++];
         block.digits[j] += a[k++] << 8;
      }
      var crypt = key.barrett.powMod(block, key.e);
      var text = key.radix == 16 ? RSAUtils.biToHex(crypt) : RSAUtils.biToString(crypt, key.radix);
      result += text + " ";
   }
   return result.substring(0, result.length - 1); // Remove last space.
};

RSAUtils.decryptedString = function(key, s) {
   var blocks = s.split(" ");
   var result = "";
   var i, j, block;
   for (i = 0; i < blocks.length; ++i) {
      var bi;
      if (key.radix == 16) {
         bi = RSAUtils.biFromHex(blocks[i]);
      }
      else {
         bi = RSAUtils.biFromString(blocks[i], key.radix);
      }
      block = key.barrett.powMod(bi, key.d);
      for (j = 0; j <= RSAUtils.biHighIndex(block); ++j) {
         result += String.fromCharCode(block.digits[j] & 255,
                                       block.digits[j] >> 8);
      }
   }
   // Remove trailing null, if any.
   if (result.charCodeAt(result.length - 1) == 0) {
      result = result.substring(0, result.length - 1);
   }
   return result;
};

RSAUtils.setMaxDigits(130);

})(window);

以上。运行后是下面这样：

点击提交后后台打印信息：

如此便完成了RSA加密和解密过程。

补充：

这里还有一点要注意：直接运行的话，页面会报错：

java.lang.NoClassDefFoundError: org.bouncycastle.jce.provider.Bounc.CastleProvider

解决办法：

原因是因为加入了jdk的第三方安全库，需要额外配置
1.查看JAVA_HOME配置路径

2.将bcprov-jdk15on-1.59.jar放入JAVA_HOME/jre/lib/ext下

(注：不知道文件放哪的，可以直接找到这个项目，查看当前的架包名，找到本地仓库地址，就可以找到了，当然你全局搜索也是可以的。。。)

3.打开JAVA_HOME/jre/lib/security下的java.security文件，在下面加上

  security.provider.x=org.bouncycastle.jce.provider.BouncyCastleProvider

如此，便能完美运行了。

本文参考博客：https://blog.csdn.net/yys79/article/details/41514871/

                       http://www.cnblogs.com/yangy608/archive/2012/08/08/2627858.html）

这里做下简单记录。