RSA是1977年由Ron Rivest、Adi Shamirh和LenAdleman在（美国麻省理工学院）开发的。RSA取名来自开发他们三者的名字。RSA是目前最有影响力的，它能够抵抗到目前为止已知的所有密码攻击，已被ISO推荐为公钥。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。
RSA公开密钥密码体制。所谓的公开密钥密码体制就是使用不同的加密密钥与解密密钥，是一种“由已知加密密钥推导出解密密钥在计算上是不可行的”密码体制。
在中，加密密钥（即公开密钥）PK是公开信息，而解密密钥（即秘密密钥）SK是需要保密的。E和解密算法D也都是公开的。虽然秘密密钥SK是由公开密钥PK决定的，但却不能根据PK计算出SK。正是基于这种理论，1978年出现了著名的RSA算法，它通常是先生成一对RSA 密钥，其中之一是保密密钥，由用户保存；另一个为公开密钥，可对外公开，甚至可在中注册。为提高保密强度，RSA密钥至少为500位长，一般推荐使用1024位。这就使加密的计算量很大。为减少计算量，在传送信息时，常采用传统加密方法与加密方法相结合的方式，即信息采用改进的DES或IDEA对话密钥加密，然后使用RSA密钥加密对话密钥和信息摘要。对方收到信息后，用不同的密钥解密并可核对信息摘要。
RSA算法是第一个能同时用于加密和的算法，也易于理解和操作。RSA是被研究得最广泛的算法，从提出到现今的三十多年里，经历了各种攻击的考验，逐渐为人们接受，普遍认为是目前最优秀的公钥方案之一。
RSA的算法涉及三个参数，n、e1、e2。其中，n是两个大质数p、q的积，n的二进制表示时所占用的位数，就是所谓的密钥长度。e1和e2是一对相关的值，e1可以任意取，
要求e1与(p-1）*(q-1）；
再选择e2，要求（e2*e1）mod((p-1）*(q-1））=1。
（n，e1）,(n，e2）就是密钥对。其中(n，e1）为，(n，e2）为私钥。
RSA加解密的算法完全相同，设A为明文，B为密文，则：
A=B^e2 mod n；
B=A^e1 mod n；
公钥加密体制中，一般用公钥加密，私钥解密
e1和e2可以互换使用，即：
A=B^e1 mod n；
B=A^e2 mod n;
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JAVAEE项目中很多时候都需要对核心数据进行加密传输，采用非对称加密算法在前段对数据进行加密，在服务端进行解密是一个不错的方式。而常用的实现是采用RSA非对称加密方法。具体步骤为：
1、在服务端用密码种子生成密钥对，保存密码种子（一个特定的密码种子，生成特定的密钥对，密码种子确定，密钥对确定）或者直接保存私钥
2、把公钥传到页面
3、页面用JS根据公钥把需要加密的数据进行加密，把加密后的数据传回服务端
4、服务端取出保存的密码种子或者直接保存的私钥，采用私钥对加密字符串进行解密，得到明文
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RSA.java(服务端代码)
注意：需要bouncycastle.jar
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package org.common.util;
import java.security.InvalidParameterException; import java.security.KeyFactory; import java.security.KeyPair; import java.security.KeyPairGenerator; import java.security.NoSuchAlgorithmException; import java.security.PrivateKey; import java.security.Provider; import java.security.SecureRandom; import java.security.interfaces.RSAPrivateKey; import java.security.interfaces.RSAPublicKey; import javax.crypto.Cipher; import org.apache.commons.lang3.StringUtils; import org.bouncycastle.jce.provider.BouncyCastleProvider; import org.bouncycastle.util.encoders.Hex; /** * RSA算法加密/解密工具类。 * * @author Administrator * */ public class RSA { /** 算法名称 */ private static final String ALGORITHOM = "RSA"; /** 密钥大小 */ private static final int KEY_SIZE = 1024; /** 默认的安全服务提供者 */ private static final Provider DEFAULT_PROVIDER = new BouncyCastleProvider(); private static KeyPairGenerator keyPairGen = null; private static KeyFactory keyFactory = null; /** 缓存的密钥对。 */ private static KeyPair oneKeyPair = null; private static String radamKey = ""; static { try { keyPairGen = KeyPairGenerator.getInstance(ALGORITHOM, DEFAULT_PROVIDER); keyFactory = KeyFactory.getInstance(ALGORITHOM, DEFAULT_PROVIDER); } catch (NoSuchAlgorithmException ex) { ex.printStackTrace(); } } /** * 生成并返回RSA密钥对。 */ private static synchronized KeyPair generateKeyPair() { try { keyPairGen.initialize(KEY_SIZE, new SecureRandom(radamKey.getBytes())); oneKeyPair = keyPairGen.generateKeyPair(); return oneKeyPair; } catch (InvalidParameterException ex) { ex.printStackTrace(); } catch (NullPointerException ex) { ex.printStackTrace(); } return null; } /** 返回已初始化的默认的公钥。 */ public static RSAPublicKey getDefaultPublicKey() { KeyPair keyPair = generateKeyPair(); if (keyPair != null) { return (RSAPublicKey) keyPair.getPublic(); } return null; } /** * 使用指定的私钥解密数据。 * * @param privateKey 给定的私钥。 * @param data 要解密的数据。 * @return 原数据。 */ public static byte[] decrypt(PrivateKey privateKey, byte[] data) throws Exception { Cipher ci = Cipher.getInstance(ALGORITHOM, DEFAULT_PROVIDER); ci.init(Cipher.DECRYPT_MODE, privateKey); return ci.doFinal(data); } /** * 使用默认的私钥解密给定的字符串。 * <p /> * 若{@code encrypttext} 为 {@code null}或空字符串则返回 {@code null}。 * 私钥不匹配时，返回 {@code null}。 * * @param encrypttext 密文。 * @return 原文字符串。 */ public static String decryptString(String encrypttext) { if(StringUtils.isBlank(encrypttext)) { return null; } KeyPair keyPair = generateKeyPair(); try { byte[] en_data = Hex.decode(encrypttext); byte[] data = decrypt((RSAPrivateKey)keyPair.getPrivate(), en_data); return new String(data); } catch(NullPointerException ex) { ex.printStackTrace(); } catch (Exception ex) { ex.printStackTrace(); } return null; } /** * 使用默认的私钥解密由JS加密（使用此类提供的公钥加密）的字符串。 * * @param encrypttext 密文。 * @return {@code encrypttext} 的原文字符串。 */ public static String decryptStringByJs(String encrypttext) { String text = decryptString(encrypttext); if(text == null) { return null; } return StringUtils.reverse(text); } public static void main(String[] args) { //密码种子，一个密码种子生产一组RSA密码 RSA.radamKey = "1111"; //获取公钥，分发公钥（e1,n） RSAPublicKey publicKey = RSA.getDefaultPublicKey(); //公钥-系数(n) System.out.println("public key modulus:" + new String(Hex.encode(publicKey.getModulus().toByteArray()))); //公钥-指数(e1) System.out.println("public key exponent:" + new String(Hex.encode(publicKey.getPublicExponent() .toByteArray()))); //JS加密后的字符串 String pppp = "6e269bdf7f7670ffaff669d86d93e63fd91f2d6dd4f7e57ca58c614de65c0828e608bdd0f3e81d3630f8533f5286e0f55caa005ebe6d3faf3b9cc130d9ecff51d1f77eeed48156431cbf5de62cf6899084a4e92890827edbebbf506ecbb022de4a0e3131f2ffefe3368c7b7f929362edb4af419b837456c275f643a5c760a4ff"; //解密后的字符串 String kkkk = RSA.decryptStringByJs(pppp); System.out.println("解密后文字：" + kkkk); } } -------------------------------------------------------------------------------------------------------------------------------html页面代码
注意：security.js工具库、jquery支持
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html> <head> <title>JavaScript RSA Encryption Demo</title> </head> <script language="JavaScript" type="text/javascript" src="security.js"></script> <script language="JavaScript" type="text/javascript" src="jquery-git1.js"></script> <script language="JavaScript"> <!-- function encry() { var modulus = $('#hid_modulus').val(), exponent = $('#hid_exponent').val(); var key = RSAUtils.getKeyPair(exponent, '', modulus); var word =$("#word").val(); var apwd1 = RSAUtils.encryptedString(key, word); $("#clj").text(apwd1); } //--> </script> <body onLoad='set_1024f4();' onClick='rng_seed_time();' onKeyPress='rng_seed_time();'> <h1>JavaScript RSA Encryption Demo</h1> 需要加密的字符串： <input type="text" id="word" value="test"/> <br/> <input type="text" id="hid_modulus" value="00c99f8aab91bccb525d6ea16c40a8eb31dfa9594d1b487167a96d24c8e2d48ed1e9d759f3d1425728016cfffb9b42311108dc6b1f749e6902d6bc072d0533adc489e87eecd980590460fe62290b6a6210e5584919bf85a9cb7b02ebb3ef89aa0a61120dc3cfac1af480905bf269890654cc94e44512b2adc2bb6054cd15971061"/> <br/> <input type="text" id="hid_exponent" value="010001"/> <input type="button" οnclick="encry()" value="加密"/> <div id="clj"></div> </body> </html> -------------------------------------------------------------------------------------------------------------------------------security.js源码
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/*
* RSA, a suite of routines for performing RSA public-key computations in JavaScript. * Copyright 1998-2005 David Shapiro. * Dave Shapiro * dave@ohdave.com * changed by Fuchun, 2010-05-06 * fcrpg2005@gmail.com */ (function($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 (rob@robsaunders.net). 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);