java RSA加密算法

【转】RSA加密算法

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。RSA取名来自开发他们三者的名字。RSA是目前最有影响力的公钥加密算法，它能够抵抗到目前为止已知的所有密码攻击，已被ISO推荐为公钥数据加密标准。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。

在公开密钥密码体制中，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。加密算法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，甚至可在网络服务器中注册。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公开密钥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数字签名的算法，也易于理解和操作。RSA是被研究得最广泛的公钥算法，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）互质；

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）为公钥，(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);

}

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html页面代码

注意：security.js工具库、jquery支持

-------------------------------------------------------------------------------------------------------------------------------

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">

<html>

<head>

<title>JavaScript RSA Encryption Demo</title>

</head>

<!--

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>

<h1>JavaScript RSA Encryption Demo</h1>

需要加密的字符串：

<br/>

<br/>

</body>

</html>

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security.js源码

-------------------------------------------------------------------------------------------------------------------------------

* RSA, a suite of routines for performing RSA public-key computations in JavaScript.

* 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);

时间： 2024-10-03 21:03:12

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