使用RSA對先後臺通訊加解密

背景:前端js+後端java,前端提交密碼等敏感信息,且後端僅能處理密碼明文。javascript

基於此背景(須要前端js加密報文全文或其中敏感字段),項目嘗試使用RSA算法,前端加密,後端解密。html

前端jsp頁面前端

<%@ page language="java" pageEncoding="UTF-8" contentType="text/html; charset=UTF-8"%>

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html:html lang="true">
<head>
	<title>login</title>

	<script type="text/javascript" src="js/RSA.js"></script>
	<script type="text/javascript" src="js/BigInt.js"></script>
	<script type="text/javascript" src="js/Barrett.js"></script>
	
	<script type="text/javascript">
function rsalogin(){
	var thisPwd = document.getElementById("password").value;
	bodyRSA();
	var result = encryptedString(key, encodeURIComponent(thisPwd));
	//alert(encodeURIComponent(thisPwd)+"\r\n"+result);
	loginForm.action="http://127.0.0.1:8081/wxpfs/test?pw="+result;
	loginForm.submit();
}
var key ;
function bodyRSA(){
	setMaxDigits(130);
  	key = new RSAKeyPair("10001","","java後臺生成的公鑰xxxxxxx"); 
}
</script>
</head>

<body>
	<form method="post" name="loginForm" action= "http://127.0.0.1:8081/wxpfs/test" ><!--target=_blank-->
		<table border="0">
			<tr>
				<td>
					Password:
				</td>
				<td>
					<input type='text' name="password" id=password style='width:400px' value="my passwd"/>
				</td>
			</tr>
			<tr>
				<td colspan="2" align="center">
					<input type="button" value="SUBMIT" onclick="rsalogin();" />
				</td>
			</tr>
		</table>
	</form>
</body>
</html:html>

RSA.jsjava

// RSA, a suite of routines for performing RSA public-key computations in
// JavaScript.
//
// Requires BigInt.js and Barrett.js.
//
// Copyright 1998-2005 David Shapiro.
//
// You may use, re-use, abuse, copy, and modify this code to your liking, but
// please keep this header.
//
// Thanks!
// 
// Dave Shapiro
// dave@ohdave.com 

function RSAKeyPair(encryptionExponent, decryptionExponent, modulus)
{
	this.e = biFromHex(encryptionExponent);
	this.d = biFromHex(decryptionExponent);
	this.m = 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 * biHighIndex(this.m);
	this.radix = 16;
	this.barrett = new BarrettMu(this.m);
}

function twoDigit(n)
{
	return (n < 10 ? "0" : "") + String(n);
}

function encryptedString(key, s)
	// 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.
{
	var a = new Array();
	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 ? biToHex(crypt) : biToString(crypt, key.radix);
		result += text + " ";
	}
	return result.substring(0, result.length - 1); // Remove last space.
}

function decryptedString(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 = biFromHex(blocks[i]);
		}
		else {
			bi = biFromString(blocks[i], key.radix);
		}
		block = key.barrett.powMod(bi, key.d);
		for (j = 0; j <= 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;
}

BigInt.jsgit

// BigInt, a suite of routines for performing multiple-precision arithmetic in
// JavaScript.
//
// Copyright 1998-2005 David Shapiro.
//
// You may use, re-use, abuse,
// copy, and modify this code to your liking, but please keep this header.
// Thanks!
//
// Dave Shapiro
// dave@ohdave.com

// IMPORTANT THING: Be sure to set maxDigits according to your precision
// needs. Use the setMaxDigits() function to do this. See comments below.
//
// Tweaked by Ian Bunning
// Alterations:
// Fix bug in function biFromHex(s) to allow
// parsing of strings of length != 0 (mod 4)

// Changes made by Dave Shapiro as of 12/30/2004:
//
// The BigInt() constructor doesn't take a string anymore. If you want to
// create a BigInt from a string, use biFromDecimal() for base-10
// representations, biFromHex() for base-16 representations, or
// biFromString() for base-2-to-36 representations.
//
// biFromArray() has been removed. Use biCopy() instead, passing a BigInt
// instead of an array.
//
// The BigInt() constructor now only constructs a zeroed-out array.
// Alternatively, if you pass <true>, it won't construct any array. See the
// biCopy() method for an example of this.
//
// Be sure to set maxDigits depending on your precision needs. The default
// zeroed-out array ZERO_ARRAY is constructed inside the setMaxDigits()
// function. So use this function to set the variable. DON'T JUST SET THE
// VALUE. USE THE FUNCTION.
//
// ZERO_ARRAY exists to hopefully speed up construction of BigInts(). By
// precalculating the zero array, we can just use slice(0) to make copies of
// it. Presumably this calls faster native code, as opposed to setting the
// elements one at a time. I have not done any timing tests to verify this
// claim.

// Max number = 10^16 - 2 = 9999999999999998;
//               2^53     = 9007199254740992;

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;

function setMaxDigits(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;
}

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

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

function biFromDecimal(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 = biFromNumber(Number(s.substr(i, fgl)));
		i += fgl;
		while (i < s.length) {
			result = biAdd(biMultiply(result, lr10),
			               biFromNumber(Number(s.substr(i, dpl10))));
			i += dpl10;
		}
		result.isNeg = isNeg;
	}
	return result;
}

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

function biFromNumber(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;
}

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

var hexatrigesimalToChar = new Array(
 '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'
);

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

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

var hexToChar = new Array('0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
                          'a', 'b', 'c', 'd', 'e', 'f');

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

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

function charToHex(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;
}

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

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

function biFromString(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 = charToHex(c);
		var biDigit = biMultiplyDigit(place, digit);
		result = biAdd(result, biDigit);
		place = biMultiplyDigit(place, radix);
	}
	result.isNeg = isNeg;
	return result;
}

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

function biAdd(x, y)
{
	var result;

	if (x.isNeg != y.isNeg) {
		y.isNeg = !y.isNeg;
		result = 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;
}

function biSubtract(x, y)
{
	var result;
	if (x.isNeg != y.isNeg) {
		y.isNeg = !y.isNeg;
		result = 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;
}


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

function biNumBits(x)
{
	var n = 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;
}

function biMultiply(x, y)
{
	var result = new BigInt();
	var c;
	var n = biHighIndex(x);
	var t = 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;
}

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

	result = new BigInt();
	n = 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;
}

function arrayCopy(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 = new Array(0x0000, 0x8000, 0xC000, 0xE000, 0xF000, 0xF800,
                             0xFC00, 0xFE00, 0xFF00, 0xFF80, 0xFFC0, 0xFFE0,
                             0xFFF0, 0xFFF8, 0xFFFC, 0xFFFE, 0xFFFF);

function biShiftLeft(x, n)
{
	var digitCount = Math.floor(n / bitsPerDigit);
	var result = new BigInt();
	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 = new Array(0x0000, 0x0001, 0x0003, 0x0007, 0x000F, 0x001F,
                            0x003F, 0x007F, 0x00FF, 0x01FF, 0x03FF, 0x07FF,
                            0x0FFF, 0x1FFF, 0x3FFF, 0x7FFF, 0xFFFF);

function biShiftRight(x, n)
{
	var digitCount = Math.floor(n / bitsPerDigit);
	var result = new BigInt();
	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;
}

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

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

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

function biCompare(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;
}

function biDivideModulo(x, y)
{
	var nb = biNumBits(x);
	var tb = biNumBits(y);
	var origYIsNeg = y.isNeg;
	var q, r;
	if (nb < tb) {
		// |x| < |y|
		if (x.isNeg) {
			q = 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 = biCopy(x);
		}
		return new Array(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 = 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 = biShiftLeft(r, lambda);
	nb += lambda; // Update the bit count for x.
	var n = Math.ceil(nb / bitsPerDigit) - 1;

	var b = biMultiplyByRadixPower(y, n - t);
	while (biCompare(r, b) != -1) {
		++q.digits[n - t];
		r = 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 = biMultiplyByRadixPower(y, i - t - 1);
		r = biSubtract(r, biMultiplyDigit(b, q.digits[i - t - 1]));
		if (r.isNeg) {
			r = biAdd(r, b);
			--q.digits[i - t - 1];
		}
	}
	r = 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 = biAdd(q, bigOne);
		} else {
			q = biSubtract(q, bigOne);
		}
		y = biShiftRight(y, lambda);
		r = biSubtract(y, r);
	}
	// Check for the unbelievably stupid degenerate case of r == -0.
	if (r.digits[0] == 0 && biHighIndex(r) == 0) r.isNeg = false;

	return new Array(q, r);
}

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

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

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

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

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

Barrett.js算法

// BarrettMu, a class for performing Barrett modular reduction computations in
// JavaScript.
//
// Requires BigInt.js.
//
// Copyright 2004-2005 David Shapiro.
//
// You may use, re-use, abuse, copy, and modify this code to your liking, but
// please keep this header.
//
// Thanks!
// 
// Dave Shapiro
// dave@ohdave.com 

function BarrettMu(m)
{
	this.modulus = biCopy(m);
	this.k = biHighIndex(this.modulus) + 1;
	var b2k = new BigInt();
	b2k.digits[2 * this.k] = 1; // b2k = b^(2k)
	this.mu = 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 q1 = biDivideByRadixPower(x, this.k - 1);
	var q2 = biMultiply(q1, this.mu);
	var q3 = biDivideByRadixPower(q2, this.k + 1);
	var r1 = biModuloByRadixPower(x, this.k + 1);
	var r2term = biMultiply(q3, this.modulus);
	var r2 = biModuloByRadixPower(r2term, this.k + 1);
	var r = biSubtract(r1, r2);
	if (r.isNeg) {
		r = biAdd(r, this.bkplus1);
	}
	var rgtem = biCompare(r, this.modulus) >= 0;
	while (rgtem) {
		r = biSubtract(r, this.modulus);
		rgtem = biCompare(r, this.modulus) >= 0;
	}
	return r;
}

function BarrettMu_multiplyMod(x, y)
{
	/*
	x = this.modulo(x);
	y = this.modulo(y);
	*/
	var xy = 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 = biShiftRight(k, 1);
		if (k.digits[0] == 0 && biHighIndex(k) == 0) break;
		a = this.multiplyMod(a, a);
	}
	return result;
}

後端RSAUtil.java後端

package com.siasun.wxpay.util;

/**
 * 
 */

import java.io.ByteArrayOutputStream;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
import java.math.BigInteger;
import java.security.KeyFactory;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import java.security.NoSuchAlgorithmException;
import java.security.PrivateKey;
import java.security.PublicKey;
import java.security.SecureRandom;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;
import java.security.spec.InvalidKeySpecException;
import java.security.spec.RSAPrivateKeySpec;
import java.security.spec.RSAPublicKeySpec;

import javax.crypto.Cipher;


/**
 * RSA 工具類。提供加密,解密,生成密鑰對等方法。
 * 須要到http://www.bouncycastle.org下載bcprov-jdk14-123.jar。
 */
public class RSAUtil {

	private static String RSAKeyStore = "磁盤路徑RSAKey.txt";

	/**
	 * * 生成密鑰對 *
	 * 
	 * @return KeyPair *
	 * @throws EncryptException
	 */
	public static KeyPair generateKeyPair() throws Exception {
		try {
			KeyPairGenerator keyPairGen = KeyPairGenerator.getInstance("RSA",
					new org.bouncycastle.jce.provider.BouncyCastleProvider());
			final int KEY_SIZE = 1024;// 沒什麼好說的了,這個值關係到塊加密的大小,能夠更改,可是不要太大,不然效率會低
			keyPairGen.initialize(KEY_SIZE, new SecureRandom());
			KeyPair keyPair = keyPairGen.generateKeyPair();

			System.out.println(keyPair.getPrivate());
			System.out.println(keyPair.getPublic());

			saveKeyPair(keyPair);
			return keyPair;
		} catch (Exception e) {
			throw new Exception(e.getMessage());
		}
	}

	public static KeyPair getKeyPair() throws Exception {
		FileInputStream fis = new FileInputStream(RSAKeyStore);
		ObjectInputStream oos = new ObjectInputStream(fis);
		KeyPair kp = (KeyPair) oos.readObject();
		oos.close();
		fis.close();
		return kp;
	}

	public static void saveKeyPair(KeyPair kp) throws Exception {

		FileOutputStream fos = new FileOutputStream(RSAKeyStore);
		ObjectOutputStream oos = new ObjectOutputStream(fos);
		// 生成密鑰
		oos.writeObject(kp);
		oos.close();
		fos.close();
	}

	/**
	 * * 生成公鑰 *
	 * 
	 * @param modulus
	 * *
	 * @param publicExponent
	 * *
	 * @return RSAPublicKey *
	 * @throws Exception
	 */
	public static RSAPublicKey generateRSAPublicKey(byte[] modulus, byte[] publicExponent) throws Exception {
		KeyFactory keyFac = null;
		try {
			keyFac = KeyFactory.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
		} catch (NoSuchAlgorithmException ex) {
			throw new Exception(ex.getMessage());
		}

		RSAPublicKeySpec pubKeySpec = new RSAPublicKeySpec(new BigInteger(modulus), new BigInteger(publicExponent));
		try {
			return (RSAPublicKey) keyFac.generatePublic(pubKeySpec);
		} catch (InvalidKeySpecException ex) {
			throw new Exception(ex.getMessage());
		}
	}

	/**
	 * * 生成私鑰 *
	 * 
	 * @param modulus
	 * *
	 * @param privateExponent
	 * *
	 * @return RSAPrivateKey *
	 * @throws Exception
	 */
	public static RSAPrivateKey generateRSAPrivateKey(byte[] modulus, byte[] privateExponent) throws Exception {
		KeyFactory keyFac = null;
		try {
			keyFac = KeyFactory.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
		} catch (NoSuchAlgorithmException ex) {
			throw new Exception(ex.getMessage());
		}

		RSAPrivateKeySpec priKeySpec = new RSAPrivateKeySpec(new BigInteger(modulus), new BigInteger(privateExponent));
		try {
			return (RSAPrivateKey) keyFac.generatePrivate(priKeySpec);
		} catch (InvalidKeySpecException ex) {
			throw new Exception(ex.getMessage());
		}
	}

	/**
	 * * 加密 *
	 * 
	 * @param key
	 *            加密的密鑰 *
	 * @param data
	 *            待加密的明文數據 *
	 * @return 加密後的數據 *
	 * @throws Exception
	 */
	public static byte[] encrypt(PublicKey pk, byte[] data) throws Exception {
		try {
			Cipher cipher = Cipher.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
			cipher.init(Cipher.ENCRYPT_MODE, pk);
			int blockSize = cipher.getBlockSize();// 得到加密塊大小,如:加密前數據爲128個byte,而key_size=1024
			// 加密塊大小爲127
			// byte,加密後爲128個byte;所以共有2個加密塊,第一個127
			// byte第二個爲1個byte
			int outputSize = cipher.getOutputSize(data.length);// 得到加密塊加密後塊大小
			int leavedSize = data.length % blockSize;
			int blocksSize = leavedSize != 0 ? data.length / blockSize + 1 : data.length / blockSize;
			byte[] raw = new byte[outputSize * blocksSize];
			int i = 0;
			while (data.length - i * blockSize > 0) {
				if (data.length - i * blockSize > blockSize)
					cipher.doFinal(data, i * blockSize, blockSize, raw, i * outputSize);
				else
					cipher.doFinal(data, i * blockSize, data.length - i * blockSize, raw, i * outputSize);
				// 這裏面doUpdate方法不可用,查看源代碼後發現每次doUpdate後並無什麼實際動做除了把byte[]放到
				// ByteArrayOutputStream中,而最後doFinal的時候纔將全部的byte[]進行加密,但是到了此時加密塊大小極可能已經超出了
				// OutputSize因此只好用dofinal方法。

				i++;
			}
			return raw;
		} catch (Exception e) {
			throw new Exception(e.getMessage());
		}
	}

	/**
	 * * 解密 *
	 * 
	 * @param key
	 *            解密的密鑰 *
	 * @param raw
	 *            已經加密的數據 *
	 * @return 解密後的明文 *
	 * @throws Exception
	 */
	public static byte[] decrypt(PrivateKey pk, byte[] raw) throws Exception {
		try {
			Cipher cipher = Cipher.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
			cipher.init(cipher.DECRYPT_MODE, pk);
			int blockSize = cipher.getBlockSize();
			ByteArrayOutputStream bout = new ByteArrayOutputStream(64);
			int j = 0;

			while (raw.length - j * blockSize > 0) {
				bout.write(cipher.doFinal(raw, j * blockSize, blockSize));
				j++;
			}
			return bout.toByteArray();
		} catch (Exception e) {
			throw new Exception(e.getMessage());
		}
	}

	/**
	 * 從新生成RSA密鑰
	 * 
	 * @param args
	 * *
	 * @throws Exception
	 */
	public static void main(String[] args) throws Exception {
		RSAPublicKey rsap = (RSAPublicKey) RSAUtil.generateKeyPair().getPublic();
		String test = "hello world";
		byte[] en_test = encrypt(getKeyPair().getPublic(), test.getBytes());
		byte[] de_test = decrypt(getKeyPair().getPrivate(), en_test);
		System.out.println(new String(de_test));
	}

	/**
	 * 16進制 To byte[]
	 * 
	 * @param hexString
	 * @return byte[]
	 */
	public static byte[] hexStringToBytes(String hexString) {
		if (hexString == null || hexString.equals("")) {
			return null;
		}
		hexString = hexString.toUpperCase();
		int length = hexString.length() / 2;
		char[] hexChars = hexString.toCharArray();
		byte[] d = new byte[length];
		for (int i = 0; i < length; i++) {
			int pos = i * 2;
			d[i] = (byte) (charToByte(hexChars[pos]) << 4 | charToByte(hexChars[pos + 1]));
		}
		return d;
	}

	/**
	 * Convert char to byte
	 * 
	 * @param c
	 *            char
	 * @return byte
	 */
	private static byte charToByte(char c) {
		return (byte) "0123456789ABCDEF".indexOf(c);
	}
}

後端解密java代碼片斷api

String pw = null;
		try {
			pw = URLDecoder
					.decode(new StringBuffer()
							.append(new String(RSAUtil.decrypt(RSAUtil.getKeyPair().getPrivate(),
									RSAUtil.hexStringToBytes(new BigInteger(pw, 16).toString(16)))))
							.reverse().toString(), "UTF-8");
		} catch (Exception e) {
			e.printStackTrace();
}
System.out.println(pw);
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