python3 rsa加密

Question

google了好久还是没懂。。都是生成随机的公钥。

js版本的原代码是这样的

var exponent='110001'
var modulus='008d74da20e11ca5646fe8581372f7179382a66ce20913ab753bc4c10ccf2ac53393cbcd12d6108940fbd84913df29ba1867b3a5eacd00fece324216476ab70b5ff943776955ad4d56851258b0718192a21b649560c6b21364ec7989cc378'
var publicKey = RSAUtils.getKeyPair(exponent, '', modulus);
RSAUtils.encryptedString(publicKey, param);

如何以python3的代码实现？

顺便还有一个问题，在安装pycrypto的时候提示

warning: GMP or MPIR library not found; Not building Crypto.PublicKey._fastmath.

，google的解决办法是

apt-get install python3-dev

但是并没有效果，依然如此报错，环境是ubuntu14.04

十分感谢

rsa的js代码在此gist

Answer 1

以你现在提供的信息 无法验证你的问题，"RSAUtils.getKeyPair"这是它js自己封装的一个方法，这个方法做了什么不得而知，你应该用它测试加密一段字符串出来。
对于pycrypto可以参考这篇文章 http://stackoverflow.com/ques...

我试了下这份js，得到了加密后的字符 然后用我的程序验证结果不一样。可能这不是一份标准的rsa加密，或许你需要将这份js放到js问题区里，让懂js的人帮你解读它

var exponent='110001'
var modulus='008d74da20e11ca5646fe8581372f7179382a66ce20913ab753bc4c10ccf2ac53393cbcd12d6108940fbd84913df29ba1867b3a5eacd00fece324216476ab70b5ff943776955ad4d56851258b0718192a21b649560c6b21364ec7989cc378'
var publicKey = RSAUtils.getKeyPair(exponent, '', modulus);
publicKey
RSAKeyPair {e: $w.BigInt, d: $w.BigInt, m: $w.BigInt, chunkSize: 92, radix: 16…}
RSAUtils.encryptedString(publicKey, 'a');
"016ea138c1797c81a9b8456eff08a7ce7992f0e6cd2747c40010cec34e49cc57a6838e73c110db4b97c33ce047bcb90b80d07610f68f5cbcdd26dcac82889e4d65617e26206780b8b9bb27b0266656c25c4d1b10cd44216295a64f637561"

Answer 2

垃圾百度，屁用没有，都是复制粘贴，大家都找不到这个解密，上stackoverflowz找

如果加密不正确，说明RSAKeyPair内部有一个对公匙n进行2次解密函数
下面的github项目rsa.js的RSAKeyPair下就有一个function r(n)的2次加密函数

对了有些RSAUtils库好像是有问题的，每次加密后的密文都一样，可以考虑用下面gayhub中的rsa.js替代

完整rsa签名认证例子
https://github.com/crud-boy/p...

JavaScript代码

e = '010001'
n = '85ec922f28cc33e35b78461cb69aac204d576f14b41f6431f0503f4c0e1d617166ceb475b4124b46d72006cc1955a422492572282aaa6b7b6c20f039a1c834bcc75e1212688eb35d6e990d9b8ebe720eed724870cfcd8498f7983cac696a9132d06a908eee010ebd26ad1aab2bedea4af77eb2905a251f078c59fa958205f491'
setMaxDigits(129)
p = new RSAKeyPair(e, '', n)
console.log(encryptedString(p, '789789'))

python代码

e = '010001'
e = int(e, 16)
n = '85ec922f28cc33e35b78461cb69aac204d576f14b41f6431f0503f4c0e1d617166ceb475b4124b46d72006cc1955a422492572282aaa6b7b6c20f039a1c834bcc75e1212688eb35d6e990d9b8ebe720eed724870cfcd8498f7983cac696a9132d06a908eee010ebd26ad1aab2bedea4af77eb2905a251f078c59fa958205f491'
n = int(n, 16)

pub_key = rsa.PublicKey(e=e, n=n)
m = rsa.encrypt('789789'.encode(),pub_key)
print(m.hex())

Answer 3

遇到了跟你一样的问题。 此js封装的源码 如下。希望看到的大神解决了的话帮我一下。
/*

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

• Copyright 1998-2005 David Shapiro.

• Dave Shapiro

• [e-mail]

• changed by Fuchun, 2010-05-06

• [e-mail]
  */

(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 ([e-mail]). 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);