rsa 解密过程

直接扣js代码

$w = {};

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

var biRadixBase = 2;

var biRadixBits = 16;

var bitsPerDigit = biRadixBits;

var biRadix = 1 << 16;

var biHalfRadix = biRadix >>> 1;

var biRadixSquared = biRadix * biRadix;

var maxDigitVal = biRadix - 1;

var maxInteger = 9999999999999998;

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);

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;

};

var lr10 = RSAUtils.biFromNumber(1000000000000000);

RSAUtils.biFromDecimal = function(s) {

    var isNeg = s.charAt(0) == '-';

    var i = isNeg ? 1 : 0;

    var result;

    while (i < s.length && s.charAt(i) == '')++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 = ['', '', '', '', '', '', '', '', '', '', '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) {

    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 = ['', '', '', '', '', '', '', '', '', '', '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;

    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;

            if (result.digits[i] < 0) result.digits[i] += biRadix;

            c = 0 - Number(n < 0);

        }

        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;

                if (result.digits[i] < 0) result.digits[i] += biRadix;

                c = 0 - Number(n < 0);

            }

            result.isNeg = !x.isNeg;

        } else {

            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;

        }

        result.digits[i + n + 1] = c;

    }

    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;

    }

    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) {

        if (x.isNeg) {

            q = RSAUtils.biCopy(bigOne);

            q.isNeg = !y.isNeg;

            x.isNeg = false;

            y.isNeg = false;

            r = biSubtract(y, x);

            x.isNeg = true;

            y.isNeg = origYIsNeg;

        } else {

            q = new BigInt();

            r = RSAUtils.biCopy(x);

        }

        return [q, r];

    }

    q = new BigInt();

    r = x;

    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;

    }

    r = RSAUtils.biShiftLeft(r, lambda);

    nb += lambda;

    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);

    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);

    }

    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;

    this.mu = RSAUtils.biDivide(b2k, this.modulus);

    this.bkplus1 = new BigInt();

    this.bkplus1.digits[this.k + 1] = 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) {

    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);

    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 ? "": "") + String(n);

    };

}

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);

};

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);

        }

    }

    if (result.charCodeAt(result.length - 1) == 0) {

        result = result.substring(0, result.length - 1);

    }

    return result;

};

RSAUtils.setMaxDigits(130);

function jiami(pwd, modulus, exponent) {

    var publicKey = RSAUtils.getKeyPair(exponent, '', modulus);

    console.log(RSAUtils.encryptedString(publicKey, pwd))

    return RSAUtils.encryptedString(publicKey, pwd);

}

var pwd = "LINlin168";

var modulus = "009cee4fec107772c16d658626b430f8a9c6dbdac59f21d3ad9c00bdb992892c35";

var exponent = "";

// 456b333048a01191715100f0e023b7d40350bd31de2ded152e656e6154b7aa66

 jiami(pwd, modulus, exponent)

运行结果：

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