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  • python爬虫破解带有RSA.js的RSA加密数据的反爬机制(3)

= 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; } // ----------------------------- /* Barrett */ 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) { 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; } // ----------------------------- function RsaFunc() { setMaxDigits(129); var key = new RSAKeyPair("010001", "", "D718814C9DA3C7F8BB1D414C6B503737886F47FD4BA3E6EF164D9BFA0783AD8255C8401AEE4083794C89D3D4F79E6541DA824E4CC357194C6B02DA19DF84F4FC046137475D089DD07304E86D9508E68633C9454019DDC4B8ED6D24381BEF9071593219067DB4B121FE95471396B07D25850EA7FA4F5E27EB24EE29E158F99831"); var val = "jP5efJMT_jb-ACPiy4oTRhq01UbQ3LOZfm3Y9ptBN4Y"; var RsaEncrypted = encryptedString(key, val); return RsaEncrypted; }
复制代码

 

好的,把那段js换成本地的,然后execjs执行js,然后得到封装到headers里就行了:

顺便再说一句,这里用js2py行不通,用execjs可行,我也不知道为啥,用js2py会直接在运行那段js代码的时候卡住,用execjs在几秒内就可以生成那段rsa_key

 

复制代码
#!/usr/bin/env python
# -*- coding:utf-8 -*-
# @Author  : Eeyhan
# @File    : test3.py

import requests
import execjs

requests.packages.urllib3.disable_warnings()
requests.adapters.DEFAULT_RETRIES = 5

js = '''
/*
    
    BigInt
    
    */        

    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; 


    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);
    var dpl10 = 15;
    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;
        }
        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;
    }

    
    // -----------------------------

    /*
    
    RSA
    
    */        
    
    function RSAKeyPair(encryptionExponent, decryptionExponent, modulus)
    {
        this.e = biFromHex(encryptionExponent);
        this.d = biFromHex(decryptionExponent);
        this.m = biFromHex(modulus);            
        this.digitSize = 2 * biHighIndex(this.m) + 2;
        this.chunkSize = this.digitSize - 11; 
        this.radix = 16;
        this.barrett = new BarrettMu(this.m);
    }

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

    function encryptedString(key, s)
    {
        if (key.chunkSize > key.digitSize - 11)
        {
            return "Error";
        }
        var a = new Array();
        var sl = s.length;
        
        var i = 0;
        while (i < sl) {
            a[i] = s.charCodeAt(i);
            i++;
        }
        var al = a.length;
        var result = "";
        var j, k, block;
        for (i = 0; i < al; i += key.chunkSize) {
            block = new BigInt();
            j = 0;
            
            var x;
            var msgLength = (i+key.chunkSize)>al ? al%key.chunkSize : key.chunkSize;
            var b = new Array();
            for (x=0; x<msgLength; x++)
            {
                b[x] = a[i+msgLength-1-x];
            }
            b[msgLength] = 0; // marker
            var paddedSize = Math.max(8, key.digitSize - 3 - msgLength);
        
            for (x=0; x<paddedSize; x++) {
                b[msgLength+1+x] = Math.floor(Math.random()*254) + 1; // [1,255]
            }
            // It can be asserted that msgLength+paddedSize == key.digitSize-3
            b[key.digitSize-2] = 2; // marker
            b[key.digitSize-1] = 0; // marker
            
            for (k = 0; k < key.digitSize; ++j) 
            {
                block.digits[j] = b[k++];
                block.digits[j] += b[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;
    }
    
    
    // -----------------------------        
    
    /*
    
    Barrett
    
    */
    
    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)
    {
        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;
    }

    // -----------------------------
    
    function RsaFunc() {
        setMaxDigits(129);
        var key = new RSAKeyPair("010001", "", "D718814C9DA3C7F8BB1D414C6B503737886F47FD4BA3E6EF164D9BFA0783AD8255C8401AEE4083794C89D3D4F79E6541DA824E4CC357194C6B02DA19DF84F4FC046137475D089DD07304E86D9508E68633C9454019DDC4B8ED6D24381BEF9071593219067DB4B121FE95471396B07D25850EA7FA4F5E27EB24EE29E158F99831");
         var val = "jP5efJMT_jb-ACPiy4oTRhq01UbQ3LOZfm3Y9ptBN4Y";
         var RsaEncrypted = encryptedString(key, val);
         return RsaEncrypted;        
    }    
'''

headers = {
    'User-Agent': 'Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/63.0.3239.132 Safari/537.36',
    }
data = {'OPtype': 'GetListNew', 'pageSize': '10', 'proArea': '-1', 'announcementType': '-1', 'ProType': '-1',
         'xmlx': '-1', 'projectName': '', 'rrr': '0.38874920439722827', 'TopTime': '2020-01-02 00:00:00',
         'EndTime': '2020-02-02 23:59:59', 'pageNo': 3, 'category': 'ZFCG'}

cx = execjs.compile(js)
cookie = cx.call('RsaFunc')
print(cookie)
cookie = {'Cookie': '_qddagsx_02095bad0b=%s' % cookie}
headers.update(cookie)
url = '' # 网址保密,自己去找同rsa加密的网站,方法相同
req = requests.post(url, headers=headers, data=data, verify=False)
res = req.content.decode('utf-8')
print(res)
复制代码

 

 

 

理论上本篇文章是完了,其实这里还有一个坑,目前还不行,因为也是我的研究发现的,有朋友要问,为什么还不行,不是已经搞定了吗?真的还没有,这里还有一个大坑:

回到刚刚解析的RSA函数那里:

 

 根据我的研究,发现圈出区域的字段是会变的,玛德,你说这里是不是个大坑?不信?我f5刷新下,再看:

 

 

变量val变了,其他还有没有变目前无法得知,那么就得每次要爬取这个网站之前,先获取一次这个网站的源码,将这个RsaFunc重组一下:

 

 

完整代码:

复制代码
#!/usr/bin/env python
# -*- coding:utf-8 -*-
# @Author  : Eeyhan
# @File    : test3.py
import time
import requests
import js2py
import execjs

start = time.time()
js = '''
/*
    
    BigInt
    
    */        

    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; 


    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);
    var dpl10 = 15;
    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;
        }
        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;
    }

    
    // -----------------------------

    /*
    
    RSA
    
    */        
    
    function RSAKeyPair(encryptionExponent, decryptionExponent, modulus)
    {
        this.e = biFromHex(encryptionExponent);
        this.d = biFromHex(decryptionExponent);
        this.m = biFromHex(modulus);            
        this.digitSize = 2 * biHighIndex(this.m) + 2;
        this.chunkSize = this.digitSize - 11; 
        this.radix = 16;
        this.barrett = new BarrettMu(this.m);
    }

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

    function encryptedString(key, s)
    {
        if (key.chunkSize > key.digitSize - 11)
        {
            return "Error";
        }
        var a = new Array();
        var sl = s.length;
        
        var i = 0;
        while (i < sl) {
            a[i] = s.charCodeAt(i);
            i++;
        }
        var al = a.length;
        var result = "";
        var j, k, block;
        for (i = 0; i < al; i += key.chunkSize) {
            block = new BigInt();
            j = 0;
            
            var x;
            var msgLength = (i+key.chunkSize)>al ? al%key.chunkSize : key.chunkSize;
            var b = new Array();
            for (x=0; x<msgLength; x++)
            {
                b[x] = a[i+msgLength-1-x];
            }
            b[msgLength] = 0; // marker
            var paddedSize = Math.max(8, key.digitSize - 3 - msgLength);
        
            for (x=0; x<paddedSize; x++) {
                b[msgLength+1+x] = Math.floor(Math.random()*254) + 1; // [1,255]
            }
            // It can be asserted that msgLength+paddedSize == key.digitSize-3
            b[key.digitSize-2] = 2; // marker
            b[key.digitSize-1] = 0; // marker
            
            for (k = 0; k < key.digitSize; ++j) 
            {
                block.digits[j] = b[k++];
                block.digits[j] += b[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;
    }
    
    
    // -----------------------------        
    
    /*
    
    Barrett
    
    */
    
    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)
    {
        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;
    }

    // -----------------------------    
    

      



  

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