crypto.jsx

// -*- mode: jsx; jsx-indent-level: 4; indent-tabs-mode: nil; -*-
/*
 * Copyright (c) 2003-2005  Tom Wu
 * All Rights Reserved.
 *
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 *
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
 * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
 *
 * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
 * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
 * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
 * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
 * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 *
 * In addition, the following condition applies:
 *
 * All redistributions must retain an intact copy of this copyright notice
 * and disclaimer.
 */

import "./base.jsx";

// The code has been adapted for use as a benchmark by Google.
class Crypto {

    static const nValue="a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd94057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074eafd036a5eb83359d2a698d3";
    static const eValue="10001";
    static const dValue="8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293fc97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891464fba23d0d965086277a161";
    static const pValue="d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bde14b2417951178ac152ceab6da7090905b478195498b352048f15e7d";
    static const qValue="cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f";
    static const dmp1Value="1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25";
    static const dmq1Value="3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d914337eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd";
    static const coeffValue="3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db1734c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250";

    function constructor() {
        Crypto.setup();

        var TEXT = "The quick brown fox jumped over the extremely lazy frog! " +
        "Now is the time for all good men to come to the party.";
        var encrypted = "";

        function encrypt() : void {
            var RSA = new RSAKey();
            RSA.setPublic(Crypto.nValue, Crypto.eValue);
            RSA.setPrivateEx(Crypto.nValue, Crypto.eValue, Crypto.dValue, Crypto.pValue, Crypto.qValue, Crypto.dmp1Value, Crypto.dmq1Value, Crypto.coeffValue);
            encrypted = RSA.encrypt(TEXT);
        }

        function decrypt() : void {
            var RSA = new RSAKey();
            RSA.setPublic(Crypto.nValue, Crypto.eValue);
            RSA.setPrivateEx(Crypto.nValue, Crypto.eValue, Crypto.dValue, Crypto.pValue, Crypto.qValue, Crypto.dmp1Value, Crypto.dmq1Value, Crypto.coeffValue);
            var decrypted = RSA.decrypt(encrypted);
            if (decrypted != TEXT) {
                throw new Error("Crypto operation failed");
            }
        }

        var crypto = new BenchmarkSuite('Crypto', 266181, [
            new Benchmark("Encrypt", encrypt),
            new Benchmark("Decrypt", decrypt)
            ]);
    }

    static function setup () : void {
        BigInteger.init();

        // JavaScript engine analysis
        var canary = 0xdeadbeefcafe;
        var j_lm = ((canary&0xffffff)==0xefcafe);

        // am3/28 is best for SM, Rhino, but am4/26 is best for v8.
        // Kestrel (Opera 9.5) gets its best result with am4/26.
        // IE7 does 9% better with am3/28 than with am4/26.
        // Firefox (SM) gets 10% faster with am3/28 than with am4/26.

        function setupEngine(fn : (number[],number,number,BigInteger,number,number,number)->number, bits : number) : void {
            BigInteger.am = fn;
            var dbits = bits;

            BigInteger.DB = dbits;
            BigInteger.DM = ((1<<dbits)-1);
            BigInteger.DV = (1<<dbits);

            BigInteger.FP = 52;
            BigInteger.FV = Math.pow(2,BigInteger.FP);
            BigInteger.F1 = BigInteger.FP-dbits;
            BigInteger.F2 = 2*dbits-BigInteger.FP;
        }

        setupEngine(Crypto.am3, 28);
    }

    // am: Compute w_j += (x*this_i), propagate carries,
    // c is initial carry, returns final carry.
    // c < 3*dvalue, x < 2*dvalue, this_i < dvalue
    // We need to select the fastest one that works in this environment.

    // am1: use a single mult and divide to get the high bits,
    // max digit bits should be 26 because
    // max internal value = 2*dvalue^2-2*dvalue (< 2^53)
    static function am1(this_array : number[], i : number, x : number, w : BigInteger, j : number, c : number, n : number) : number {
        var w_array    = w.array;
        while(--n >= 0) {
            var v = x*this_array[i++]+w_array[j]+c;
            c = Math.floor(v/0x4000000);
            w_array[j++] = v&0x3ffffff;
        }
        return c;
    }

    // am2 avoids a big mult-and-extract completely.
    // Max digit bits should be <= 30 because we do bitwise ops
    // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
    static function am2(this_array : number[], i : number, x : number, w : BigInteger, j : number, c : number, n : number) : number {
        var w_array    = w.array;
        var xl = x&0x7fff, xh = x>>15;
        while(--n >= 0) {
            var l = this_array[i]&0x7fff;
            var h = this_array[i++]>>15;
            var m = xh*l+h*xl;
            l = xl*l+((m&0x7fff)<<15)+w_array[j]+(c&0x3fffffff);
            c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
            w_array[j++] = l&0x3fffffff;
        }
        return c;
    }

    // Alternately, set max digit bits to 28 since some
    // browsers slow down when dealing with 32-bit numbers.
    static function am3(this_array : number[], i : number, x : number, w : BigInteger, j : number, c : number, n : number) : number{
        var w_array    = w.array;

        var xl = x&0x3fff, xh = x>>14;
        while(--n >= 0) {
            var l = this_array[i]&0x3fff;
            var h = this_array[i++]>>14;
            var m = xh*l+h*xl;
            l = xl*l+((m&0x3fff)<<14)+w_array[j]+c;
            c = (l>>28)+(m>>14)+xh*h;
            w_array[j++] = l&0xfffffff;
        }
        return c;
    }

    // This is tailored to VMs with 2-bit tagging. It makes sure
    // that all the computations stay within the 29 bits available.
    static function am4(this_array : number[], i : number, x : number, w : BigInteger, j : number, c : number, n : number) : number {
        var w_array    = w.array;

        var xl = x&0x1fff, xh = x>>13;
        while(--n >= 0) {
            var l = this_array[i]&0x1fff;
            var h = this_array[i++]>>13;
            var m = xh*l+h*xl;
            l = xl*l+((m&0x1fff)<<13)+w_array[j]+c;
            c = (l>>26)+(m>>13)+xh*h;
            w_array[j++] = l&0x3ffffff;
        }
        return c;
    }
}


class BigInteger {

    // "constants"
    static const ZERO = BigInteger.nbv(0);
    static const ONE = BigInteger.nbv(1);

    static var DB : number;
    static var DM : number;
    static var DV : number;

    static var FP : number;
    static var FV : number;
    static var F1 : number;
    static var F2 : number;

    static var am : (number[],number,number,BigInteger,number,number,number)->number;

    var array : number[];
    var s : number;
    var t : number;

    // (public) Constructors
    function constructor() {
        this.array = new Array.<number>();
    }

    function constructor(a : number, b : number, c : SecureRandom) {
        this();
        this.fromNumber(a,b,c);
    }

    function constructor(a : number[]) {
        // when b == null && "string" != typeof a,
        this();
        this.fromNumberArray(a);
    }

    function constructor(a : string, b : number) {
        this();
        this.fromString(a,b);
    }

    // return new, unset BigInteger
    static function nbi() : BigInteger { return new BigInteger(); }

    // Digit conversion
    static const RM = "0123456789abcdefghijklmnopqrstuvwxyz";
    static const RC = new Array.<number>();

    static function init() : void {
        var rr,vv;
        rr = "0".charCodeAt(0);
        for(vv = 0; vv <= 9; ++vv) BigInteger.RC[rr++] = vv;
        rr = "a".charCodeAt(0);
        for(vv = 10; vv < 36; ++vv) BigInteger.RC[rr++] = vv;
        rr = "A".charCodeAt(0);
        for(vv = 10; vv < 36; ++vv) BigInteger.RC[rr++] = vv;
    }

    static function int2char(n : number) : string { return BigInteger.RM.charAt(n); }

    static function intAt(s : string,i : number) : number {
        var c = BigInteger.RC[s.charCodeAt(i)];
        return (c==null)?-1:c as number;
    }

    // (protected) copy this to r
    function copyTo(r : BigInteger) : void {
        var this_array = this.array;
        var r_array    = r.array;

        for(var i = this.t-1; i >= 0; --i) r_array[i] = this_array[i];
        r.t = this.t;
        r.s = this.s;
    }

    // convert a (hex) string to a bignum object
    static function parseBigInt(str : string, r : number) : BigInteger {
        return new BigInteger(str,r);
    }

    // (protected) set from integer value x, -DV <= x < DV
    function fromInt(x : number) : void {
        var this_array = this.array;
        this.t = 1;
        this.s = (x<0)?-1:0;
        if(x > 0) this_array[0] = x;
        else if(x < -1) this_array[0] = x+BigInteger.DV;
        else this.t = 0;
    }

    // return bigint initialized to value
    static function nbv(i : number) : BigInteger { var r = BigInteger.nbi(); r.fromInt(i); return r; }

    // (protected) set from string and radix
    function fromString(s : string, b : number) : void {
        var this_array = this.array;
        var k;
        if(b == 16) k = 4;
        else if(b == 8) k = 3;
        else if(b == 256) k = 8; // byte array
        else if(b == 2) k = 1;
        else if(b == 32) k = 5;
        else if(b == 4) k = 2;
        else { this.fromRadix(s,b); return; }
        this.t = 0;
        this.s = 0;
        var i = s.length, mi = false, sh = 0;
        while(--i >= 0) {
            var x = (k==8)?s.charAt(i) as number&0xff:BigInteger.intAt(s,i);
            if(x < 0) {
                if(s.charAt(i) == "-") mi = true;
                continue;
            }
            mi = false;
            if(sh == 0)
                this_array[this.t++] = x;
            else if(sh+k > BigInteger.DB) {
                this_array[this.t-1] |= (x&((1<<(BigInteger.DB-sh))-1))<<sh;
                this_array[this.t++] = (x>>(BigInteger.DB-sh));
            }
            else
                this_array[this.t-1] |= x<<sh;
            sh += k;
            if(sh >= BigInteger.DB) sh -= BigInteger.DB;
        }
        if(k == 8 && (s.charAt(0) as number&0x80) != 0) {
            this.s = -1;
            if(sh > 0) this_array[this.t-1] |= ((1<<(BigInteger.DB-sh))-1)<<sh;
        }
        this.clamp();
        if(mi) BigInteger.ZERO.subTo(this,this);
    }

    function fromNumberArray(s : number[]) : void {
        this.fromRadix(s,256);
    }

    // (protected) clamp off excess high words
    function clamp() : void {
        var this_array = this.array;
        var c = this.s&BigInteger.DM;
        while(this.t > 0 && this_array[this.t-1] == c) --this.t;
    }

    // (public) return string representation in given radix
    function toString(b : number) : string {
        var this_array = this.array;
        if(this.s < 0) return "-"+this.negate().toString(b);
        var k;
        if(b == 16) k = 4;
        else if(b == 8) k = 3;
        else if(b == 2) k = 1;
        else if(b == 32) k = 5;
        else if(b == 4) k = 2;
        else return this.toRadix(b);
        var km = (1<<k)-1, d, m = false, r = "", i = this.t;
        var p = BigInteger.DB-(i*BigInteger.DB)%k;
        if(i-- > 0) {
            if(p < BigInteger.DB && (d = this_array[i]>>p) > 0) { m = true; r = BigInteger.int2char(d); }
            while(i >= 0) {
                if(p < k) {
                    d = (this_array[i]&((1<<p)-1))<<(k-p);
                    d |= this_array[--i]>>(p+=BigInteger.DB-k);
                }
                else {
                    d = (this_array[i]>>(p-=k))&km;
                    if(p <= 0) { p += BigInteger.DB; --i; }
                }
                if(d > 0) m = true;
                if(m) r += BigInteger.int2char(d);
            }
        }
        return m?r:"0";
    }

    // (public) -this
    function negate() : BigInteger { var r = BigInteger.nbi(); BigInteger.ZERO.subTo(this,r); return r; }

    // (public) |this|
    function abs() : BigInteger { return (this.s<0)?this.negate():this; }

    // (public) return + if this > a, - if this < a, 0 if equal
    function compareTo(a : BigInteger) : number {
        var this_array = this.array;
        var a_array = a.array;

        var r = this.s-a.s;
        if(r != 0) return r;
        var i = this.t;
        r = i-a.t;
        if(r != 0) return r;
        while(--i >= 0) if((r=this_array[i]-a_array[i]) != 0) return r;
        return 0;
    }

    // returns bit length of the integer x
    static function nbits(x : number) : number {
        var r = 1, t;
        if((t=x>>>16) != 0) { x = t; r += 16; }
        if((t=x>>8) != 0) { x = t; r += 8; }
        if((t=x>>4) != 0) { x = t; r += 4; }
        if((t=x>>2) != 0) { x = t; r += 2; }
        if((t=x>>1) != 0) { x = t; r += 1; }
        return r;
    }

    // (public) return the number of bits in "this"
    function bitLength() : number {
        var this_array = this.array;
        if(this.t <= 0) return 0;
        return BigInteger.DB*(this.t-1)+BigInteger.nbits(this_array[this.t-1]^(this.s&BigInteger.DM));
    }

    // (protected) r = this << n*DB
    function dlShiftTo(n : number, r : BigInteger) : void {
        var this_array = this.array;
        var r_array = r.array;
        var i;
        for(i = this.t-1; i >= 0; --i) r_array[i+n] = this_array[i];
        for(i = n-1; i >= 0; --i) r_array[i] = 0;
        r.t = this.t+n;
        r.s = this.s;
    }

    // (protected) r = this >> n*DB
    function drShiftTo(n : number, r : BigInteger) : void {
        var this_array = this.array;
        var r_array = r.array;
        for(var i = n; i < this.t; ++i) r_array[i-n] = this_array[i];
        r.t = Math.max(this.t-n,0);
        r.s = this.s;
    }

    // (protected) r = this << n
    function lShiftTo(n : number, r : BigInteger) : void {
        var this_array = this.array;
        var r_array = r.array;
        var bs = n%BigInteger.DB;
        var cbs = BigInteger.DB-bs;
        var bm = (1<<cbs)-1;
        var ds = Math.floor(n/BigInteger.DB), c = (this.s<<bs)&BigInteger.DM, i;
        for(i = this.t-1; i >= 0; --i) {
            r_array[i+ds+1] = (this_array[i]>>cbs)|c;
            c = (this_array[i]&bm)<<bs;
        }
        for(i = ds-1; i >= 0; --i) r_array[i] = 0;
        r_array[ds] = c;
        r.t = this.t+ds+1;
        r.s = this.s;
        r.clamp();
    }

    // (protected) r = this >> n
    function rShiftTo(n : number, r : BigInteger) : void {
        var this_array = this.array;
        var r_array = r.array;
        r.s = this.s;
        var ds = Math.floor(n/BigInteger.DB);
        if(ds >= this.t) { r.t = 0; return; }
        var bs = n%BigInteger.DB;
        var cbs = BigInteger.DB-bs;
        var bm = (1<<bs)-1;
        r_array[0] = this_array[ds]>>bs;
        for(var i = ds+1; i < this.t; ++i) {
            r_array[i-ds-1] |= (this_array[i]&bm)<<cbs;
            r_array[i-ds] = this_array[i]>>bs;
        }
        if(bs > 0) r_array[this.t-ds-1] |= (this.s&bm)<<cbs;
        r.t = this.t-ds;
        r.clamp();
    }

    // (protected) r = this - a
    function subTo(a : BigInteger, r : BigInteger) : void {
        var this_array = this.array;
        var r_array = r.array;
        var a_array = a.array;
        var i = 0, c = 0, m = Math.min(a.t,this.t);
        while(i < m) {
            c += this_array[i]-a_array[i];
            r_array[i++] = c&BigInteger.DM;
            c >>= BigInteger.DB;
        }
        if(a.t < this.t) {
            c -= a.s;
            while(i < this.t) {
                c += this_array[i];
                r_array[i++] = c&BigInteger.DM;
                c >>= BigInteger.DB;
            }
            c += this.s;
        }
        else {
            c += this.s;
            while(i < a.t) {
                c -= a_array[i];
                r_array[i++] = c&BigInteger.DM;
                c >>= BigInteger.DB;
            }
            c -= a.s;
        }
        r.s = (c<0)?-1:0;
        if(c < -1) r_array[i++] = BigInteger.DV+c;
        else if(c > 0) r_array[i++] = c;
        r.t = i;
        r.clamp();
    }

    // (protected) r = this * a, r != this,a (HAC 14.12)
    // "this" should be the larger one if appropriate.
    function multiplyTo(a : BigInteger, r : BigInteger) : void {
        var this_array = this.array;
        var r_array = r.array;
        var x = this.abs(), y = a.abs();
        var y_array = y.array;

        var i = x.t;
        r.t = i+y.t;
        while(--i >= 0) r_array[i] = 0;
        for(i = 0; i < y.t; ++i) r_array[i+x.t] = BigInteger.am(x.array,0,y_array[i],r,i,0,x.t);
        r.s = 0;
        r.clamp();
        if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
    }

    // (protected) r = this^2, r != this (HAC 14.16)
    function squareTo(r : BigInteger) : void {
        var x = this.abs();
        var x_array = x.array;
        var r_array = r.array;

        var i = r.t = 2*x.t;
        while(--i >= 0) r_array[i] = 0;
        for(i = 0; i < x.t-1; ++i) {
            var c = BigInteger.am(x.array,i,x_array[i],r,2*i,0,1);
            if((r_array[i+x.t]+=BigInteger.am(x.array,i+1,2*x_array[i],r,2*i+1,c,x.t-i-1)) >= BigInteger.DV) {
                r_array[i+x.t] -= BigInteger.DV;
                r_array[i+x.t+1] = 1;
            }
        }
        if(r.t > 0) r_array[r.t-1] += BigInteger.am(x.array,i,x_array[i],r,2*i,0,1);
        r.s = 0;
        r.clamp();
    }

    // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
    // r != q, this != m.  q or r may be null.
    function divRemTo(m : BigInteger, q : BigInteger, r : BigInteger) : void {
        var pm = m.abs();
        if(pm.t <= 0) return;
        var pt = this.abs();
        if(pt.t < pm.t) {
            if(q != null) q.fromInt(0);
            if(r != null) this.copyTo(r);
            return;
        }
        if(r == null) r = BigInteger.nbi();
        var y = BigInteger.nbi(), ts = this.s, ms = m.s;
        var pm_array = pm.array;
        var nsh = BigInteger.DB-BigInteger.nbits(pm_array[pm.t-1]);     // normalize modulus
        if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
        else { pm.copyTo(y); pt.copyTo(r); }
        var ys = y.t;

        var y_array = y.array;
        var y0 = y_array[ys-1];
        if(y0 == 0) return;
        var yt = y0*(1<<BigInteger.F1)+((ys>1)?y_array[ys-2]>>BigInteger.F2:0);
        var d1 = BigInteger.FV/yt, d2 = (1<<BigInteger.F1)/yt, e = 1<<BigInteger.F2;
        var i = r.t, j = i-ys, t = (q==null)?BigInteger.nbi():q;
        y.dlShiftTo(j,t);

        var r_array = r.array;
        if(r.compareTo(t) >= 0) {
            r_array[r.t++] = 1;
            r.subTo(t,r);
        }
        BigInteger.ONE.dlShiftTo(ys,t);
        t.subTo(y,y);   // "negative" y so we can replace sub with am later
        while(y.t < ys) y_array[y.t++] = 0;
        while(--j >= 0) {
            // Estimate quotient digit
            var qd = (r_array[--i]==y0)?BigInteger.DM:Math.floor(r_array[i]*d1+(r_array[i-1]+e)*d2);
            if((r_array[i]+=BigInteger.am(y.array,0,qd,r,j,0,ys)) < qd) {       // Try it out
                y.dlShiftTo(j,t);
                r.subTo(t,r);
                while(r_array[i] < --qd) r.subTo(t,r);
            }
        }
        if(q != null) {
            r.drShiftTo(ys,q);
            if(ts != ms) BigInteger.ZERO.subTo(q,q);
        }
        r.t = ys;
        r.clamp();
        if(nsh > 0) r.rShiftTo(nsh,r);  // Denormalize remainder
        if(ts < 0) BigInteger.ZERO.subTo(r,r);
    }

    // (public) this mod a
    function mod(a : BigInteger) : BigInteger {
        var r = BigInteger.nbi();
        this.abs().divRemTo(a,null,r);
        if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
        return r;
    }

    // (protected) return "-1/this % 2^DB"; useful for Mont. reduction
    // justification:
    //         xy == 1 (mod m)
    //         xy =  1+km
    //   xy(2-xy) = (1+km)(1-km)
    // x[y(2-xy)] = 1-k^2m^2
    // x[y(2-xy)] == 1 (mod m^2)
    // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
    // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
    // JS multiply "overflows" differently from C/C++, so care is needed here.
    function invDigit() : number {
        var this_array = this.array;
        if(this.t < 1) return 0;
        var x = this_array[0];
        if((x&1) == 0) return 0;
        var y = x&3;            // y == 1/x mod 2^2
        y = (y*(2-(x&0xf)*y))&0xf;      // y == 1/x mod 2^4
        y = (y*(2-(x&0xff)*y))&0xff;    // y == 1/x mod 2^8
        y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;     // y == 1/x mod 2^16
        // last step - calculate inverse mod DV directly;
        // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
        y = (y*(2-x*y%BigInteger.DV))%BigInteger.DV;            // y == 1/x mod 2^dbits
        // we really want the negative inverse, and -DV < y < DV
        return (y>0)?BigInteger.DV-y:-y;
    }

    // (protected) true iff this is even
    function isEven() : boolean {
        var this_array = this.array;
        return ((this.t>0)?(this_array[0]&1):this.s) == 0;
    }

    // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
    function exp(e : number, z : Reducer) : BigInteger {
        if(e > 0xffffffff || e < 1) return BigInteger.ONE;
        var r = BigInteger.nbi(), r2 = BigInteger.nbi(), g = z.convert(this), i = BigInteger.nbits(e)-1;
        g.copyTo(r);
        while(--i >= 0) {
            z.sqrTo(r,r2);
            if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
            else { var t = r; r = r2; r2 = t; }
        }
        return z.revert(r);
    }

    // (public) this^e % m, 0 <= e < 2^32
    function modPowInt(e : number, m : BigInteger) : BigInteger {
        var z : Reducer;
        if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
        return this.exp(e,z);
    }


    //--------------------------------------------------------------------------
    // Extended JavaScript BN functions, required for RSA private ops.
    //--------------------------------------------------------------------------

    // (public)
    function clone() : BigInteger { var r = BigInteger.nbi(); this.copyTo(r); return r; }

    // (public) return value as integer
    function intValue() : number {
        var this_array = this.array;
        if(this.s < 0) {
            if(this.t == 1) return this_array[0]-BigInteger.DV;
            else if(this.t == 0) return -1;
        }
        else if(this.t == 1) return this_array[0];
        else if(this.t == 0) return 0;
        // assumes 16 < DB < 32
        return ((this_array[1]&((1<<(32-BigInteger.DB))-1))<<BigInteger.DB)|this_array[0];
    }

    // (public) return value as byte
    function byteValue() : number {
        var this_array = this.array;
        return (this.t==0)?this.s:(this_array[0]<<24)>>24;
    }

    // (public) return value as short (assumes DB>=16)
    function shortValue() : number {
        var this_array = this.array;
        return (this.t==0)?this.s:(this_array[0]<<16)>>16;
    }

    // (protected) return x s.t. r^x < DV
    function chunkSize(r : number) : number { return Math.floor(Math.LN2*BigInteger.DB/Math.log(r)); }

    // (public) 0 if this == 0, 1 if this > 0
    function signum() : number {
        var this_array = this.array;
        if(this.s < 0) return -1;
        else if(this.t <= 0 || (this.t == 1 && this_array[0] <= 0)) return 0;
        else return 1;
    }

    // (protected) convert to radix string
    function toRadix() : string {
        return this.toRadix(10);
    }

    function toRadix(b : number) : string {
        if(this.signum() == 0 || b < 2 || b > 36) return "0";
        var cs = this.chunkSize(b);
        var a = Math.pow(b,cs);
        var d = BigInteger.nbv(a), y = BigInteger.nbi(), z = BigInteger.nbi(), r = "";
        this.divRemTo(d,y,z);
        while(y.signum() > 0) {
            r = (a+z.intValue()).toString(b).substring(1) + r;
            y.divRemTo(d,y,z);
        }
        return z.intValue().toString(b) + r;
    }

    // (protected) convert from radix string
    function fromRadix(s : string) : void {
        this.fromRadix(s, 10);
    }

    function fromRadix(s : string, b : number) : void {
        this.fromInt(0);
        var cs = this.chunkSize(b);
        var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
        for(var i = 0; i < s.length; ++i) {
            var x = BigInteger.intAt(s,i);
            if(x < 0) {
                if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
                continue;
            }
            w = b*w+x;
            if(++j >= cs) {
                this.dMultiply(d);
                this.dAddOffset(w,0);
                j = 0;
                w = 0;
            }
        }
        if(j > 0) {
            this.dMultiply(Math.pow(b,j));
            this.dAddOffset(w,0);
        }
        if(mi) BigInteger.ZERO.subTo(this,this);
    }

    function fromRadix(s : number[], b : number) : void {
        this.fromInt(0);
        var cs = this.chunkSize(b);
        var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
        for(var i = 0; i < s.length; ++i) {
            var x = s[i];
            w = b*w+x;
            if(++j >= cs) {
                this.dMultiply(d);
                this.dAddOffset(w,0);
                j = 0;
                w = 0;
            }
        }
        if(j > 0) {
            this.dMultiply(Math.pow(b,j));
            this.dAddOffset(w,0);
        }
        if(mi) BigInteger.ZERO.subTo(this,this);
    }

    // (protected) alternate constructor
    function fromNumber(a : number, b : number, c : SecureRandom) : void {
        // new BigInteger(int,int,RNG)
        if(a < 2) this.fromInt(1);
        else {
            this.fromNumber(a,c);
            if(!this.testBit(a-1))      // force MSB set
                this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),BigInteger.op_or,this);
            if(this.isEven()) this.dAddOffset(1,0); // force odd
            while(!this.isProbablePrime(b)) {
                this.dAddOffset(2,0);
                if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
            }
        }
    }

    function fromNumber(a : number, b : SecureRandom) : void {
        // new BigInteger(int,RNG)
        var x = new Array.<number>(), t = a&7;
        x.length = (a>>3)+1;
        b.nextBytes(x);
        if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
        this.fromNumberArray(x);
    }

    // (public) convert to bigendian byte array
    function toByteArray() : number[] {
        var this_array = this.array;
        var i = this.t, r = new Array.<number>();
        r[0] = this.s;
        var p = BigInteger.DB-(i*BigInteger.DB)%8, d, k = 0;
        if(i-- > 0) {
            if(p < BigInteger.DB && (d = this_array[i]>>p) != (this.s&BigInteger.DM)>>p)
                r[k++] = d|(this.s<<(BigInteger.DB-p));
            while(i >= 0) {
                if(p < 8) {
                    d = (this_array[i]&((1<<p)-1))<<(8-p);
                    d |= this_array[--i]>>(p+=BigInteger.DB-8);
                }
                else {
                    d = (this_array[i]>>(p-=8))&0xff;
                    if(p <= 0) { p += BigInteger.DB; --i; }
                }
                if((d&0x80) != 0) d |= -256;
                if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
                if(k > 0 || d != this.s) r[k++] = d;
            }
        }
        return r;
    }

    function equals(a : BigInteger) : boolean { return(this.compareTo(a)==0); }
    function min(a : BigInteger) : BigInteger { return(this.compareTo(a)<0)?this:a; }
    function max(a : BigInteger) : BigInteger { return(this.compareTo(a)>0)?this:a; }

    // (protected) r = this op a (bitwise)
    function bitwiseTo(a : BigInteger, op : (number, number) -> number, r : BigInteger) : void {
        var this_array = this.array;
        var a_array    = a.array;
        var r_array    = r.array;
        var i, f, m = Math.min(a.t,this.t);
        for(i = 0; i < m; ++i) r_array[i] = op(this_array[i],a_array[i]);
        if(a.t < this.t) {
            f = a.s&BigInteger.DM;
            for(i = m; i < this.t; ++i) r_array[i] = op(this_array[i],f);
            r.t = this.t;
        }
        else {
            f = this.s&BigInteger.DM;
            for(i = m; i < a.t; ++i) r_array[i] = op(f,a_array[i]);
            r.t = a.t;
        }
        r.s = op(this.s,a.s);
        r.clamp();
    }

    static function op_and(x : number, y : number) : number { return x&y; }
    static function op_or(x : number, y : number) : number { return x|y; }
    static function op_xor(x : number, y : number) : number { return x^y; }
    static function op_andnot(x : number, y : number) : number { return x&~y; }

    // (public) this & a
    function and(a : BigInteger) : BigInteger {
        var r = BigInteger.nbi();
        this.bitwiseTo(a,BigInteger.op_and,r);
        return r;
    }

    // (public) this | a
    function or(a : BigInteger) : BigInteger {
        var r = BigInteger.nbi();
        this.bitwiseTo(a,BigInteger.op_or,r);
        return r;
    }

    // (public) this ^ a
    function xor(a : BigInteger) : BigInteger {
        var r = BigInteger.nbi();
        this.bitwiseTo(a,BigInteger.op_xor,r);
        return r;
    }

    // (public) this & ~a
    function andNot(a : BigInteger) : BigInteger {
        var r = BigInteger.nbi();
        this.bitwiseTo(a,BigInteger.op_andnot,r);
        return r;
    }

    // (public) ~this
    function not() : BigInteger {
        var this_array = this.array;
        var r = BigInteger.nbi();
        var r_array = r.array;

        for(var i = 0; i < this.t; ++i) r_array[i] = BigInteger.DM&~this_array[i];
        r.t = this.t;
        r.s = ~this.s;
        return r;
    }

    // (public) this << n
    function shiftLeft(n : number) : BigInteger {
        var r = BigInteger.nbi();
        if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
        return r;
    }

    // (public) this >> n
    function shiftRight(n : number) : BigInteger {
        var r = BigInteger.nbi();
        if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
        return r;
    }

    // return index of lowest 1-bit in x, x < 2^31
    static function lbit(x : number) : number {
        if(x == 0) return -1;
        var r = 0;
        if((x&0xffff) == 0) { x >>= 16; r += 16; }
        if((x&0xff) == 0) { x >>= 8; r += 8; }
        if((x&0xf) == 0) { x >>= 4; r += 4; }
        if((x&3) == 0) { x >>= 2; r += 2; }
        if((x&1) == 0) ++r;
        return r;
    }

    // (public) returns index of lowest 1-bit (or -1 if none)
    function getLowestSetBit() : number {
        var this_array = this.array;
        for(var i = 0; i < this.t; ++i)
            if(this_array[i] != 0) return i*BigInteger.DB+BigInteger.lbit(this_array[i]);
        if(this.s < 0) return this.t*BigInteger.DB;
        return -1;
    }

    // return number of 1 bits in x
    static function cbit(x : number) : number {
        var r = 0;
        while(x != 0) { x &= x-1; ++r; }
        return r;
    }

    // (public) return number of set bits
    function bitCount() : number {
        var this_array = this.array;
        var r = 0, x = this.s&BigInteger.DM;
        for(var i = 0; i < this.t; ++i) r += BigInteger.cbit(this_array[i]^x);
        return r;
    }

    // (public) true iff nth bit is set
    function testBit(n : number) : boolean {
        var this_array = this.array;
        var j = Math.floor(n/BigInteger.DB);
        if(j >= this.t) return(this.s!=0);
        return((this_array[j]&(1<<(n%BigInteger.DB)))!=0);
    }

    // (protected) this op (1<<n)
    function changeBit(n : number, op : (number,number) -> number) : BigInteger {
        var r = BigInteger.ONE.shiftLeft(n);
        this.bitwiseTo(r,op,r);
        return r;
    }

    // (public) this | (1<<n)
    function setBit(n : number) : BigInteger { return this.changeBit(n,BigInteger.op_or); }

    // (public) this & ~(1<<n)
    function clearBit(n : number) : BigInteger { return this.changeBit(n,BigInteger.op_andnot); }

    // (public) this ^ (1<<n)
    function flipBit(n : number) : BigInteger { return this.changeBit(n,BigInteger.op_xor); }

    // (protected) r = this + a
    function addTo(a : BigInteger, r : BigInteger) : void {
        var this_array = this.array;
        var a_array = a.array;
        var r_array = r.array;
        var i = 0, c = 0, m = Math.min(a.t,this.t);
        while(i < m) {
            c += this_array[i]+a_array[i];
            r_array[i++] = c&BigInteger.DM;
            c >>= BigInteger.DB;
        }
        if(a.t < this.t) {
            c += a.s;
            while(i < this.t) {
                c += this_array[i];
                r_array[i++] = c&BigInteger.DM;
                c >>= BigInteger.DB;
            }
            c += this.s;
        }
        else {
            c += this.s;
            while(i < a.t) {
                c += a_array[i];
                r_array[i++] = c&BigInteger.DM;
                c >>= BigInteger.DB;
            }
            c += a.s;
        }
        r.s = (c<0)?-1:0;
        if(c > 0) r_array[i++] = c;
        else if(c < -1) r_array[i++] = BigInteger.DV+c;
        r.t = i;
        r.clamp();
    }

    // (public) this + a
    function add(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.addTo(a,r); return r; }

    // (public) this - a
    function subtract(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.subTo(a,r); return r; }

    // (public) this * a
    function multiply(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.multiplyTo(a,r); return r; }

    // (public) this / a
    function divide(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.divRemTo(a,r,null); return r; }

    // (public) this % a
    function remainder(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.divRemTo(a,null,r); return r; }

    // (public) [this/a,this%a]
    function divideAndRemainder(a : BigInteger) : BigInteger[] {
        var q = BigInteger.nbi(), r = BigInteger.nbi();
        this.divRemTo(a,q,r);
        return [q,r];
    }

    // (protected) this *= n, this >= 0, 1 < n < DV
    function dMultiply(n : number) : void {
        var this_array = this.array;
        this_array[this.t] = BigInteger.am(this.array,0,n-1,this,0,0,this.t);
        ++this.t;
        this.clamp();
    }

    // (protected) this += n << w words, this >= 0
    function dAddOffset(n : number, w : number) : void {
        var this_array = this.array;
        while(this.t <= w) this_array[this.t++] = 0;
        this_array[w] += n;
        while(this_array[w] >= BigInteger.DV) {
            this_array[w] -= BigInteger.DV;
            if(++w >= this.t) this_array[this.t++] = 0;
            ++this_array[w];
        }
    }


    // (public) this^e
    function pow(e : number) : BigInteger { return this.exp(e,new NullExp()); }

    // (protected) r = lower n words of "this * a", a.t <= n
    // "this" should be the larger one if appropriate.
    function multiplyLowerTo(a : BigInteger, n : number, r : BigInteger) : void {
        var r_array = r.array;
        var a_array = a.array;
        var i = Math.min(this.t+a.t,n);
        r.s = 0; // assumes a,this >= 0
        r.t = i;
        while(i > 0) r_array[--i] = 0;
        var j;
        for(j = r.t-this.t; i < j; ++i) r_array[i+this.t] = BigInteger.am(this.array,0,a_array[i],r,i,0,this.t);
        for(j = Math.min(a.t,n); i < j; ++i) BigInteger.am(this.array,0,a_array[i],r,i,0,n-i);
        r.clamp();
    }

    // (protected) r = "this * a" without lower n words, n > 0
    // "this" should be the larger one if appropriate.
    function multiplyUpperTo(a : BigInteger, n : number, r : BigInteger) : void {
        var r_array = r.array;
        var a_array = a.array;
        --n;
        var i = r.t = this.t+a.t-n;
        r.s = 0; // assumes a,this >= 0
        while(--i >= 0) r_array[i] = 0;
        for(i = Math.max(n-this.t,0); i < a.t; ++i)
            r_array[this.t+i-n] = BigInteger.am(this.array,n-i,a_array[i],r,0,0,this.t+i-n);
        r.clamp();
        r.drShiftTo(1,r);
    }

    // (public) this^e % m (HAC 14.85)
    function modPow(e : BigInteger, m : BigInteger) : BigInteger {
        var e_array = e.array;
        var i = e.bitLength(), k, r = BigInteger.nbv(1), z = null : Reducer;
        if(i <= 0) return r;
        else if(i < 18) k = 1;
        else if(i < 48) k = 3;
        else if(i < 144) k = 4;
        else if(i < 768) k = 5;
        else k = 6;
        if(i < 8)
            z = new Classic(m);
        else if(m.isEven())
            z = new Barrett(m);
        else
            z = new Montgomery(m);

        // precomputation
        var g = new Array.<BigInteger>(), n = 3, k1 = k-1, km = (1<<k)-1;
        g[1] = z.convert(this);
        if(k > 1) {
            var g2 = BigInteger.nbi();
            z.sqrTo(g[1],g2);
            while(n <= km) {
                g[n] = BigInteger.nbi();
                z.mulTo(g2,g[n-2],g[n]);
                n += 2;
            }
        }

        var j = e.t-1, w, is1 = true, r2 = BigInteger.nbi(), t;
        i = BigInteger.nbits(e_array[j])-1;
        while(j >= 0) {
            if(i >= k1) w = (e_array[j]>>(i-k1))&km;
            else {
                w = (e_array[j]&((1<<(i+1))-1))<<(k1-i);
                if(j > 0) w |= e_array[j-1]>>(BigInteger.DB+i-k1);
            }

            n = k;
            while((w&1) == 0) { w >>= 1; --n; }
            if((i -= n) < 0) { i += BigInteger.DB; --j; }
            if(is1) {   // ret == 1, don't bother squaring or multiplying it
                g[w].copyTo(r);
                is1 = false;
            }
            else {
                while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
                if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
                z.mulTo(r2,g[w],r);
            }

            while(j >= 0 && (e_array[j]&(1<<i)) == 0) {
                z.sqrTo(r,r2); t = r; r = r2; r2 = t;
                if(--i < 0) { i = BigInteger.DB-1; --j; }
            }
        }
        return z.revert(r);
    }

    // (public) gcd(this,a) (HAC 14.54)
    function gcd(a : BigInteger) : BigInteger {
        var x = (this.s<0)?this.negate():this.clone();
        var y = (a.s<0)?a.negate():a.clone();
        if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
        var i = x.getLowestSetBit(), g = y.getLowestSetBit();
        if(g < 0) return x;
        if(i < g) g = i;
        if(g > 0) {
            x.rShiftTo(g,x);
            y.rShiftTo(g,y);
        }
        while(x.signum() > 0) {
            if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
            if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
            if(x.compareTo(y) >= 0) {
                x.subTo(y,x);
                x.rShiftTo(1,x);
            }
            else {
                y.subTo(x,y);
                y.rShiftTo(1,y);
            }
        }
        if(g > 0) y.lShiftTo(g,y);
        return y;
    }

    // (protected) this % n, n < 2^26
    function modInt(n : number) : number {
        var this_array = this.array;
        if(n <= 0) return 0;
        var d = BigInteger.DV%n, r = (this.s<0)?n-1:0;
        if(this.t > 0)
            if(d == 0) r = this_array[0]%n;
        else for(var i = this.t-1; i >= 0; --i) r = (d*r+this_array[i])%n;
        return r;
    }

    // (public) 1/this % m (HAC 14.61)
    function modInverse(m : BigInteger) : BigInteger {
        var ac = m.isEven();
        if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
        var u = m.clone(), v = this.clone();
        var a = BigInteger.nbv(1), b = BigInteger.nbv(0), c = BigInteger.nbv(0), d = BigInteger.nbv(1);
        while(u.signum() != 0) {
            while(u.isEven()) {
                u.rShiftTo(1,u);
                if(ac) {
                    if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
                    a.rShiftTo(1,a);
                }
                else if(!b.isEven()) b.subTo(m,b);
                b.rShiftTo(1,b);
            }
            while(v.isEven()) {
                v.rShiftTo(1,v);
                if(ac) {
                    if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
                    c.rShiftTo(1,c);
                }
                else if(!d.isEven()) d.subTo(m,d);
                d.rShiftTo(1,d);
            }
            if(u.compareTo(v) >= 0) {
                u.subTo(v,u);
                if(ac) a.subTo(c,a);
                b.subTo(d,b);
            }
            else {
                v.subTo(u,v);
                if(ac) c.subTo(a,c);
                d.subTo(b,d);
            }
        }
        if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
        if(d.compareTo(m) >= 0) return d.subtract(m);
        if(d.signum() < 0) d.addTo(m,d); else return d;
        if(d.signum() < 0) return d.add(m); else return d;
    }

    static const lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
    static const lplim = (1<<26)/BigInteger.lowprimes[BigInteger.lowprimes.length-1];

    // (public) test primality with certainty >= 1-.5^t
    function isProbablePrime(t : number) : boolean {
        var i, x = this.abs();
        var x_array = x.array;
        if(x.t == 1 && x_array[0] <= BigInteger.lowprimes[BigInteger.lowprimes.length-1]) {
            for(i = 0; i < BigInteger.lowprimes.length; ++i)
                if(x_array[0] == BigInteger.lowprimes[i]) return true;
            return false;
        }
        if(x.isEven()) return false;
        i = 1;
        while(i < BigInteger.lowprimes.length) {
            var m = BigInteger.lowprimes[i], j = i+1;
            while(j < BigInteger.lowprimes.length && m < BigInteger.lplim) m *= BigInteger.lowprimes[j++];
            m = x.modInt(m);
            while(i < j) if(m%BigInteger.lowprimes[i++] == 0) return false;
        }
        return x.millerRabin(t);
    }

    // (protected) true if probably prime (HAC 4.24, Miller-Rabin)
    function millerRabin(t : number) : boolean {
        var n1 = this.subtract(BigInteger.ONE);
        var k = n1.getLowestSetBit();
        if(k <= 0) return false;
        var r = n1.shiftRight(k);
        t = (t+1)>>1;
        if(t > BigInteger.lowprimes.length) t = BigInteger.lowprimes.length;
        var a = BigInteger.nbi();
        for(var i = 0; i < t; ++i) {
            a.fromInt(BigInteger.lowprimes[i]);
            var y = a.modPow(r,this);
            if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
                var j = 1;
                while(j++ < k && y.compareTo(n1) != 0) {
                    y = y.modPowInt(2,this);
                    if(y.compareTo(BigInteger.ONE) == 0) return false;
                }
                if(y.compareTo(n1) != 0) return false;
            }
        }
        return true;
    }

// BigInteger interfaces not implemented in jsbn:

// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
}



interface Reducer {

    function convert(x : BigInteger) : BigInteger;

    function revert(x : BigInteger) : BigInteger;

    function reduce(x : BigInteger) : void;

    function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void;

    function sqrTo(x : BigInteger, r : BigInteger) : void;
}

// Modular reduction using "classic" algorithm
class Classic implements Reducer {

    var m : BigInteger;

    function constructor(m : BigInteger) {
        this.m = m;
    }

    override function convert(x : BigInteger) : BigInteger {
        if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
        else return x;
    }

    override function revert(x : BigInteger) : BigInteger {
        return x;
    }

    override function reduce(x : BigInteger) : void {
        x.divRemTo(this.m,null,x);
    }

    override function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void {
        x.multiplyTo(y,r);
        this.reduce(r);
    }

    override function sqrTo(x : BigInteger, r : BigInteger) : void {
        x.squareTo(r);
        this.reduce(r);
    }
}

// Montgomery reduction
class Montgomery implements Reducer {

    var m       : BigInteger;
    var mp      : number;
    var mpl     : number;
    var mph     : number;
    var um      : number;
    var mt2     : number;

    function constructor(m : BigInteger) {
        this.m = m;
        this.mp = m.invDigit();
        this.mpl = this.mp&0x7fff;
        this.mph = this.mp>>15;
        this.um = (1<<(BigInteger.DB-15))-1;
        this.mt2 = 2*m.t;
    }

    // xR mod m
    override function convert(x : BigInteger) : BigInteger {
        var r = BigInteger.nbi();
        x.abs().dlShiftTo(this.m.t,r);
        r.divRemTo(this.m,null,r);
        if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
        return r;
    }

    // x/R mod m
    override function revert(x : BigInteger) : BigInteger {
        var r = BigInteger.nbi();
        x.copyTo(r);
        this.reduce(r);
        return r;
    }

    // x = x/R mod m (HAC 14.32)
    override function reduce(x : BigInteger) : void {
        var x_array = x.array;
        while(x.t <= this.mt2)  // pad x so am has enough room later
            x_array[x.t++] = 0;
        for(var i = 0; i < this.m.t; ++i) {
            // faster way of calculating u0 = x[i]*mp mod DV
            var j = x_array[i]&0x7fff;
            var u0 = (j*this.mpl+(((j*this.mph+(x_array[i]>>15)*this.mpl)&this.um)<<15))&BigInteger.DM;
            // use am to combine the multiply-shift-add into one call
            j = i+this.m.t;
            x_array[j] += BigInteger.am(this.m.array,0,u0,x,i,0,this.m.t);
            // propagate carry
            while(x_array[j] >= BigInteger.DV) { x_array[j] -= BigInteger.DV; x_array[++j]++; }
        }
        x.clamp();
        x.drShiftTo(this.m.t,x);
        if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
    }

    // r = "x^2/R mod m"; x != r
    override function sqrTo(x : BigInteger, r : BigInteger) : void {
        x.squareTo(r);
        this.reduce(r);
    }

    // r = "xy/R mod m"; x,y != r
    override function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void {
        x.multiplyTo(y,r);
        this.reduce(r);
    }
}


// A "null" reducer
class NullExp implements Reducer {

    function constructor() {
    }

    override function convert(x : BigInteger) : BigInteger {
        return x;
    }

    override function revert(x : BigInteger) : BigInteger {
        return x;
    }

    override function reduce(x : BigInteger) : void {
    }

    override function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void {
        x.multiplyTo(y,r);
    }

    override function sqrTo(x : BigInteger, r : BigInteger) : void {
        x.squareTo(r);
    }
}


// Barrett modular reduction
class Barrett implements Reducer {

    var r2 : BigInteger;
    var q3 : BigInteger;
    var mu : BigInteger;
    var m : BigInteger;

    function constructor(m : BigInteger) {
        // setup Barrett
        this.r2 = BigInteger.nbi();
        this.q3 = BigInteger.nbi();
        BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
        this.mu = this.r2.divide(m);
        this.m = m;
    }

    override function convert(x : BigInteger) : BigInteger {
        if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
        else if(x.compareTo(this.m) < 0) return x;
        else { var r = BigInteger.nbi(); x.copyTo(r); this.reduce(r); return r; }
    }

    override function revert(x : BigInteger) : BigInteger { return x; }

    // x = x mod m (HAC 14.42)
    override function reduce(x : BigInteger) : void {
        x.drShiftTo(this.m.t-1,this.r2);
        if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
        this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
        this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
        while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
        x.subTo(this.r2,x);
        while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
    }

    // r = x^2 mod m; x != r
    override function sqrTo(x : BigInteger, r : BigInteger) : void { x.squareTo(r); this.reduce(r); }

    // r = x*y mod m; x,y != r
    override function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void { x.multiplyTo(y,r); this.reduce(r); }
}

// prng4.js - uses Arcfour as a PRNG
class Arcfour {

    var i : number;
    var j : number;
    var S : number[];

    function constructor() {
        this.i = 0;
        this.j = 0;
        this.S = new Array.<number>();
    }

    // Initialize arcfour context from key, an array of ints, each from [0..255]
    function init(key : number[]) : void {
        var i, j, t;
        for(i = 0; i < 256; ++i)
            this.S[i] = i;
        j = 0;
        for(i = 0; i < 256; ++i) {
            j = (j + this.S[i] + key[i % key.length]) & 255;
            t = this.S[i];
            this.S[i] = this.S[j];
            this.S[j] = t;
        }
        this.i = 0;
        this.j = 0;
    }

    function next() : number {
        var t;
        this.i = (this.i + 1) & 255;
        this.j = (this.j + this.S[this.i]) & 255;
        t = this.S[this.i];
        this.S[this.i] = this.S[this.j];
        this.S[this.j] = t;
        return this.S[(t + this.S[this.i]) & 255];
    }
}


// Random number generator - requires a PRNG backend, e.g. prng4.js
class RNG {

    // Pool size must be a multiple of 4 and greater than 32.
    // An array of bytes the size of the pool will be passed to init()
    static const psize = 256;

    // For best results, put code like
    // <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
    // in your main HTML document.

    static var state : Arcfour;
    static var pool = null : number[];
    static var pptr : number;

    // Initialize the pool with junk if needed.
    static function init() : void {
        if(RNG.pool == null) {
            RNG.pool = new Array.<number>();
            RNG.pptr = 0;
            var t;
            while(RNG.pptr < RNG.psize) {  // extract some randomness from Math.random()
                t = Math.floor(65536 * Math.random());
                RNG.pool[RNG.pptr++] = t >>> 8;
                RNG.pool[RNG.pptr++] = t & 255;
            }
            RNG.pptr = 0;
            RNG.seed_time();
            //RNG.seed_int(window.screenX);
            //RNG.seed_int(window.screenY);
        }
    }

    // Plug in your RNG constructor here
    static function newstate() : Arcfour {
        return new Arcfour();
    }

    // Mix in a 32-bit integer into the pool
    static function seed_int(x : number) : void {
        RNG.pool[RNG.pptr++] ^= x & 255;
        RNG.pool[RNG.pptr++] ^= (x >> 8) & 255;
        RNG.pool[RNG.pptr++] ^= (x >> 16) & 255;
        RNG.pool[RNG.pptr++] ^= (x >> 24) & 255;
        if(RNG.pptr >= RNG.psize) RNG.pptr -= RNG.psize;
    }

    // Mix in the current time (w/milliseconds) into the pool
    static function seed_time() : void {
        // Use pre-computed date to avoid making the benchmark
        // results dependent on the current date.
        RNG.seed_int(1122926989487);
    }

    static function get_byte() : number {
        if(RNG.state == null) {
            RNG.seed_time();
            RNG.state = RNG.newstate();
            RNG.state.init(RNG.pool);
            for(RNG.pptr = 0; RNG.pptr < RNG.pool.length; ++RNG.pptr)
                RNG.pool[RNG.pptr] = 0;
            RNG.pptr = 0;
            //RNG.pool = null;
        }
        // TODO: allow reseeding after first request
        return RNG.state.next();
    }

    static function get_bytes(ba : number[]) : void {
        var i;
        for(i = 0; i < ba.length; ++i) ba[i] = RNG.get_byte();
    }
}

class SecureRandom {

    function constructor() {
        RNG.init();
    }

    function nextBytes(ba : number[]) : void {
        RNG.get_bytes(ba);
    }
}

class RSAKey {

    var n       : BigInteger;
    var e       : number;
    var d       : BigInteger;
    var p       : BigInteger;
    var q       : BigInteger;
    var dmp1    : BigInteger;
    var dmq1    : BigInteger;
    var coeff   : BigInteger;

    // "empty" RSA key constructor
    function constructor() {
        this.n = null;
        this.e = 0;
        this.d = null;
        this.p = null;
        this.q = null;
        this.dmp1 = null;
        this.dmq1 = null;
        this.coeff = null;
    }

    // Set the public key fields N and e from hex strings
    function setPublic(N : Nullable.<string>, E : Nullable.<string>) : void {
        if(N != null && E != null && N.length > 0 && E.length > 0) {
            this.n = BigInteger.parseBigInt(N,16);
            this.e = Number.parseInt(E,16);
        }
        else
            log "Invalid RSA public key";
    }

    // Perform raw public operation on "x": return x^e (mod n)
    function doPublic(x : BigInteger) : BigInteger {
        return x.modPowInt(this.e, this.n);
    }

    // Return the PKCS#1 RSA encryption of "text" as an even-length hex string
    function encrypt(text : string) : Nullable.<string> {
        var m = RSAKey.pkcs1pad2(text,(this.n.bitLength()+7)>>3);
        if(m == null) return null;
        var c = this.doPublic(m);
        if(c == null) return null;
        var h = c.toString(16);
        if((h.length & 1) == 0) return h; else return "0" + h;
    }

    // Return the PKCS#1 RSA encryption of "text" as a Base64-encoded string
    //function encrypt_b64(text) {
    //  var h = this.encrypt(text);
    //  if(h) return hex2b64(h); else return null;
    //}

    // Set the private key fields N, e, and d from hex strings
    function setPrivate(N : Nullable.<string>, E : Nullable.<string>, D : string) : void {
        if(N != null && E != null && N.length > 0 && E.length > 0) {
            this.n = BigInteger.parseBigInt(N,16);
            this.e = Number.parseInt(E,16);
            this.d = BigInteger.parseBigInt(D,16);
        }
        else
            log "Invalid RSA private key";
    }

    // Set the private key fields N, e, d and CRT params from hex strings
    function setPrivateEx(N : Nullable.<string>, E : Nullable.<string>, D : string, P : string, Q : string, DP : string, DQ : string, C : string) : void {
        if(N != null && E != null && N.length > 0 && E.length > 0) {
            this.n = BigInteger.parseBigInt(N,16);
            this.e = Number.parseInt(E,16);
            this.d = BigInteger.parseBigInt(D,16);
            this.p = BigInteger.parseBigInt(P,16);
            this.q = BigInteger.parseBigInt(Q,16);
            this.dmp1 = BigInteger.parseBigInt(DP,16);
            this.dmq1 = BigInteger.parseBigInt(DQ,16);
            this.coeff = BigInteger.parseBigInt(C,16);
        }
        else
            log "Invalid RSA private key";
    }

    // Generate a new random private key B bits long, using public expt E
    function generate(B : number, E : string) : void {
        var rng = new SecureRandom();
        var qs = B>>1;
        this.e = Number.parseInt(E,16);
        var ee = new BigInteger(E,16);
        for(;;) {
            for(;;) {
                this.p = new BigInteger(B-qs,1,rng);
                if(this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.p.isProbablePrime(10)) break;
            }
            for(;;) {
                this.q = new BigInteger(qs,1,rng);
                if(this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.q.isProbablePrime(10)) break;
            }
            if(this.p.compareTo(this.q) <= 0) {
                var t = this.p;
                this.p = this.q;
                this.q = t;
            }
            var p1 = this.p.subtract(BigInteger.ONE);
            var q1 = this.q.subtract(BigInteger.ONE);
            var phi = p1.multiply(q1);
            if(phi.gcd(ee).compareTo(BigInteger.ONE) == 0) {
                this.n = this.p.multiply(this.q);
                this.d = ee.modInverse(phi);
                this.dmp1 = this.d.mod(p1);
                this.dmq1 = this.d.mod(q1);
                this.coeff = this.q.modInverse(this.p);
                break;
            }
        }
    }

    // Perform raw private operation on "x": return x^d (mod n)
    function doPrivate(x : BigInteger) : BigInteger {
        if(this.p == null || this.q == null)
            return x.modPow(this.d, this.n);

        // TODO: re-calculate any missing CRT params
        var xp = x.mod(this.p).modPow(this.dmp1, this.p);
        var xq = x.mod(this.q).modPow(this.dmq1, this.q);

        while(xp.compareTo(xq) < 0)
            xp = xp.add(this.p);
        return xp.subtract(xq).multiply(this.coeff).mod(this.p).multiply(this.q).add(xq);
    }

    // Return the PKCS#1 RSA decryption of "ctext".
    // "ctext" is an even-length hex string and the output is a plain string.
    function decrypt(ctext : string) : Nullable.<string> {
        var c = BigInteger.parseBigInt(ctext, 16);
        var m = this.doPrivate(c);
        if(m == null) return null;
        return RSAKey.pkcs1unpad2(m, (this.n.bitLength()+7)>>3);
    }

    // Return the PKCS#1 RSA decryption of "ctext".
    // "ctext" is a Base64-encoded string and the output is a plain string.
    //function b64_decrypt(ctext) {
    //  var h = b64tohex(ctext);
    //  if(h) return this.decrypt(h); else return null;
    //}

    // PKCS#1 (type 2, random) pad input string s to n bytes, and return a bigint
    static function pkcs1pad2(s : string, n : number) : BigInteger {
        if(n < s.length + 11) {
            log "Message too long for RSA";
            return null;
        }
        var ba = new Array.<number>();
        var i = s.length - 1;
        while(i >= 0 && n > 0) ba[--n] = s.charCodeAt(i--);
        ba[--n] = 0;
        var rng = new SecureRandom();
        var x = new Array.<number>();
        while(n > 2) { // random non-zero pad
            x[0] = 0;
            while(x[0] == 0) rng.nextBytes(x);
            ba[--n] = x[0];
        }
        ba[--n] = 2;
        ba[--n] = 0;
        return new BigInteger(ba);
    }

    // Undo PKCS#1 (type 2, random) padding and, if valid, return the plaintext
    static function pkcs1unpad2(d : BigInteger, n : number) : Nullable.<string> {
        var b = d.toByteArray();
        var i = 0;
        while(i < b.length && b[i] == 0) ++i;
        if(b.length-i != n-1 || b[i] != 2)
            return null;
        ++i;
        while(b[i] != 0)
            if(++i >= b.length) return null;
        var ret = "";
        while(++i < b.length)
            ret += String.fromCharCode(b[i]);
        return ret;
    }
}

// vim: set expandtab: