15c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/* 25c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Copyright (c) 2003-2005 Tom Wu 35c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * All Rights Reserved. 45c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * 55c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Permission is hereby granted, free of charge, to any person obtaining 65c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * a copy of this software and associated documentation files (the 75c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * "Software"), to deal in the Software without restriction, including 85c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * without limitation the rights to use, copy, modify, merge, publish, 95c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * distribute, sublicense, and/or sell copies of the Software, and to 105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * permit persons to whom the Software is furnished to do so, subject to 115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * the following conditions: 125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * 135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * The above copyright notice and this permission notice shall be 145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * included in all copies or substantial portions of the Software. 155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * 165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. 195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * 205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL, 215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER 225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF 235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT 245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * 265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * In addition, the following condition applies: 275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * 285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * All redistributions must retain an intact copy of this copyright notice 295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * and disclaimer. 305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */ 315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Basic JavaScript BN library - subset useful for RSA encryption. 335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Bits per digit 355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var dbits; 365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_DB; 375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_DM; 385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_DV; 395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_FP; 415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_FV; 425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_F1; 435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_F2; 445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// JavaScript engine analysis 465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var canary = 0xdeadbeefcafe; 475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var j_lm = ((canary&0xffffff)==0xefcafe); 485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) Constructor 505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function BigInteger(a,b,c) { 515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.array = new Array(); 525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(a != null) 535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if("number" == typeof a) this.fromNumber(a,b,c); 545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == null && "string" != typeof a) this.fromString(a,256); 555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else this.fromString(a,b); 565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// return new, unset BigInteger 595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function nbi() { return new BigInteger(null); } 605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// am: Compute w_j += (x*this_i), propagate carries, 625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// c is initial carry, returns final carry. 635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// c < 3*dvalue, x < 2*dvalue, this_i < dvalue 645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// We need to select the fastest one that works in this environment. 655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// am1: use a single mult and divide to get the high bits, 675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// max digit bits should be 26 because 685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// max internal value = 2*dvalue^2-2*dvalue (< 2^53) 695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function am1(i,x,w,j,c,n) { 705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var w_array = w.array; 725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--n >= 0) { 735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var v = x*this_array[i++]+w_array[j]+c; 745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c = Math.floor(v/0x4000000); 755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) w_array[j++] = v&0x3ffffff; 765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return c; 785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// am2 avoids a big mult-and-extract completely. 815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Max digit bits should be <= 30 because we do bitwise ops 825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31) 835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function am2(i,x,w,j,c,n) { 845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var w_array = w.array; 865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var xl = x&0x7fff, xh = x>>15; 875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--n >= 0) { 885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var l = this_array[i]&0x7fff; 895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var h = this_array[i++]>>15; 905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var m = xh*l+h*xl; 915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) l = xl*l+((m&0x7fff)<<15)+w_array[j]+(c&0x3fffffff); 925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c = (l>>>30)+(m>>>15)+xh*h+(c>>>30); 935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) w_array[j++] = l&0x3fffffff; 945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return c; 965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Alternately, set max digit bits to 28 since some 995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// browsers slow down when dealing with 32-bit numbers. 1005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function am3(i,x,w,j,c,n) { 1015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 1025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var w_array = w.array; 1035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var xl = x&0x3fff, xh = x>>14; 1055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--n >= 0) { 1065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var l = this_array[i]&0x3fff; 1075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var h = this_array[i++]>>14; 1085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var m = xh*l+h*xl; 1095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) l = xl*l+((m&0x3fff)<<14)+w_array[j]+c; 1105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c = (l>>28)+(m>>14)+xh*h; 1115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) w_array[j++] = l&0xfffffff; 1125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 1135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return c; 1145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 1155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// This is tailored to VMs with 2-bit tagging. It makes sure 1175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// that all the computations stay within the 29 bits available. 1185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function am4(i,x,w,j,c,n) { 1195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 1205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var w_array = w.array; 1215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var xl = x&0x1fff, xh = x>>13; 1235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--n >= 0) { 1245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var l = this_array[i]&0x1fff; 1255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var h = this_array[i++]>>13; 1265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var m = xh*l+h*xl; 1275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) l = xl*l+((m&0x1fff)<<13)+w_array[j]+c; 1285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c = (l>>26)+(m>>13)+xh*h; 1295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) w_array[j++] = l&0x3ffffff; 1305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 1315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return c; 1325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 1335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// am3/28 is best for SM, Rhino, but am4/26 is best for v8. 1355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Kestrel (Opera 9.5) gets its best result with am4/26. 1365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// IE7 does 9% better with am3/28 than with am4/26. 1375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Firefox (SM) gets 10% faster with am3/28 than with am4/26. 1385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)setupEngine = function(fn, bits) { 1405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BigInteger.prototype.am = fn; 1415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) dbits = bits; 1425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BI_DB = dbits; 1445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BI_DM = ((1<<dbits)-1); 1455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BI_DV = (1<<dbits); 1465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BI_FP = 52; 1485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BI_FV = Math.pow(2,BI_FP); 1495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BI_F1 = BI_FP-dbits; 1505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BI_F2 = 2*dbits-BI_FP; 1515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 1525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Digit conversions 1555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz"; 1565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var BI_RC = new Array(); 1575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var rr,vv; 1585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)rr = "0".charCodeAt(0); 1595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv; 1605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)rr = "a".charCodeAt(0); 1615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv; 1625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)rr = "A".charCodeAt(0); 1635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv; 1645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function int2char(n) { return BI_RM.charAt(n); } 1665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function intAt(s,i) { 1675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var c = BI_RC[s.charCodeAt(i)]; 1685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return (c==null)?-1:c; 1695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 1705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) copy this to r 1725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpCopyTo(r) { 1735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 1745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 1755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = this.t-1; i >= 0; --i) r_array[i] = this_array[i]; 1775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = this.t; 1785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = this.s; 1795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 1805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) set from integer value x, -DV <= x < DV 1825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpFromInt(x) { 1835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 1845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.t = 1; 1855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.s = (x<0)?-1:0; 1865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x > 0) this_array[0] = x; 1875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(x < -1) this_array[0] = x+DV; 1885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else this.t = 0; 1895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 1905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// return bigint initialized to value 1925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function nbv(i) { var r = nbi(); r.fromInt(i); return r; } 1935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 1945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) set from string and radix 1955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpFromString(s,b) { 1965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 1975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var k; 1985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(b == 16) k = 4; 1995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 8) k = 3; 2005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 256) k = 8; // byte array 2015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 2) k = 1; 2025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 32) k = 5; 2035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 4) k = 2; 2045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { this.fromRadix(s,b); return; } 2055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.t = 0; 2065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.s = 0; 2075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = s.length, mi = false, sh = 0; 2085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--i >= 0) { 2095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x = (k==8)?s[i]&0xff:intAt(s,i); 2105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x < 0) { 2115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(s.charAt(i) == "-") mi = true; 2125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) continue; 2135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 2145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) mi = false; 2155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(sh == 0) 2165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this_array[this.t++] = x; 2175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(sh+k > BI_DB) { 2185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this_array[this.t-1] |= (x&((1<<(BI_DB-sh))-1))<<sh; 2195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this_array[this.t++] = (x>>(BI_DB-sh)); 2205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 2215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else 2225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this_array[this.t-1] |= x<<sh; 2235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) sh += k; 2245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(sh >= BI_DB) sh -= BI_DB; 2255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 2265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(k == 8 && (s[0]&0x80) != 0) { 2275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.s = -1; 2285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(sh > 0) this_array[this.t-1] |= ((1<<(BI_DB-sh))-1)<<sh; 2295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 2305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.clamp(); 2315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(mi) BigInteger.ZERO.subTo(this,this); 2325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 2335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 2345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) clamp off excess high words 2355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpClamp() { 2365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 2375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var c = this.s&BI_DM; 2385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(this.t > 0 && this_array[this.t-1] == c) --this.t; 2395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 2405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 2415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) return string representation in given radix 2425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnToString(b) { 2435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 2445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.s < 0) return "-"+this.negate().toString(b); 2455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var k; 2465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(b == 16) k = 4; 2475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 8) k = 3; 2485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 2) k = 1; 2495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 32) k = 5; 2505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(b == 4) k = 2; 2515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else return this.toRadix(b); 2525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var km = (1<<k)-1, d, m = false, r = "", i = this.t; 2535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var p = BI_DB-(i*BI_DB)%k; 2545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(i-- > 0) { 2555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(p < BI_DB && (d = this_array[i]>>p) > 0) { m = true; r = int2char(d); } 2565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i >= 0) { 2575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(p < k) { 2585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) d = (this_array[i]&((1<<p)-1))<<(k-p); 2595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) d |= this_array[--i]>>(p+=BI_DB-k); 2605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 2615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 2625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) d = (this_array[i]>>(p-=k))&km; 2635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(p <= 0) { p += BI_DB; --i; } 2645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 2655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(d > 0) m = true; 2665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(m) r += int2char(d); 2675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 2685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 2695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return m?r:"0"; 2705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 2715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 2725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) -this 2735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; } 2745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 2755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) |this| 2765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnAbs() { return (this.s<0)?this.negate():this; } 2775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 2785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) return + if this > a, - if this < a, 0 if equal 2795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnCompareTo(a) { 2805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 2815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a_array = a.array; 2825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 2835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = this.s-a.s; 2845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(r != 0) return r; 2855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = this.t; 2865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r = i-a.t; 2875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(r != 0) return r; 2885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--i >= 0) if((r=this_array[i]-a_array[i]) != 0) return r; 2895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return 0; 2905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 2915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 2925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// returns bit length of the integer x 2935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function nbits(x) { 2945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = 1, t; 2955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((t=x>>>16) != 0) { x = t; r += 16; } 2965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((t=x>>8) != 0) { x = t; r += 8; } 2975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((t=x>>4) != 0) { x = t; r += 4; } 2985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((t=x>>2) != 0) { x = t; r += 2; } 2995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((t=x>>1) != 0) { x = t; r += 1; } 3005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 3015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 3025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 3035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) return the number of bits in "this" 3045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnBitLength() { 3055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 3065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.t <= 0) return 0; 3075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return BI_DB*(this.t-1)+nbits(this_array[this.t-1]^(this.s&BI_DM)); 3085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 3095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 3105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this << n*DB 3115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpDLShiftTo(n,r) { 3125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 3135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 3145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i; 3155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = this.t-1; i >= 0; --i) r_array[i+n] = this_array[i]; 3165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = n-1; i >= 0; --i) r_array[i] = 0; 3175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = this.t+n; 3185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = this.s; 3195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 3205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 3215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this >> n*DB 3225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpDRShiftTo(n,r) { 3235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 3245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 3255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = n; i < this.t; ++i) r_array[i-n] = this_array[i]; 3265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = Math.max(this.t-n,0); 3275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = this.s; 3285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 3295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 3305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this << n 3315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpLShiftTo(n,r) { 3325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 3335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 3345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var bs = n%BI_DB; 3355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var cbs = BI_DB-bs; 3365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var bm = (1<<cbs)-1; 3375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var ds = Math.floor(n/BI_DB), c = (this.s<<bs)&BI_DM, i; 3385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = this.t-1; i >= 0; --i) { 3395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i+ds+1] = (this_array[i]>>cbs)|c; 3405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c = (this_array[i]&bm)<<bs; 3415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 3425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = ds-1; i >= 0; --i) r_array[i] = 0; 3435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[ds] = c; 3445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = this.t+ds+1; 3455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = this.s; 3465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 3475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 3485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 3495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this >> n 3505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpRShiftTo(n,r) { 3515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 3525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 3535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = this.s; 3545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var ds = Math.floor(n/BI_DB); 3555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(ds >= this.t) { r.t = 0; return; } 3565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var bs = n%BI_DB; 3575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var cbs = BI_DB-bs; 3585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var bm = (1<<bs)-1; 3595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[0] = this_array[ds]>>bs; 3605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = ds+1; i < this.t; ++i) { 3615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i-ds-1] |= (this_array[i]&bm)<<cbs; 3625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i-ds] = this_array[i]>>bs; 3635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 3645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(bs > 0) r_array[this.t-ds-1] |= (this.s&bm)<<cbs; 3655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = this.t-ds; 3665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 3675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 3685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 3695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this - a 3705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpSubTo(a,r) { 3715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 3725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 3735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a_array = a.array; 3745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = 0, c = 0, m = Math.min(a.t,this.t); 3755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < m) { 3765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += this_array[i]-a_array[i]; 3775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i++] = c&BI_DM; 3785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c >>= BI_DB; 3795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 3805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(a.t < this.t) { 3815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c -= a.s; 3825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < this.t) { 3835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += this_array[i]; 3845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i++] = c&BI_DM; 3855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c >>= BI_DB; 3865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 3875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += this.s; 3885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 3895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 3905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += this.s; 3915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < a.t) { 3925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c -= a_array[i]; 3935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i++] = c&BI_DM; 3945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c >>= BI_DB; 3955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 3965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c -= a.s; 3975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 3985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = (c<0)?-1:0; 3995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(c < -1) r_array[i++] = BI_DV+c; 4005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(c > 0) r_array[i++] = c; 4015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = i; 4025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 4035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 4045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 4055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this * a, r != this,a (HAC 14.12) 4065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// "this" should be the larger one if appropriate. 4075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpMultiplyTo(a,r) { 4085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 4095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 4105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x = this.abs(), y = a.abs(); 4115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var y_array = y.array; 4125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 4135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = x.t; 4145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = i+y.t; 4155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--i >= 0) r_array[i] = 0; 4165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = 0; i < y.t; ++i) r_array[i+x.t] = x.am(0,y_array[i],r,i,0,x.t); 4175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = 0; 4185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 4195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.s != a.s) BigInteger.ZERO.subTo(r,r); 4205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 4215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 4225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this^2, r != this (HAC 14.16) 4235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpSquareTo(r) { 4245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x = this.abs(); 4255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x_array = x.array; 4265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 4275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 4285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = r.t = 2*x.t; 4295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--i >= 0) r_array[i] = 0; 4305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = 0; i < x.t-1; ++i) { 4315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var c = x.am(i,x_array[i],r,2*i,0,1); 4325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((r_array[i+x.t]+=x.am(i+1,2*x_array[i],r,2*i+1,c,x.t-i-1)) >= BI_DV) { 4335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i+x.t] -= BI_DV; 4345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i+x.t+1] = 1; 4355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 4365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 4375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(r.t > 0) r_array[r.t-1] += x.am(i,x_array[i],r,2*i,0,1); 4385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = 0; 4395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 4405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 4415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 4425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20) 4435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// r != q, this != m. q or r may be null. 4445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpDivRemTo(m,q,r) { 4455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var pm = m.abs(); 4465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(pm.t <= 0) return; 4475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var pt = this.abs(); 4485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(pt.t < pm.t) { 4495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(q != null) q.fromInt(0); 4505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(r != null) this.copyTo(r); 4515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return; 4525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 4535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(r == null) r = nbi(); 4545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var y = nbi(), ts = this.s, ms = m.s; 4555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var pm_array = pm.array; 4565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var nsh = BI_DB-nbits(pm_array[pm.t-1]); // normalize modulus 4575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); } 4585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { pm.copyTo(y); pt.copyTo(r); } 4595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var ys = y.t; 4605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 4615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var y_array = y.array; 4625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var y0 = y_array[ys-1]; 4635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(y0 == 0) return; 4645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var yt = y0*(1<<BI_F1)+((ys>1)?y_array[ys-2]>>BI_F2:0); 4655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var d1 = BI_FV/yt, d2 = (1<<BI_F1)/yt, e = 1<<BI_F2; 4665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = r.t, j = i-ys, t = (q==null)?nbi():q; 4675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y.dlShiftTo(j,t); 4685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 4695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 4705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(r.compareTo(t) >= 0) { 4715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[r.t++] = 1; 4725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.subTo(t,r); 4735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 4745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BigInteger.ONE.dlShiftTo(ys,t); 4755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) t.subTo(y,y); // "negative" y so we can replace sub with am later 4765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(y.t < ys) y_array[y.t++] = 0; 4775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--j >= 0) { 4785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // Estimate quotient digit 4795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var qd = (r_array[--i]==y0)?BI_DM:Math.floor(r_array[i]*d1+(r_array[i-1]+e)*d2); 4805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((r_array[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out 4815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y.dlShiftTo(j,t); 4825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.subTo(t,r); 4835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(r_array[i] < --qd) r.subTo(t,r); 4845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 4855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 4865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(q != null) { 4875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.drShiftTo(ys,q); 4885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(ts != ms) BigInteger.ZERO.subTo(q,q); 4895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 4905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = ys; 4915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 4925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder 4935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(ts < 0) BigInteger.ZERO.subTo(r,r); 4945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 4955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 4965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this mod a 4975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnMod(a) { 4985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = nbi(); 4995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.abs().divRemTo(a,null,r); 5005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r); 5015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 5025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 5035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Modular reduction using "classic" algorithm 5055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function Classic(m) { this.m = m; } 5065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function cConvert(x) { 5075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m); 5085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else return x; 5095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 5105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function cRevert(x) { return x; } 5115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function cReduce(x) { x.divRemTo(this.m,null,x); } 5125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); } 5135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); } 5145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Classic.prototype.convert = cConvert; 5165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Classic.prototype.revert = cRevert; 5175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Classic.prototype.reduce = cReduce; 5185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Classic.prototype.mulTo = cMulTo; 5195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Classic.prototype.sqrTo = cSqrTo; 5205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) return "-1/this % 2^DB"; useful for Mont. reduction 5225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// justification: 5235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// xy == 1 (mod m) 5245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// xy = 1+km 5255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// xy(2-xy) = (1+km)(1-km) 5265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// x[y(2-xy)] = 1-k^2m^2 5275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// x[y(2-xy)] == 1 (mod m^2) 5285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2 5295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// should reduce x and y(2-xy) by m^2 at each step to keep size bounded. 5305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// JS multiply "overflows" differently from C/C++, so care is needed here. 5315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpInvDigit() { 5325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 5335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.t < 1) return 0; 5345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x = this_array[0]; 5355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((x&1) == 0) return 0; 5365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var y = x&3; // y == 1/x mod 2^2 5375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4 5385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8 5395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16 5405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // last step - calculate inverse mod DV directly; 5415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints 5425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y = (y*(2-x*y%BI_DV))%BI_DV; // y == 1/x mod 2^dbits 5435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // we really want the negative inverse, and -DV < y < DV 5445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return (y>0)?BI_DV-y:-y; 5455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 5465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Montgomery reduction 5485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function Montgomery(m) { 5495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.m = m; 5505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.mp = m.invDigit(); 5515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.mpl = this.mp&0x7fff; 5525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.mph = this.mp>>15; 5535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.um = (1<<(BI_DB-15))-1; 5545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.mt2 = 2*m.t; 5555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 5565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// xR mod m 5585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function montConvert(x) { 5595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = nbi(); 5605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.abs().dlShiftTo(this.m.t,r); 5615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.divRemTo(this.m,null,r); 5625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r); 5635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 5645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 5655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// x/R mod m 5675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function montRevert(x) { 5685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = nbi(); 5695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.copyTo(r); 5705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.reduce(r); 5715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 5725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 5735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// x = x/R mod m (HAC 14.32) 5755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function montReduce(x) { 5765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x_array = x.array; 5775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(x.t <= this.mt2) // pad x so am has enough room later 5785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x_array[x.t++] = 0; 5795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = 0; i < this.m.t; ++i) { 5805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // faster way of calculating u0 = x[i]*mp mod DV 5815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var j = x_array[i]&0x7fff; 5825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var u0 = (j*this.mpl+(((j*this.mph+(x_array[i]>>15)*this.mpl)&this.um)<<15))&BI_DM; 5835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // use am to combine the multiply-shift-add into one call 5845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) j = i+this.m.t; 5855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x_array[j] += this.m.am(0,u0,x,i,0,this.m.t); 5865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // propagate carry 5875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(x_array[j] >= BI_DV) { x_array[j] -= BI_DV; x_array[++j]++; } 5885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 5895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.clamp(); 5905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.drShiftTo(this.m.t,x); 5915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.compareTo(this.m) >= 0) x.subTo(this.m,x); 5925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 5935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// r = "x^2/R mod m"; x != r 5955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); } 5965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 5975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// r = "xy/R mod m"; x,y != r 5985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); } 5995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Montgomery.prototype.convert = montConvert; 6015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Montgomery.prototype.revert = montRevert; 6025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Montgomery.prototype.reduce = montReduce; 6035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Montgomery.prototype.mulTo = montMulTo; 6045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Montgomery.prototype.sqrTo = montSqrTo; 6055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) true iff this is even 6075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpIsEven() { 6085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 6095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return ((this.t>0)?(this_array[0]&1):this.s) == 0; 6105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 6115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79) 6135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpExp(e,z) { 6145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(e > 0xffffffff || e < 1) return BigInteger.ONE; 6155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1; 6165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) g.copyTo(r); 6175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--i >= 0) { 6185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) z.sqrTo(r,r2); 6195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((e&(1<<i)) > 0) z.mulTo(r2,g,r); 6205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { var t = r; r = r2; r2 = t; } 6215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 6225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return z.revert(r); 6235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 6245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this^e % m, 0 <= e < 2^32 6265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnModPowInt(e,m) { 6275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var z; 6285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m); 6295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return this.exp(e,z); 6305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 6315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// protected 6335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.copyTo = bnpCopyTo; 6345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.fromInt = bnpFromInt; 6355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.fromString = bnpFromString; 6365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.clamp = bnpClamp; 6375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.dlShiftTo = bnpDLShiftTo; 6385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.drShiftTo = bnpDRShiftTo; 6395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.lShiftTo = bnpLShiftTo; 6405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.rShiftTo = bnpRShiftTo; 6415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.subTo = bnpSubTo; 6425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.multiplyTo = bnpMultiplyTo; 6435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.squareTo = bnpSquareTo; 6445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.divRemTo = bnpDivRemTo; 6455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.invDigit = bnpInvDigit; 6465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.isEven = bnpIsEven; 6475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.exp = bnpExp; 6485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// public 6505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.toString = bnToString; 6515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.negate = bnNegate; 6525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.abs = bnAbs; 6535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.compareTo = bnCompareTo; 6545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.bitLength = bnBitLength; 6555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.mod = bnMod; 6565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.modPowInt = bnModPowInt; 6575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// "constants" 6595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.ZERO = nbv(0); 6605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.ONE = nbv(1); 6615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Copyright (c) 2005 Tom Wu 6625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// All Rights Reserved. 6635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// See "LICENSE" for details. 6645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Extended JavaScript BN functions, required for RSA private ops. 6665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) 6685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnClone() { var r = nbi(); this.copyTo(r); return r; } 6695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) return value as integer 6715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnIntValue() { 6725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 6735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.s < 0) { 6745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.t == 1) return this_array[0]-BI_DV; 6755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(this.t == 0) return -1; 6765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 6775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(this.t == 1) return this_array[0]; 6785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(this.t == 0) return 0; 6795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // assumes 16 < DB < 32 6805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return ((this_array[1]&((1<<(32-BI_DB))-1))<<BI_DB)|this_array[0]; 6815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 6825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) return value as byte 6845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnByteValue() { 6855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 6865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return (this.t==0)?this.s:(this_array[0]<<24)>>24; 6875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 6885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) return value as short (assumes DB>=16) 6905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnShortValue() { 6915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 6925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return (this.t==0)?this.s:(this_array[0]<<16)>>16; 6935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 6945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) return x s.t. r^x < DV 6965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpChunkSize(r) { return Math.floor(Math.LN2*BI_DB/Math.log(r)); } 6975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 6985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) 0 if this == 0, 1 if this > 0 6995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnSigNum() { 7005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 7015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.s < 0) return -1; 7025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(this.t <= 0 || (this.t == 1 && this_array[0] <= 0)) return 0; 7035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else return 1; 7045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 7055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 7065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) convert to radix string 7075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpToRadix(b) { 7085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(b == null) b = 10; 7095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.signum() == 0 || b < 2 || b > 36) return "0"; 7105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var cs = this.chunkSize(b); 7115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a = Math.pow(b,cs); 7125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var d = nbv(a), y = nbi(), z = nbi(), r = ""; 7135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.divRemTo(d,y,z); 7145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(y.signum() > 0) { 7155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r = (a+z.intValue()).toString(b).substr(1) + r; 7165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y.divRemTo(d,y,z); 7175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return z.intValue().toString(b) + r; 7195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 7205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 7215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) convert from radix string 7225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpFromRadix(s,b) { 7235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.fromInt(0); 7245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(b == null) b = 10; 7255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var cs = this.chunkSize(b); 7265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var d = Math.pow(b,cs), mi = false, j = 0, w = 0; 7275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = 0; i < s.length; ++i) { 7285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x = intAt(s,i); 7295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x < 0) { 7305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(s.charAt(i) == "-" && this.signum() == 0) mi = true; 7315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) continue; 7325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) w = b*w+x; 7345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(++j >= cs) { 7355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dMultiply(d); 7365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dAddOffset(w,0); 7375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) j = 0; 7385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) w = 0; 7395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(j > 0) { 7425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dMultiply(Math.pow(b,j)); 7435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dAddOffset(w,0); 7445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(mi) BigInteger.ZERO.subTo(this,this); 7465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 7475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 7485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) alternate constructor 7495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpFromNumber(a,b,c) { 7505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if("number" == typeof b) { 7515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // new BigInteger(int,int,RNG) 7525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(a < 2) this.fromInt(1); 7535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 7545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.fromNumber(a,c); 7555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(!this.testBit(a-1)) // force MSB set 7565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this); 7575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.isEven()) this.dAddOffset(1,0); // force odd 7585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(!this.isProbablePrime(b)) { 7595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dAddOffset(2,0); 7605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this); 7615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 7655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // new BigInteger(int,RNG) 7665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x = new Array(), t = a&7; 7675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.length = (a>>3)+1; 7685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) b.nextBytes(x); 7695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0; 7705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.fromString(x,256); 7715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 7735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 7745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) convert to bigendian byte array 7755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnToByteArray() { 7765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 7775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = this.t, r = new Array(); 7785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r[0] = this.s; 7795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var p = BI_DB-(i*BI_DB)%8, d, k = 0; 7805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(i-- > 0) { 7815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(p < BI_DB && (d = this_array[i]>>p) != (this.s&BI_DM)>>p) 7825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r[k++] = d|(this.s<<(BI_DB-p)); 7835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i >= 0) { 7845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(p < 8) { 7855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) d = (this_array[i]&((1<<p)-1))<<(8-p); 7865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) d |= this_array[--i]>>(p+=BI_DB-8); 7875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 7895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) d = (this_array[i]>>(p-=8))&0xff; 7905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(p <= 0) { p += BI_DB; --i; } 7915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((d&0x80) != 0) d |= -256; 7935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(k == 0 && (this.s&0x80) != (d&0x80)) ++k; 7945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(k > 0 || d != this.s) r[k++] = d; 7955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 7975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 7985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 7995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnEquals(a) { return(this.compareTo(a)==0); } 8015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnMin(a) { return(this.compareTo(a)<0)?this:a; } 8025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnMax(a) { return(this.compareTo(a)>0)?this:a; } 8035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this op a (bitwise) 8055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpBitwiseTo(a,op,r) { 8065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 8075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a_array = a.array; 8085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 8095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i, f, m = Math.min(a.t,this.t); 8105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = 0; i < m; ++i) r_array[i] = op(this_array[i],a_array[i]); 8115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(a.t < this.t) { 8125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) f = a.s&BI_DM; 8135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = m; i < this.t; ++i) r_array[i] = op(this_array[i],f); 8145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = this.t; 8155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 8165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 8175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) f = this.s&BI_DM; 8185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = m; i < a.t; ++i) r_array[i] = op(f,a_array[i]); 8195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = a.t; 8205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 8215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = op(this.s,a.s); 8225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 8235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 8245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this & a 8265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function op_and(x,y) { return x&y; } 8275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; } 8285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this | a 8305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function op_or(x,y) { return x|y; } 8315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; } 8325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this ^ a 8345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function op_xor(x,y) { return x^y; } 8355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; } 8365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this & ~a 8385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function op_andnot(x,y) { return x&~y; } 8395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; } 8405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) ~this 8425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnNot() { 8435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 8445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = nbi(); 8455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 8465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = 0; i < this.t; ++i) r_array[i] = BI_DM&~this_array[i]; 8485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = this.t; 8495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = ~this.s; 8505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 8515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 8525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this << n 8545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnShiftLeft(n) { 8555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = nbi(); 8565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r); 8575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 8585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 8595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this >> n 8615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnShiftRight(n) { 8625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = nbi(); 8635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r); 8645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 8655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 8665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// return index of lowest 1-bit in x, x < 2^31 8685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function lbit(x) { 8695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x == 0) return -1; 8705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = 0; 8715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((x&0xffff) == 0) { x >>= 16; r += 16; } 8725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((x&0xff) == 0) { x >>= 8; r += 8; } 8735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((x&0xf) == 0) { x >>= 4; r += 4; } 8745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((x&3) == 0) { x >>= 2; r += 2; } 8755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((x&1) == 0) ++r; 8765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 8775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 8785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) returns index of lowest 1-bit (or -1 if none) 8805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnGetLowestSetBit() { 8815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 8825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = 0; i < this.t; ++i) 8835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this_array[i] != 0) return i*BI_DB+lbit(this_array[i]); 8845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.s < 0) return this.t*BI_DB; 8855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return -1; 8865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 8875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// return number of 1 bits in x 8895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function cbit(x) { 8905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = 0; 8915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(x != 0) { x &= x-1; ++r; } 8925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 8935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 8945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 8955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) return number of set bits 8965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnBitCount() { 8975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = 0, x = this.s&BI_DM; 8985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = 0; i < this.t; ++i) r += cbit(this_array[i]^x); 8995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 9005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 9015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) true iff nth bit is set 9035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnTestBit(n) { 9045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 9055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var j = Math.floor(n/BI_DB); 9065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(j >= this.t) return(this.s!=0); 9075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return((this_array[j]&(1<<(n%BI_DB)))!=0); 9085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 9095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) this op (1<<n) 9115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpChangeBit(n,op) { 9125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = BigInteger.ONE.shiftLeft(n); 9135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.bitwiseTo(r,op,r); 9145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 9155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 9165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this | (1<<n) 9185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnSetBit(n) { return this.changeBit(n,op_or); } 9195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this & ~(1<<n) 9215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnClearBit(n) { return this.changeBit(n,op_andnot); } 9225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this ^ (1<<n) 9245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnFlipBit(n) { return this.changeBit(n,op_xor); } 9255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = this + a 9275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpAddTo(a,r) { 9285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 9295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a_array = a.array; 9305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 9315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = 0, c = 0, m = Math.min(a.t,this.t); 9325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < m) { 9335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += this_array[i]+a_array[i]; 9345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i++] = c&BI_DM; 9355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c >>= BI_DB; 9365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 9375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(a.t < this.t) { 9385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += a.s; 9395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < this.t) { 9405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += this_array[i]; 9415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i++] = c&BI_DM; 9425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c >>= BI_DB; 9435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 9445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += this.s; 9455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 9465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 9475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += this.s; 9485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < a.t) { 9495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += a_array[i]; 9505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[i++] = c&BI_DM; 9515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c >>= BI_DB; 9525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 9535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c += a.s; 9545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 9555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = (c<0)?-1:0; 9565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(c > 0) r_array[i++] = c; 9575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(c < -1) r_array[i++] = BI_DV+c; 9585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = i; 9595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 9605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 9615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this + a 9635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; } 9645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this - a 9665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; } 9675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this * a 9695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; } 9705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this / a 9725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; } 9735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this % a 9755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; } 9765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) [this/a,this%a] 9785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnDivideAndRemainder(a) { 9795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var q = nbi(), r = nbi(); 9805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.divRemTo(a,q,r); 9815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return new Array(q,r); 9825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 9835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) this *= n, this >= 0, 1 < n < DV 9855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpDMultiply(n) { 9865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 9875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this_array[this.t] = this.am(0,n-1,this,0,0,this.t); 9885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ++this.t; 9895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.clamp(); 9905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 9915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 9925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) this += n << w words, this >= 0 9935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpDAddOffset(n,w) { 9945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 9955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(this.t <= w) this_array[this.t++] = 0; 9965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this_array[w] += n; 9975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(this_array[w] >= BI_DV) { 9985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this_array[w] -= BI_DV; 9995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(++w >= this.t) this_array[this.t++] = 0; 10005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ++this_array[w]; 10015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 10025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 10035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// A "null" reducer 10055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function NullExp() {} 10065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function nNop(x) { return x; } 10075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function nMulTo(x,y,r) { x.multiplyTo(y,r); } 10085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function nSqrTo(x,r) { x.squareTo(r); } 10095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)NullExp.prototype.convert = nNop; 10115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)NullExp.prototype.revert = nNop; 10125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)NullExp.prototype.mulTo = nMulTo; 10135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)NullExp.prototype.sqrTo = nSqrTo; 10145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this^e 10165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnPow(e) { return this.exp(e,new NullExp()); } 10175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = lower n words of "this * a", a.t <= n 10195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// "this" should be the larger one if appropriate. 10205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpMultiplyLowerTo(a,n,r) { 10215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 10225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a_array = a.array; 10235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = Math.min(this.t+a.t,n); 10245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = 0; // assumes a,this >= 0 10255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.t = i; 10265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i > 0) r_array[--i] = 0; 10275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var j; 10285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(j = r.t-this.t; i < j; ++i) r_array[i+this.t] = this.am(0,a_array[i],r,i,0,this.t); 10295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a_array[i],r,i,0,n-i); 10305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 10315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 10325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) r = "this * a" without lower n words, n > 0 10345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// "this" should be the larger one if appropriate. 10355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpMultiplyUpperTo(a,n,r) { 10365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r_array = r.array; 10375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a_array = a.array; 10385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) --n; 10395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = r.t = this.t+a.t-n; 10405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.s = 0; // assumes a,this >= 0 10415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(--i >= 0) r_array[i] = 0; 10425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = Math.max(n-this.t,0); i < a.t; ++i) 10435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r_array[this.t+i-n] = this.am(n-i,a_array[i],r,0,0,this.t+i-n); 10445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.clamp(); 10455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) r.drShiftTo(1,r); 10465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 10475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Barrett modular reduction 10495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function Barrett(m) { 10505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // setup Barrett 10515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.r2 = nbi(); 10525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.q3 = nbi(); 10535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) BigInteger.ONE.dlShiftTo(2*m.t,this.r2); 10545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.mu = this.r2.divide(m); 10555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.m = m; 10565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 10575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function barrettConvert(x) { 10595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m); 10605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(x.compareTo(this.m) < 0) return x; 10615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; } 10625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 10635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function barrettRevert(x) { return x; } 10655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// x = x mod m (HAC 14.42) 10675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function barrettReduce(x) { 10685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.drShiftTo(this.m.t-1,this.r2); 10695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); } 10705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3); 10715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2); 10725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1); 10735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.subTo(this.r2,x); 10745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(x.compareTo(this.m) >= 0) x.subTo(this.m,x); 10755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 10765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// r = x^2 mod m; x != r 10785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); } 10795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// r = x*y mod m; x,y != r 10815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); } 10825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Barrett.prototype.convert = barrettConvert; 10845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Barrett.prototype.revert = barrettRevert; 10855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Barrett.prototype.reduce = barrettReduce; 10865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Barrett.prototype.mulTo = barrettMulTo; 10875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Barrett.prototype.sqrTo = barrettSqrTo; 10885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 10895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) this^e % m (HAC 14.85) 10905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnModPow(e,m) { 10915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var e_array = e.array; 10925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = e.bitLength(), k, r = nbv(1), z; 10935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(i <= 0) return r; 10945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(i < 18) k = 1; 10955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(i < 48) k = 3; 10965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(i < 144) k = 4; 10975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(i < 768) k = 5; 10985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else k = 6; 10995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(i < 8) 11005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) z = new Classic(m); 11015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(m.isEven()) 11025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) z = new Barrett(m); 11035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else 11045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) z = new Montgomery(m); 11055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 11065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // precomputation 11075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1; 11085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) g[1] = z.convert(this); 11095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(k > 1) { 11105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var g2 = nbi(); 11115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) z.sqrTo(g[1],g2); 11125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(n <= km) { 11135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) g[n] = nbi(); 11145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) z.mulTo(g2,g[n-2],g[n]); 11155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) n += 2; 11165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 11195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var j = e.t-1, w, is1 = true, r2 = nbi(), t; 11205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) i = nbits(e_array[j])-1; 11215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(j >= 0) { 11225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(i >= k1) w = (e_array[j]>>(i-k1))&km; 11235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 11245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) w = (e_array[j]&((1<<(i+1))-1))<<(k1-i); 11255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(j > 0) w |= e_array[j-1]>>(BI_DB+i-k1); 11265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 11285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) n = k; 11295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while((w&1) == 0) { w >>= 1; --n; } 11305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((i -= n) < 0) { i += BI_DB; --j; } 11315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(is1) { // ret == 1, don't bother squaring or multiplying it 11325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) g[w].copyTo(r); 11335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) is1 = false; 11345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 11365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; } 11375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; } 11385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) z.mulTo(r2,g[w],r); 11395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 11415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(j >= 0 && (e_array[j]&(1<<i)) == 0) { 11425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) z.sqrTo(r,r2); t = r; r = r2; r2 = t; 11435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(--i < 0) { i = BI_DB-1; --j; } 11445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return z.revert(r); 11475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 11485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 11495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) gcd(this,a) (HAC 14.54) 11505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnGCD(a) { 11515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x = (this.s<0)?this.negate():this.clone(); 11525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var y = (a.s<0)?a.negate():a.clone(); 11535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.compareTo(y) < 0) { var t = x; x = y; y = t; } 11545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = x.getLowestSetBit(), g = y.getLowestSetBit(); 11555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(g < 0) return x; 11565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(i < g) g = i; 11575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(g > 0) { 11585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.rShiftTo(g,x); 11595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y.rShiftTo(g,y); 11605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(x.signum() > 0) { 11625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x); 11635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y); 11645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.compareTo(y) >= 0) { 11655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.subTo(y,x); 11665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x.rShiftTo(1,x); 11675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 11695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y.subTo(x,y); 11705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y.rShiftTo(1,y); 11715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 11735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(g > 0) y.lShiftTo(g,y); 11745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return y; 11755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 11765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 11775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) this % n, n < 2^26 11785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpModInt(n) { 11795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var this_array = this.array; 11805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(n <= 0) return 0; 11815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var d = BI_DV%n, r = (this.s<0)?n-1:0; 11825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.t > 0) 11835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(d == 0) r = this_array[0]%n; 11845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else for(var i = this.t-1; i >= 0; --i) r = (d*r+this_array[i])%n; 11855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return r; 11865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 11875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 11885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) 1/this % m (HAC 14.61) 11895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnModInverse(m) { 11905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var ac = m.isEven(); 11915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO; 11925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var u = m.clone(), v = this.clone(); 11935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1); 11945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(u.signum() != 0) { 11955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(u.isEven()) { 11965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) u.rShiftTo(1,u); 11975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(ac) { 11985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); } 11995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) a.rShiftTo(1,a); 12005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(!b.isEven()) b.subTo(m,b); 12025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) b.rShiftTo(1,b); 12035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(v.isEven()) { 12055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) v.rShiftTo(1,v); 12065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(ac) { 12075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); } 12085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) c.rShiftTo(1,c); 12095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else if(!d.isEven()) d.subTo(m,d); 12115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) d.rShiftTo(1,d); 12125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(u.compareTo(v) >= 0) { 12145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) u.subTo(v,u); 12155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(ac) a.subTo(c,a); 12165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) b.subTo(d,b); 12175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else { 12195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) v.subTo(u,v); 12205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(ac) c.subTo(a,c); 12215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) d.subTo(b,d); 12225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO; 12255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(d.compareTo(m) >= 0) return d.subtract(m); 12265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(d.signum() < 0) d.addTo(m,d); else return d; 12275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(d.signum() < 0) return d.add(m); else return d; 12285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 12295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 12305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var 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]; 12315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var lplim = (1<<26)/lowprimes[lowprimes.length-1]; 12325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 12335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (public) test primality with certainty >= 1-.5^t 12345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnIsProbablePrime(t) { 12355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i, x = this.abs(); 12365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x_array = x.array; 12375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.t == 1 && x_array[0] <= lowprimes[lowprimes.length-1]) { 12385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = 0; i < lowprimes.length; ++i) 12395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x_array[0] == lowprimes[i]) return true; 12405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return false; 12415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(x.isEven()) return false; 12435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) i = 1; 12445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < lowprimes.length) { 12455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var m = lowprimes[i], j = i+1; 12465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(j < lowprimes.length && m < lplim) m *= lowprimes[j++]; 12475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) m = x.modInt(m); 12485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < j) if(m%lowprimes[i++] == 0) return false; 12495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return x.millerRabin(t); 12515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 12525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 12535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (protected) true if probably prime (HAC 4.24, Miller-Rabin) 12545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function bnpMillerRabin(t) { 12555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var n1 = this.subtract(BigInteger.ONE); 12565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var k = n1.getLowestSetBit(); 12575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(k <= 0) return false; 12585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var r = n1.shiftRight(k); 12595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) t = (t+1)>>1; 12605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(t > lowprimes.length) t = lowprimes.length; 12615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var a = nbi(); 12625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(var i = 0; i < t; ++i) { 12635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) a.fromInt(lowprimes[i]); 12645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var y = a.modPow(r,this); 12655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) { 12665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var j = 1; 12675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(j++ < k && y.compareTo(n1) != 0) { 12685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) y = y.modPowInt(2,this); 12695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(y.compareTo(BigInteger.ONE) == 0) return false; 12705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(y.compareTo(n1) != 0) return false; 12725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 12745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return true; 12755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 12765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 12775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// protected 12785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.chunkSize = bnpChunkSize; 12795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.toRadix = bnpToRadix; 12805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.fromRadix = bnpFromRadix; 12815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.fromNumber = bnpFromNumber; 12825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.bitwiseTo = bnpBitwiseTo; 12835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.changeBit = bnpChangeBit; 12845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.addTo = bnpAddTo; 12855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.dMultiply = bnpDMultiply; 12865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.dAddOffset = bnpDAddOffset; 12875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo; 12885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo; 12895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.modInt = bnpModInt; 12905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.millerRabin = bnpMillerRabin; 12915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 12925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// public 12935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.clone = bnClone; 12945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.intValue = bnIntValue; 12955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.byteValue = bnByteValue; 12965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.shortValue = bnShortValue; 12975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.signum = bnSigNum; 12985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.toByteArray = bnToByteArray; 12995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.equals = bnEquals; 13005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.min = bnMin; 13015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.max = bnMax; 13025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.and = bnAnd; 13035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.or = bnOr; 13045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.xor = bnXor; 13055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.andNot = bnAndNot; 13065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.not = bnNot; 13075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.shiftLeft = bnShiftLeft; 13085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.shiftRight = bnShiftRight; 13095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit; 13105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.bitCount = bnBitCount; 13115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.testBit = bnTestBit; 13125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.setBit = bnSetBit; 13135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.clearBit = bnClearBit; 13145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.flipBit = bnFlipBit; 13155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.add = bnAdd; 13165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.subtract = bnSubtract; 13175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.multiply = bnMultiply; 13185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.divide = bnDivide; 13195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.remainder = bnRemainder; 13205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder; 13215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.modPow = bnModPow; 13225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.modInverse = bnModInverse; 13235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.pow = bnPow; 13245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.gcd = bnGCD; 13255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)BigInteger.prototype.isProbablePrime = bnIsProbablePrime; 13265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// BigInteger interfaces not implemented in jsbn: 13285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// BigInteger(int signum, byte[] magnitude) 13305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// double doubleValue() 13315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// float floatValue() 13325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// int hashCode() 13335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// long longValue() 13345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// static BigInteger valueOf(long val) 13355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// prng4.js - uses Arcfour as a PRNG 13365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function Arcfour() { 13385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.i = 0; 13395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.j = 0; 13405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.S = new Array(); 13415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 13425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Initialize arcfour context from key, an array of ints, each from [0..255] 13445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function ARC4init(key) { 13455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i, j, t; 13465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = 0; i < 256; ++i) 13475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.S[i] = i; 13485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) j = 0; 13495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = 0; i < 256; ++i) { 13505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) j = (j + this.S[i] + key[i % key.length]) & 255; 13515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) t = this.S[i]; 13525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.S[i] = this.S[j]; 13535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.S[j] = t; 13545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 13555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.i = 0; 13565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.j = 0; 13575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 13585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function ARC4next() { 13605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var t; 13615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.i = (this.i + 1) & 255; 13625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.j = (this.j + this.S[this.i]) & 255; 13635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) t = this.S[this.i]; 13645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.S[this.i] = this.S[this.j]; 13655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.S[this.j] = t; 13665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return this.S[(t + this.S[this.i]) & 255]; 13675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 13685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Arcfour.prototype.init = ARC4init; 13705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)Arcfour.prototype.next = ARC4next; 13715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Plug in your RNG constructor here 13735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function prng_newstate() { 13745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return new Arcfour(); 13755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 13765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Pool size must be a multiple of 4 and greater than 32. 13785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// An array of bytes the size of the pool will be passed to init() 13795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var rng_psize = 256; 13805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Random number generator - requires a PRNG backend, e.g. prng4.js 13815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// For best results, put code like 13835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'> 13845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// in your main HTML document. 13855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var rng_state; 13875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var rng_pool; 13885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var rng_pptr; 13895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Mix in a 32-bit integer into the pool 13915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function rng_seed_int(x) { 13925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pool[rng_pptr++] ^= x & 255; 13935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pool[rng_pptr++] ^= (x >> 8) & 255; 13945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pool[rng_pptr++] ^= (x >> 16) & 255; 13955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pool[rng_pptr++] ^= (x >> 24) & 255; 13965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(rng_pptr >= rng_psize) rng_pptr -= rng_psize; 13975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 13985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 13995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Mix in the current time (w/milliseconds) into the pool 14005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function rng_seed_time() { 14015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // Use pre-computed date to avoid making the benchmark 14025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // results dependent on the current date. 14035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_seed_int(1122926989487); 14045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 14055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Initialize the pool with junk if needed. 14075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)if(rng_pool == null) { 14085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pool = new Array(); 14095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pptr = 0; 14105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var t; 14115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(rng_pptr < rng_psize) { // extract some randomness from Math.random() 14125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) t = Math.floor(65536 * Math.random()); 14135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pool[rng_pptr++] = t >>> 8; 14145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pool[rng_pptr++] = t & 255; 14155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 14165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pptr = 0; 14175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_seed_time(); 14185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) //rng_seed_int(window.screenX); 14195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) //rng_seed_int(window.screenY); 14205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 14215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function rng_get_byte() { 14235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(rng_state == null) { 14245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_seed_time(); 14255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_state = prng_newstate(); 14265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_state.init(rng_pool); 14275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr) 14285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pool[rng_pptr] = 0; 14295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) rng_pptr = 0; 14305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) //rng_pool = null; 14315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 14325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // TODO: allow reseeding after first request 14335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return rng_state.next(); 14345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 14355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function rng_get_bytes(ba) { 14375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i; 14385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(i = 0; i < ba.length; ++i) ba[i] = rng_get_byte(); 14395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 14405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function SecureRandom() {} 14425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SecureRandom.prototype.nextBytes = rng_get_bytes; 14445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Depends on jsbn.js and rng.js 14455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// convert a (hex) string to a bignum object 14475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function parseBigInt(str,r) { 14485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return new BigInteger(str,r); 14495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 14505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function linebrk(s,n) { 14525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var ret = ""; 14535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = 0; 14545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i + n < s.length) { 14555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ret += s.substring(i,i+n) + "\n"; 14565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) i += n; 14575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 14585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return ret + s.substring(i,s.length); 14595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 14605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function byte2Hex(b) { 14625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(b < 0x10) 14635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return "0" + b.toString(16); 14645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else 14655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return b.toString(16); 14665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 14675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// PKCS#1 (type 2, random) pad input string s to n bytes, and return a bigint 14695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function pkcs1pad2(s,n) { 14705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(n < s.length + 11) { 14715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) alert("Message too long for RSA"); 14725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return null; 14735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 14745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var ba = new Array(); 14755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = s.length - 1; 14765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i >= 0 && n > 0) ba[--n] = s.charCodeAt(i--); 14775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ba[--n] = 0; 14785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var rng = new SecureRandom(); 14795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var x = new Array(); 14805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(n > 2) { // random non-zero pad 14815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) x[0] = 0; 14825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(x[0] == 0) rng.nextBytes(x); 14835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ba[--n] = x[0]; 14845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 14855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ba[--n] = 2; 14865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ba[--n] = 0; 14875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return new BigInteger(ba); 14885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 14895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 14905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// "empty" RSA key constructor 14915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSAKey() { 14925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.n = null; 14935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.e = 0; 14945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.d = null; 14955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.p = null; 14965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.q = null; 14975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dmp1 = null; 14985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dmq1 = null; 14995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.coeff = null; 15005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 15015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Set the public key fields N and e from hex strings 15035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSASetPublic(N,E) { 15045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(N != null && E != null && N.length > 0 && E.length > 0) { 15055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.n = parseBigInt(N,16); 15065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.e = parseInt(E,16); 15075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 15085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else 15095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) alert("Invalid RSA public key"); 15105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 15115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Perform raw public operation on "x": return x^e (mod n) 15135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSADoPublic(x) { 15145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return x.modPowInt(this.e, this.n); 15155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 15165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Return the PKCS#1 RSA encryption of "text" as an even-length hex string 15185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSAEncrypt(text) { 15195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var m = pkcs1pad2(text,(this.n.bitLength()+7)>>3); 15205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(m == null) return null; 15215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var c = this.doPublic(m); 15225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(c == null) return null; 15235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var h = c.toString(16); 15245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if((h.length & 1) == 0) return h; else return "0" + h; 15255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 15265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Return the PKCS#1 RSA encryption of "text" as a Base64-encoded string 15285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//function RSAEncryptB64(text) { 15295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// var h = this.encrypt(text); 15305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// if(h) return hex2b64(h); else return null; 15315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//} 15325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// protected 15345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)RSAKey.prototype.doPublic = RSADoPublic; 15355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// public 15375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)RSAKey.prototype.setPublic = RSASetPublic; 15385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)RSAKey.prototype.encrypt = RSAEncrypt; 15395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//RSAKey.prototype.encrypt_b64 = RSAEncryptB64; 15405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Depends on rsa.js and jsbn2.js 15415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Undo PKCS#1 (type 2, random) padding and, if valid, return the plaintext 15435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function pkcs1unpad2(d,n) { 15445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var b = d.toByteArray(); 15455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var i = 0; 15465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(i < b.length && b[i] == 0) ++i; 15475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(b.length-i != n-1 || b[i] != 2) 15485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return null; 15495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ++i; 15505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(b[i] != 0) 15515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(++i >= b.length) return null; 15525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var ret = ""; 15535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(++i < b.length) 15545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) ret += String.fromCharCode(b[i]); 15555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return ret; 15565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 15575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Set the private key fields N, e, and d from hex strings 15595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSASetPrivate(N,E,D) { 15605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(N != null && E != null && N.length > 0 && E.length > 0) { 15615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.n = parseBigInt(N,16); 15625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.e = parseInt(E,16); 15635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.d = parseBigInt(D,16); 15645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 15655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else 15665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) alert("Invalid RSA private key"); 15675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 15685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Set the private key fields N, e, d and CRT params from hex strings 15705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSASetPrivateEx(N,E,D,P,Q,DP,DQ,C) { 15715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(N != null && E != null && N.length > 0 && E.length > 0) { 15725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.n = parseBigInt(N,16); 15735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.e = parseInt(E,16); 15745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.d = parseBigInt(D,16); 15755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.p = parseBigInt(P,16); 15765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.q = parseBigInt(Q,16); 15775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dmp1 = parseBigInt(DP,16); 15785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dmq1 = parseBigInt(DQ,16); 15795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.coeff = parseBigInt(C,16); 15805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 15815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) else 15825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) alert("Invalid RSA private key"); 15835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 15845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 15855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Generate a new random private key B bits long, using public expt E 15865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSAGenerate(B,E) { 15875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var rng = new SecureRandom(); 15885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var qs = B>>1; 15895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.e = parseInt(E,16); 15905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var ee = new BigInteger(E,16); 15915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(;;) { 15925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(;;) { 15935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.p = new BigInteger(B-qs,1,rng); 15945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.p.isProbablePrime(10)) break; 15955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 15965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) for(;;) { 15975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.q = new BigInteger(qs,1,rng); 15985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.q.isProbablePrime(10)) break; 15995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 16005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.p.compareTo(this.q) <= 0) { 16015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var t = this.p; 16025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.p = this.q; 16035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.q = t; 16045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 16055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var p1 = this.p.subtract(BigInteger.ONE); 16065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var q1 = this.q.subtract(BigInteger.ONE); 16075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var phi = p1.multiply(q1); 16085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(phi.gcd(ee).compareTo(BigInteger.ONE) == 0) { 16095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.n = this.p.multiply(this.q); 16105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.d = ee.modInverse(phi); 16115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dmp1 = this.d.mod(p1); 16125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.dmq1 = this.d.mod(q1); 16135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) this.coeff = this.q.modInverse(this.p); 16145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) break; 16155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 16165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 16175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 16185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Perform raw private operation on "x": return x^d (mod n) 16205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSADoPrivate(x) { 16215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(this.p == null || this.q == null) 16225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return x.modPow(this.d, this.n); 16235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) // TODO: re-calculate any missing CRT params 16255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var xp = x.mod(this.p).modPow(this.dmp1, this.p); 16265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var xq = x.mod(this.q).modPow(this.dmq1, this.q); 16275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) while(xp.compareTo(xq) < 0) 16295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) xp = xp.add(this.p); 16305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return xp.subtract(xq).multiply(this.coeff).mod(this.p).multiply(this.q).add(xq); 16315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 16325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Return the PKCS#1 RSA decryption of "ctext". 16345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// "ctext" is an even-length hex string and the output is a plain string. 16355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function RSADecrypt(ctext) { 16365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var c = parseBigInt(ctext, 16); 16375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var m = this.doPrivate(c); 16385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if(m == null) return null; 16395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) return pkcs1unpad2(m, (this.n.bitLength()+7)>>3); 16405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 16415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Return the PKCS#1 RSA decryption of "ctext". 16435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// "ctext" is a Base64-encoded string and the output is a plain string. 16445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//function RSAB64Decrypt(ctext) { 16455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// var h = b64tohex(ctext); 16465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// if(h) return this.decrypt(h); else return null; 16475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//} 16485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// protected 16505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)RSAKey.prototype.doPrivate = RSADoPrivate; 16515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// public 16535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)RSAKey.prototype.setPrivate = RSASetPrivate; 16545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)RSAKey.prototype.setPrivateEx = RSASetPrivateEx; 16555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)RSAKey.prototype.generate = RSAGenerate; 16565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)RSAKey.prototype.decrypt = RSADecrypt; 16575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//RSAKey.prototype.b64_decrypt = RSAB64Decrypt; 16585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)nValue="a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd94057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074eafd036a5eb83359d2a698d3"; 16615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)eValue="10001"; 16625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)dValue="8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293fc97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891464fba23d0d965086277a161"; 16635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)pValue="d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bde14b2417951178ac152ceab6da7090905b478195498b352048f15e7d"; 16645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)qValue="cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f"; 16655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)dmp1Value="1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25"; 16665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)dmq1Value="3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d914337eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd"; 16675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)coeffValue="3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db1734c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250"; 16685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)setupEngine(am3, 28); 16705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var TEXT = "The quick brown fox jumped over the extremely lazy frog! " + 16725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) "Now is the time for all good men to come to the party."; 16735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var encrypted; 16745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function encrypt() { 16765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var RSA = new RSAKey(); 16775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) RSA.setPublic(nValue, eValue); 16785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue); 16795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) encrypted = RSA.encrypt(TEXT); 16805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 16815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function decrypt() { 16835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var RSA = new RSAKey(); 16845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) RSA.setPublic(nValue, eValue); 16855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue); 16865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) var decrypted = RSA.decrypt(encrypted); 16875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) if (decrypted != TEXT) { 16885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) throw new Error("Crypto operation failed"); 16895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) } 16905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 16915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) 16925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)for (var i = 0; i < 8; ++i) { 16935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) encrypt(); 16945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) decrypt(); 16955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)} 1696