/flash-src/third-party/com/hurlant/math/MontgomeryReduction.as

 1package com.hurlant.math
 2{
 3	use namespace bi_internal;
 4	/**
 5	 * Montgomery reduction
 6	 */
 7	internal class MontgomeryReduction implements IReduction
 8	{
 9		private var m:BigInteger;
10		private var mp:int;
11		private var mpl:int;
12		private var mph:int;
13		private var um:int;
14		private var mt2:int;
15		public function MontgomeryReduction(m:BigInteger) {
16			this.m = m;
17			mp = m.invDigit();
18			mpl = mp & 0x7fff;
19			mph = mp>>15;
20			um = (1<<(BigInteger.DB-15))-1;
21			mt2 = 2*m.t;
22		}
23		/**
24		 * xR mod m
25		 */
26		public function convert(x:BigInteger):BigInteger {
27			var r:BigInteger = new BigInteger;
28		 	x.abs().dlShiftTo(m.t, r);
29		 	r.divRemTo(m, null, r);
30		 	if (x.s<0 && r.compareTo(BigInteger.ZERO)>0) {
31		 		m.subTo(r,r);
32		 	}
33		 	return r;
34		}
35		/**
36		 * x/R mod m
37		 */
38		public function revert(x:BigInteger):BigInteger {
39			var r:BigInteger = new BigInteger;
40			x.copyTo(r);
41			reduce(r);
42			return r;
43		}
44		/**
45		 * x = x/R mod m (HAC 14.32)
46		 */
47		public function reduce(x:BigInteger):void {
48			while (x.t<=mt2) {		// pad x so am has enough room later
49				x.a[x.t++] = 0;
50			}
51			for (var i:int=0; i<m.t; ++i) {
52				// faster way of calculating u0 = x[i]*mp mod DV
53				var j:int = x.a[i]&0x7fff;
54				var u0:int = (j*mpl+(((j*mph+(x.a[i]>>15)*mpl)&um)<<15))&BigInteger.DM;
55				// use am to combine the multiply-shift-add into one call
56				j = i+m.t;
57				x.a[j] += m.am(0, u0, x, i, 0, m.t);
58				// propagate carry
59				while (x.a[j]>=BigInteger.DV) {
60					x.a[j] -= BigInteger.DV;
61					x.a[++j]++;
62				}
63			}
64	 		x.clamp();
65		 	x.drShiftTo(m.t, x);
66	 		if (x.compareTo(m)>=0) {
67	 			x.subTo(m,x);
68	 		}
69		}
70		/**
71		 * r = "x^2/R mod m"; x != r
72		 */
73		public function sqrTo(x:BigInteger, r:BigInteger):void {
74			x.squareTo(r);
75			reduce(r);
76		}
77		/**
78		 * r = "xy/R mod m"; x,y != r
79		 */
80		public function mulTo(x:BigInteger, y:BigInteger, r:BigInteger):void {
81			x.multiplyTo(y,r);
82			reduce(r);
83		}
84	}
85}