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apache / incubator-milagro-crypto-js / 382a4df384ea7f427fc44e8a619ab505b4669804 / . / src / fp48.js
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/*
Licensed to the Apache Software Foundation (ASF) under one
or more contributor license agreements. See the NOTICE file
distributed with this work for additional information
regarding copyright ownership. The ASF licenses this file
to you under the Apache License, Version 2.0 (the
"License"); you may not use this file except in compliance
with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing,
software distributed under the License is distributed on an
"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
KIND, either express or implied. See the License for the
specific language governing permissions and limitations
under the License.
*/
/* AMCL Fp^48 functions */
/* FP48 elements are of the form a+i.b+i^2.c */
var FP48 = function(ctx) {
"use strict";
/**
* Creates an instance of FP48.
*
* @constructor
* @this {FP48}
*/
var FP48 = function(d, e, f) {
if (!isNaN(d))
{
this.a = new ctx.FP16(d);
this.b = new ctx.FP16(0);
this.c = new ctx.FP16(0);
if (d==1) this.stype=ctx.FP.ONE;
else this.stype=ctx.FP.SPARSER;
}
else
{
if (d instanceof FP48) {
this.a = new ctx.FP16(d.a);
this.b = new ctx.FP16(d.b);
this.c = new ctx.FP16(d.c);
} else {
this.a = new ctx.FP16(d);
this.b = new ctx.FP16(e);
this.c = new ctx.FP16(f);
}
this.stype=ctx.FP.DENSE;
}
};
FP48.prototype = {
/**
* Reduces all components of possibly unreduced FP48 mod Modulus
*
* @this {FP48}
*/
reduce: function() {
this.a.reduce();
this.b.reduce();
this.c.reduce();
},
/**
* Normalises the components of an FP48
*
* @this {FP48}
*/
norm: function() {
this.a.norm();
this.b.norm();
this.c.norm();
},
/**
* Tests for FP48 equal to zero
*
* @this {FP48}
*/
iszilch: function() {
return (this.a.iszilch() && this.b.iszilch() && this.c.iszilch());
},
/**
* Tests for FP48 equal to unity
*
* @this {FP48}
*/
isunity: function() {
var one = new ctx.FP16(1);
return (this.a.equals(one) && this.b.iszilch() && this.c.iszilch());
},
/**
* Conditional copy of FP48 number
*
* @this {FP48}
* @param g FP48 instance
* @param d copy depends on this value
*/
cmove: function(g, d) {
this.a.cmove(g.a, d);
this.b.cmove(g.b, d);
this.c.cmove(g.c, d);
d=~(d-1);
this.stype^=(this.stype^g.stype)&d;
},
/**
* Constant time select from pre-computed table
*
* @this {FP48}
*/
select: function(g, b) {
var invf = new FP48(0),
m, babs;
m = b >> 31;
babs = (b ^ m) - m;
babs = (babs - 1) / 2;
this.cmove(g[0], FP48.teq(babs, 0)); // conditional move
this.cmove(g[1], FP48.teq(babs, 1));
this.cmove(g[2], FP48.teq(babs, 2));
this.cmove(g[3], FP48.teq(babs, 3));
this.cmove(g[4], FP48.teq(babs, 4));
this.cmove(g[5], FP48.teq(babs, 5));
this.cmove(g[6], FP48.teq(babs, 6));
this.cmove(g[7], FP48.teq(babs, 7));
invf.copy(this);
invf.conj();
this.cmove(invf, (m & 1));
},
settype: function(w) {
this.stype=w;
},
gettype: function() {
return this.stype;
},
/**
* extract a from this
*
* @this {FP48}
*/
geta: function() {
return this.a;
},
/**
* extract b from this
*
* @this {FP48}
*/
getb: function() {
return this.b;
},
/**
* extract c from this
*
* @this {FP48}
*/
getc: function() {
return this.c;
},
/**
* Tests for equality of two FP48s
*
* @this {FP48}
* @param x FP48 instance to compare
*/
equals: function(x) {
return (this.a.equals(x.a) && this.b.equals(x.b) && this.c.equals(x.c));
},
/**
* Copy FP48 to another FP48
*
* @this {FP48}
* @param x FP48 instance to be copied
*/
copy: function(x) {
this.a.copy(x.a);
this.b.copy(x.b);
this.c.copy(x.c);
this.stype=x.stype;
},
/**
* Set FP48 to unity
*
* @this {FP48}
* @param x FP48 instance to be set to one
*/
one: function() {
this.a.one();
this.b.zero();
this.c.zero();
this.stype=ctx.FP.ONE;
},
/**
* Set FP48 to zero
*
* @this {FP48}
*/
zero: function() {
this.a.zero();
this.b.zero();
this.c.zero();
this.stype=ctx.FP.ZERO;
},
/**
* Conjugation of FP48
*
* @this {FP48}
*/
conj: function() {
this.a.conj();
this.b.nconj();
this.c.conj();
},
/**
* Set FP48 from three FP16 values
*
* @this {FP48}
* @param d FP16 instance
* @param e FP16 instance
* @param f FP16 instance
*/
set: function(d, e, f) {
this.a.copy(d);
this.b.copy(e);
this.c.copy(f);
this.stype=ctx.FP.DENSE;
},
/**
* Set FP48 from one FP16 value
*
* @this {FP48}
* @param c FP16 instance
*/
seta: function(d) {
this.a.copy(d);
this.b.zero();
this.c.zero();
this.stype=ctx.FP.SPARSER
},
/**
* Fast Squaring of an FP48 in "unitary" form
*
* @this {FP48}
*/
usqr: function() {
var A = new ctx.FP16(this.a),
B = new ctx.FP16(this.c),
C = new ctx.FP16(this.b),
D = new ctx.FP16(0);
this.a.sqr();
D.copy(this.a);
D.add(this.a);
this.a.add(D);
A.nconj();
A.add(A);
this.a.add(A);
B.sqr();
B.times_i();
D.copy(B);
D.add(B);
B.add(D);
C.sqr();
D.copy(C);
D.add(C);
C.add(D);
this.b.conj();
this.b.add(this.b);
this.c.nconj();
this.c.add(this.c);
this.b.add(B);
this.c.add(C);
this.stype=ctx.FP.DENSE;
this.reduce();
},
/**
* Fast Squaring of an FP48
*
* @this {FP48}
*/
sqr: function() {
if (this.stype==ctx.FP.ONE)
return;
var A = new ctx.FP16(this.a),
B = new ctx.FP16(this.b),
C = new ctx.FP16(this.c),
D = new ctx.FP16(this.a);
A.sqr();
B.mul(this.c);
B.add(B);
C.sqr();
D.mul(this.b);
D.add(D);
this.c.add(this.a);
this.c.add(this.b);
this.c.norm();
this.c.sqr();
this.a.copy(A);
A.add(B);
A.add(C);
A.add(D);
A.neg();
B.times_i();
C.times_i();
this.a.add(B);
this.b.copy(C);
this.b.add(D);
this.c.add(A);
if (this.stype==ctx.FP.SPARSER)
this.stype=ctx.FP.SPARSE;
else
this.stype=ctx.FP.DENSE;
this.norm();
},
/**
* Full unconditional Multiplication of two FP48s
*
* @this {FP48}
* @param y FP48 instance, the multiplier
*/
mul: function(y) {
var z0 = new ctx.FP16(this.a),
z1 = new ctx.FP16(0),
z2 = new ctx.FP16(this.b),
z3 = new ctx.FP16(0),
t0 = new ctx.FP16(this.a),
t1 = new ctx.FP16(y.a);
z0.mul(y.a);
z2.mul(y.b);
t0.add(this.b);
t1.add(y.b);
t0.norm();
t1.norm();
z1.copy(t0);
z1.mul(t1);
t0.copy(this.b);
t0.add(this.c);
t1.copy(y.b);
t1.add(y.c);
t0.norm();
t1.norm();
z3.copy(t0);
z3.mul(t1);
t0.copy(z0);
t0.neg();
t1.copy(z2);
t1.neg();
z1.add(t0);
this.b.copy(z1);
this.b.add(t1);
z3.add(t1);
z2.add(t0);
t0.copy(this.a);
t0.add(this.c);
t1.copy(y.a);
t1.add(y.c);
t0.norm();
t1.norm();
t0.mul(t1);
z2.add(t0);
t0.copy(this.c);
t0.mul(y.c);
t1.copy(t0);
t1.neg();
this.c.copy(z2);
this.c.add(t1);
z3.add(t1);
t0.times_i();
this.b.add(t0);
z3.times_i();
this.a.copy(z0);
this.a.add(z3);
this.stype=ctx.FP.DENSE;
this.norm();
},
/* FP48 multiplication w=w*y */
/* catering for special case that arises from special form of ATE pairing line function */
/* w and y are both sparser line functions - cost = 6m */
/**
* Fast multiplication of two sparse FP48s that arises from ATE pairing line functions
*
* @this {FP48}
* @param y FP48 instance, the multiplier
*/
smul: function(y) {
if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.D_TYPE)
{
var w1=new ctx.FP8(this.a.geta());
var w2=new ctx.FP8(this.a.getb());
var w3=new ctx.FP8(this.b.geta());
w1.mul(y.a.geta());
w2.mul(y.a.getb());
w3.mul(y.b.geta());
var ta=new ctx.FP8(this.a.geta());
var tb=new ctx.FP8(y.a.geta());
ta.add(this.a.getb()); ta.norm();
tb.add(y.a.getb()); tb.norm();
var tc=new ctx.FP8(ta);
tc.mul(tb);
var t=new ctx.FP8(w1);
t.add(w2);
t.neg();
tc.add(t);
ta.copy(this.a.geta()); ta.add(this.b.geta()); ta.norm();
tb.copy(y.a.geta()); tb.add(y.b.geta()); tb.norm();
var td=new ctx.FP8(ta);
td.mul(tb);
t.copy(w1);
t.add(w3);
t.neg();
td.add(t);
ta.copy(this.a.getb()); ta.add(this.b.geta()); ta.norm();
tb.copy(y.a.getb()); tb.add(y.b.geta()); tb.norm();
var te=new ctx.FP8(ta);
te.mul(tb);
t.copy(w2);
t.add(w3);
t.neg();
te.add(t);
w2.times_i();
w1.add(w2);
this.a.geta().copy(w1); this.a.getb().copy(tc);
this.b.geta().copy(td); this.b.getb().copy(te);
this.c.geta().copy(w3); this.c.getb().zero();
this.a.norm();
this.b.norm();
} else {
var w1=new ctx.FP8(this.a.geta());
var w2=new ctx.FP8(this.a.getb());
var w3=new ctx.FP8(this.c.getb());
w1.mul(y.a.geta());
w2.mul(y.a.getb());
w3.mul(y.c.getb());
var ta=new ctx.FP8(this.a.geta());
var tb=new ctx.FP8(y.a.geta());
ta.add(this.a.getb()); ta.norm();
tb.add(y.a.getb()); tb.norm();
var tc=new ctx.FP8(ta);
tc.mul(tb);
var t=new ctx.FP8(w1);
t.add(w2);
t.neg();
tc.add(t);
ta.copy(this.a.geta()); ta.add(this.c.getb()); ta.norm();
tb.copy(y.a.geta()); tb.add(y.c.getb()); tb.norm();
var td=new ctx.FP8(ta);
td.mul(tb);
t.copy(w1);
t.add(w3);
t.neg();
td.add(t);
ta.copy(this.a.getb()); ta.add(this.c.getb()); ta.norm();
tb.copy(y.a.getb()); tb.add(y.c.getb()); tb.norm();
var te=new ctx.FP8(ta);
te.mul(tb);
t.copy(w2);
t.add(w3);
t.neg();
te.add(t);
w2.times_i();
w1.add(w2);
this.a.geta().copy(w1); this.a.getb().copy(tc);
w3.times_i();
w3.norm();
this.b.geta().zero(); this.b.getb().copy(w3);
te.norm();
te.times_i();
this.c.geta().copy(te);
this.c.getb().copy(td);
this.a.norm();
this.c.norm();
}
this.stype=ctx.FP.SPARSE;
},
/* FP48 full multiplication w=w*y */
/* Supports sparse multiplicands */
/* Usually w is denser than y */
/**
* Fast multiplication of what may be sparse multiplicands
*
* @this {FP48}
* @param y FP48 instance, the multiplier
*/
ssmul: function(y) {
if (this.stype==ctx.FP.ONE)
{
this.copy(y);
return;
}
if (y.stype==ctx.FP.ONE)
return;
if (y.stype>=ctx.FP.SPARSE)
{
var z0=new ctx.FP16(this.a);
var z1=new ctx.FP16(0);
var z2=new ctx.FP16(0);
var z3=new ctx.FP16(0);
z0.mul(y.a);
if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.M_TYPE)
{
if (y.stype==ctx.FP.SPARSE || this.stype==ctx.FP.SPARSE)
{
z2.getb().copy(this.b.getb());
z2.getb().mul(y.b.getb());
z2.geta().zero();
if (y.stype!=ctx.FP.SPARSE)
{
z2.geta().copy(this.b.getb());
z2.geta().mul(y.b.geta());
}
if (this.stype!=ctx.FP.SPARSE)
{
z2.geta().copy(this.b.geta());
z2.geta().mul(y.b.getb());
}
z2.times_i();
} else {
z2.copy(this.b);
z2.mul(y.b);
}
} else {
z2.copy(this.b);
z2.mul(y.b);
}
var t0=new ctx.FP16(this.a);
var t1=new ctx.FP16(y.a);
t0.add(this.b); t0.norm();
t1.add(y.b); t1.norm();
z1.copy(t0); z1.mul(t1);
t0.copy(this.b); t0.add(this.c); t0.norm();
t1.copy(y.b); t1.add(y.c); t1.norm();
z3.copy(t0); z3.mul(t1);
t0.copy(z0); t0.neg();
t1.copy(z2); t1.neg();
z1.add(t0);
this.b.copy(z1); this.b.add(t1);
z3.add(t1);
z2.add(t0);
t0.copy(this.a); t0.add(this.c); t0.norm();
t1.copy(y.a); t1.add(y.c); t1.norm();
t0.mul(t1);
z2.add(t0);
if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.D_TYPE)
{
if (y.stype==ctx.FP.SPARSE || this.stype==ctx.FP.SPARSE)
{
t0.geta().copy(this.c.geta());
t0.geta().mul(y.c.geta());
t0.getb().zero();
if (y.stype!=ctx.FP.SPARSE)
{
t0.getb().copy(this.c.geta());
t0.getb().mul(y.c.getb());
}
if (this.stype!=ctx.FP.SPARSE)
{
t0.getb().copy(this.c.getb());
t0.getb().mul(y.c.geta());
}
} else {
t0.copy(this.c);
t0.mul(y.c);
}
} else {
t0.copy(this.c);
t0.mul(y.c);
}
t1.copy(t0); t1.neg();
this.c.copy(z2); this.c.add(t1);
z3.add(t1);
t0.times_i();
this.b.add(t0);
z3.norm();
z3.times_i();
this.a.copy(z0); this.a.add(z3);
} else {
if (this.stype==ctx.FP.SPARSER)
{
this.smul(y);
return;
}
if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.D_TYPE)
{ // dense by sparser - 13m
var z0=new ctx.FP16(this.a);
var z2=new ctx.FP16(this.b);
var z3=new ctx.FP16(this.b);
var t0=new ctx.FP16(0);
var t1=new ctx.FP16(y.a);
z0.mul(y.a);
z2.pmul(y.b.real());
this.b.add(this.a);
t1.real().add(y.b.real());
t1.norm();
this.b.norm();
this.b.mul(t1);
z3.add(this.c);
z3.norm();
z3.pmul(y.b.real());
t0.copy(z0); t0.neg();
t1.copy(z2); t1.neg();
this.b.add(t0);
this.b.add(t1);
z3.add(t1);
z2.add(t0);
t0.copy(this.a); t0.add(this.c); t0.norm();
z3.norm();
t0.mul(y.a);
this.c.copy(z2); this.c.add(t0);
z3.times_i();
this.a.copy(z0); this.a.add(z3);
}
if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.M_TYPE)
{
var z0=new ctx.FP16(this.a);
var z1=new ctx.FP16(0);
var z2=new ctx.FP16(0);
var z3=new ctx.FP16(0);
var t0=new ctx.FP16(this.a);
var t1=new ctx.FP16(0);
z0.mul(y.a);
t0.add(this.b); t0.norm();
z1.copy(t0); z1.mul(y.a);
t0.copy(this.b); t0.add(this.c);
t0.norm();
z3.copy(t0);
z3.pmul(y.c.getb());
z3.times_i();
t0.copy(z0); t0.neg();
z1.add(t0);
this.b.copy(z1);
z2.copy(t0);
t0.copy(this.a); t0.add(this.c); t0.norm();
t1.copy(y.a); t1.add(y.c); t1.norm();
t0.mul(t1);
z2.add(t0);
t0.copy(this.c);
t0.pmul(y.c.getb());
t0.times_i();
t1.copy(t0); t1.neg();
this.c.copy(z2); this.c.add(t1);
z3.add(t1);
t0.times_i();
this.b.add(t0);
z3.norm();
z3.times_i();
this.a.copy(z0); this.a.add(z3);
}
}
this.stype=ctx.FP.DENSE;
this.norm();
},
/**
* Inverting an FP48
*
* @this {FP48}
*/
inverse: function() {
var f0 = new ctx.FP16(this.a),
f1 = new ctx.FP16(this.b),
f2 = new ctx.FP16(this.a),
f3 = new ctx.FP16(0);
f0.sqr();
f1.mul(this.c);
f1.times_i();
f0.sub(f1);
f0.norm();
f1.copy(this.c);
f1.sqr();
f1.times_i();
f2.mul(this.b);
f1.sub(f2);
f1.norm();
f2.copy(this.b);
f2.sqr();
f3.copy(this.a);
f3.mul(this.c);
f2.sub(f3);
f2.norm();
f3.copy(this.b);
f3.mul(f2);
f3.times_i();
this.a.mul(f0);
f3.add(this.a);
this.c.mul(f1);
this.c.times_i();
f3.add(this.c);
f3.norm();
f3.inverse();
this.a.copy(f0);
this.a.mul(f3);
this.b.copy(f1);
this.b.mul(f3);
this.c.copy(f2);
this.c.mul(f3);
this.stype=ctx.FP.DENSE;
},
/**
* Raises an FP48 to the power of the internal modulus p, using the Frobenius
*
* @this {FP48}
* @param f Modulus
*/
frob: function(f,n) {
var f2 = new ctx.FP2(f),
f3 = new ctx.FP2(f),
i;
f2.sqr();
f3.mul(f2);
f3.mul_ip(); f3.norm();
f3.mul_ip(); f3.norm();
for (i=0;i<n;i++) {
this.a.frob(f3);
this.b.frob(f3);
this.c.frob(f3);
this.b.qmul(f); this.b.times_i4(); this.b.times_i2();
this.c.qmul(f2); this.c.times_i4(); this.c.times_i4(); this.c.times_i4();
}
this.stype=ctx.FP.DENSE;
},
/**
* Calculate the trace of an FP48
*
* @this {FP48}
*/
trace: function() {
var t = new ctx.FP16(0);
t.copy(this.a);
t.imul(3);
t.reduce();
return t;
},
/**
* convert this to hex string
*
* @this {FP48}
*/
toString: function() {
return ("[" + this.a.toString() + "," + this.b.toString() + "," + this.c.toString() + "]");
},
/**
* convert this to byte array
*
* @this {FP48}
* @param w Byte array
*/
toBytes: function(w) {
var t = [],
i;
this.a.geta().geta().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i] = t[i];
}
this.a.geta().geta().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + ctx.BIG.MODBYTES] = t[i];
}
this.a.geta().geta().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 2 * ctx.BIG.MODBYTES] = t[i];
}
this.a.geta().geta().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 3 * ctx.BIG.MODBYTES] = t[i];
}
this.a.geta().getb().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 4 * ctx.BIG.MODBYTES] = t[i];
}
this.a.geta().getb().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 5 * ctx.BIG.MODBYTES] = t[i];
}
this.a.geta().getb().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 6 * ctx.BIG.MODBYTES] = t[i];
}
this.a.geta().getb().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 7 * ctx.BIG.MODBYTES] = t[i];
}
this.a.getb().geta().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 8 * ctx.BIG.MODBYTES] = t[i];
}
this.a.getb().geta().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 9 * ctx.BIG.MODBYTES] = t[i];
}
this.a.getb().geta().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 10 * ctx.BIG.MODBYTES] = t[i];
}
this.a.getb().geta().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 11 * ctx.BIG.MODBYTES] = t[i];
}
this.a.getb().getb().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 12 * ctx.BIG.MODBYTES] = t[i];
}
this.a.getb().getb().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 13 * ctx.BIG.MODBYTES] = t[i];
}
this.a.getb().getb().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 14 * ctx.BIG.MODBYTES] = t[i];
}
this.a.getb().getb().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 15 * ctx.BIG.MODBYTES] = t[i];
}
this.b.geta().geta().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 16 * ctx.BIG.MODBYTES] = t[i];
}
this.b.geta().geta().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 17 * ctx.BIG.MODBYTES] = t[i];
}
this.b.geta().geta().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 18 * ctx.BIG.MODBYTES] = t[i];
}
this.b.geta().geta().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 19 * ctx.BIG.MODBYTES] = t[i];
}
this.b.geta().getb().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 20 * ctx.BIG.MODBYTES] = t[i];
}
this.b.geta().getb().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 21 * ctx.BIG.MODBYTES] = t[i];
}
this.b.geta().getb().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 22 * ctx.BIG.MODBYTES] = t[i];
}
this.b.geta().getb().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 23 * ctx.BIG.MODBYTES] = t[i];
}
this.b.getb().geta().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 24 * ctx.BIG.MODBYTES] = t[i];
}
this.b.getb().geta().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 25 * ctx.BIG.MODBYTES] = t[i];
}
this.b.getb().geta().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 26 * ctx.BIG.MODBYTES] = t[i];
}
this.b.getb().geta().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 27 * ctx.BIG.MODBYTES] = t[i];
}
this.b.getb().getb().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 28 * ctx.BIG.MODBYTES] = t[i];
}
this.b.getb().getb().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 29 * ctx.BIG.MODBYTES] = t[i];
}
this.b.getb().getb().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 30 * ctx.BIG.MODBYTES] = t[i];
}
this.b.getb().getb().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 31 * ctx.BIG.MODBYTES] = t[i];
}
this.c.geta().geta().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 32 * ctx.BIG.MODBYTES] = t[i];
}
this.c.geta().geta().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 33 * ctx.BIG.MODBYTES] = t[i];
}
this.c.geta().geta().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 34 * ctx.BIG.MODBYTES] = t[i];
}
this.c.geta().geta().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 35 * ctx.BIG.MODBYTES] = t[i];
}
this.c.geta().getb().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 36 * ctx.BIG.MODBYTES] = t[i];
}
this.c.geta().getb().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 37 * ctx.BIG.MODBYTES] = t[i];
}
this.c.geta().getb().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 38 * ctx.BIG.MODBYTES] = t[i];
}
this.c.geta().getb().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 39 * ctx.BIG.MODBYTES] = t[i];
}
this.c.getb().geta().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 40 * ctx.BIG.MODBYTES] = t[i];
}
this.c.getb().geta().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 41 * ctx.BIG.MODBYTES] = t[i];
}
this.c.getb().geta().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 42 * ctx.BIG.MODBYTES] = t[i];
}
this.c.getb().geta().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 43 * ctx.BIG.MODBYTES] = t[i];
}
this.c.getb().getb().geta().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 44 * ctx.BIG.MODBYTES] = t[i];
}
this.c.getb().getb().geta().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 45 * ctx.BIG.MODBYTES] = t[i];
}
this.c.getb().getb().getb().getA().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 46 * ctx.BIG.MODBYTES] = t[i];
}
this.c.getb().getb().getb().getB().toBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
w[i + 47 * ctx.BIG.MODBYTES] = t[i];
}
},
/**
* Raises an FP48 to the power of a BIG
*
* @this {FP48}
* @param e BIG instance exponent
*/
pow: function(e) {
var e1, e3, w, nb, i, bt, sf;
sf = new FP48(this);
sf.norm();
e1 = new ctx.BIG(e);
e1.norm();
e3 = new ctx.BIG(e1);
e3.pmul(3);
e3.norm();
w = new FP48(sf); //w.copy(this);
nb = e3.nbits();
for (i = nb - 2; i >= 1; i--) {
w.usqr();
bt = e3.bit(i) - e1.bit(i);
if (bt == 1) {
w.mul(sf);
}
if (bt == -1) {
sf.conj();
w.mul(sf);
sf.conj();
}
}
w.reduce();
return w;
},
/**
* Raises an FP48 instance x to a small integer power, side-channel resistant
*
* @this {FP48}
* @param e small integer exponent
* @param bts maximum number of bits in exponent
*/
pinpow: function(e, bts) {
var R = [],
i, b;
R[0] = new FP48(1);
R[1] = new FP48(this);
for (i = bts - 1; i >= 0; i--) {
b = (e >> i) & 1;
R[1 - b].mul(R[b]);
R[b].usqr();
}
this.copy(R[0]);
},
/**
* Raises an FP48 instance to a BIG power, compressed to FP4
*
* @this {FP48}
* @param e BIG exponent
* @param r BIG group order
*/
compow: function(e, r) {
var fa, fb, f, q, m, a, b, g1, g2, c, cp, cpm1, cpm2;
fa = new ctx.BIG(0);
fa.rcopy(ctx.ROM_FIELD.Fra);
fb = new ctx.BIG(0);
fb.rcopy(ctx.ROM_FIELD.Frb);
f = new ctx.FP2(fa, fb);
q = new ctx.BIG(0);
q.rcopy(ctx.ROM_FIELD.Modulus);
m = new ctx.BIG(q);
m.mod(r);
a = new ctx.BIG(e);
a.mod(m);
b = new ctx.BIG(e);
b.div(m);
g1 = new FP48(0);
g2 = new FP48(0);
g1.copy(this);
c = g1.trace();
if (b.iszilch()) {
c=c.xtr_pow(e);
return c;
}
g2.copy(g1);
g2.frob(f,1);
cp = g2.trace();
g1.conj();
g2.mul(g1);
cpm1 = g2.trace();
g2.mul(g1);
cpm2 = g2.trace();
c = c.xtr_pow2(cp, cpm1, cpm2, a, b);
return c;
}
};
/**
* convert from byte array to FP48
*
* @this {FP48}
* @param w Byte array
*/
FP48.fromBytes = function(w) {
var t = [],
i, a, b, c, d, e, f, g, r, ea, eb, fa, fb;
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 2 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 3 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b); //d.bset(a,b);
ea = new ctx.FP4(c, d); //e.set(c,d);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 4 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 5 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 6 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 7 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b); //d.bset(a,b);
eb = new ctx.FP4(c, d); //e.set(c,d);
fa = new ctx.FP8(ea,eb);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 8 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 9 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 10 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 11 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b); //d.bset(a,b);
ea = new ctx.FP4(c, d); //e.set(c,d);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 12 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 13 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 14 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 15 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b); //d.bset(a,b);
eb = new ctx.FP4(c, d); //e.set(c,d);
fb = new ctx.FP8(ea,eb);
e = new ctx.FP16(fa,fb);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 16 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 17 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 18 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 19 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b);
ea = new ctx.FP4(c, d); //e.set(c,d);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 20 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 21 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 22 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 23 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b);
eb = new ctx.FP4(c, d); //e.set(c,d);
fa = new ctx.FP8(ea,eb);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 24 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 25 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 26 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 27 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b);
ea = new ctx.FP4(c, d); //e.set(c,d);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 28 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 29 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 30 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 31 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b);
eb = new ctx.FP4(c, d); //e.set(c,d);
fb = new ctx.FP8(ea,eb);
f = new ctx.FP16(fa, fb); //f.set(c,d);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 32 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 33 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 34 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 35 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b); //d.bset(a,b);
ea = new ctx.FP4(c, d); //e.set(c,d);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 36 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 37 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 38 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 39 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b); //d.bset(a,b);
eb = new ctx.FP4(c, d); //e.set(c,d);
fa = new ctx.FP8(ea,eb);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 40 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 41 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 42 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 43 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b); //d.bset(a,b);
ea = new ctx.FP4(c, d); //e.set(c,d);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 44 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 45 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
c = new ctx.FP2(a, b); //c.bset(a,b);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 46 * ctx.BIG.MODBYTES];
}
a = ctx.BIG.fromBytes(t);
for (i = 0; i < ctx.BIG.MODBYTES; i++) {
t[i] = w[i + 47 * ctx.BIG.MODBYTES];
}
b = ctx.BIG.fromBytes(t);
d = new ctx.FP2(a, b); //d.bset(a,b);
eb = new ctx.FP4(c, d); //e.set(c,d);
fb = new ctx.FP8(ea,eb);
g = new ctx.FP16(fa, fb); //g.set(c,d);
r = new FP48(e, f, g); //r.set(e,f,g);
return r;
};
/**
* return 1 if b==c, no branching
*
* @this {FP48}
*/
FP48.teq = function(b, c) {
var x = b ^ c;
x -= 1; // if x=0, x now -1
return ((x >> 31) & 1);
};
/* p=q0^u0.q1^u1.q2^u2.q3^u3... */
// Bos & Costello https://eprint.iacr.org/2013/458.pdf
// Faz-Hernandez & Longa & Sanchez https://eprint.iacr.org/2013/158.pdf
// Side channel attack secure
/**
* p=q0^u0.q1^u1.q2^u2.q3^u3...
*
* @this {FP48}
*/
FP48.pow16 = function(q, u) {
var g1 = [],
g2 = [],
g3 = [],
g4 = [],
r = new FP48(0),
p = new FP48(0),
t = [],
mt = new ctx.BIG(0),
fa = new ctx.BIG(0),
fb = new ctx.BIG(0),
w1 = [],
s1 = [],
w2 = [],
s2 = [],
w3 = [],
s3 = [],
w4 = [],
s4 = [],
i, j, k, nb, bt, pb1, pb2, pb3, pb4, f;
for (i = 0; i < 16; i++) {
t[i] = new ctx.BIG(u[i]); t[i].norm();
}
g1[0] = new FP48(q[0]); // q[0]
g1[1] = new FP48(g1[0]); g1[1].mul(q[1]); // q[0].q[1]
g1[2] = new FP48(g1[0]); g1[2].mul(q[2]); // q[0].q[2]
g1[3] = new FP48(g1[1]); g1[3].mul(q[2]); // q[0].q[1].q[2]
g1[4] = new FP48(q[0]); g1[4].mul(q[3]); // q[0].q[3]
g1[5] = new FP48(g1[1]); g1[5].mul(q[3]); // q[0].q[1].q[3]
g1[6] = new FP48(g1[2]); g1[6].mul(q[3]); // q[0].q[2].q[3]
g1[7] = new FP48(g1[3]); g1[7].mul(q[3]); // q[0].q[1].q[2].q[3]
// Use Frobenius
fa.rcopy(ctx.ROM_FIELD.Fra);
fb.rcopy(ctx.ROM_FIELD.Frb);
f = new ctx.FP2(fa, fb);
for (i=0;i<8;i++) {
g2[i]=new FP48(g1[i]);
g2[i].frob(f,4);
g3[i]=new FP48(g2[i]);
g3[i].frob(f,4);
g4[i]=new FP48(g3[i]);
g4[i].frob(f,4);
}
// Make it odd
pb1=1-t[0].parity();
t[0].inc(pb1);
t[0].norm();
pb2=1-t[4].parity();
t[4].inc(pb2);
t[4].norm();
pb3=1-t[8].parity();
t[8].inc(pb3);
t[8].norm();
pb4=1-t[12].parity();
t[12].inc(pb4);
t[12].norm();
// Number of bits
mt.zero();
for (i=0;i<16;i++) {
mt.or(t[i]);
}
nb=1+mt.nbits();
// Sign pivot
s1[nb-1]=1;
s2[nb-1]=1;
s3[nb-1]=1;
s4[nb-1]=1;
for (i=0;i<nb-1;i++) {
t[0].fshr(1);
s1[i]=2*t[0].parity()-1;
t[4].fshr(1);
s2[i]=2*t[4].parity()-1;
t[8].fshr(1);
s3[i]=2*t[8].parity()-1;
t[12].fshr(1);
s4[i]=2*t[12].parity()-1;
}
// Recoded exponent
for (i=0; i<nb; i++) {
w1[i]=0;
k=1;
for (j=1; j<4; j++) {
bt=s1[i]*t[j].parity();
t[j].fshr(1);
t[j].dec(bt>>1);
t[j].norm();
w1[i]+=bt*k;
k*=2;
}
w2[i]=0;
k=1;
for (j=5; j<8; j++) {
bt=s2[i]*t[j].parity();
t[j].fshr(1);
t[j].dec(bt>>1);
t[j].norm();
w2[i]+=bt*k;
k*=2;
}
w3[i]=0;
k=1;
for (j=9; j<12; j++) {
bt=s3[i]*t[j].parity();
t[j].fshr(1);
t[j].dec(bt>>1);
t[j].norm();
w3[i]+=bt*k;
k*=2;
}
w4[i]=0;
k=1;
for (j=13; j<16; j++) {
bt=s4[i]*t[j].parity();
t[j].fshr(1);
t[j].dec(bt>>1);
t[j].norm();
w4[i]+=bt*k;
k*=2;
}
}
// Main loop
p.select(g1,2*w1[nb-1]+1);
r.select(g2,2*w2[nb-1]+1);
p.mul(r);
r.select(g3,2*w3[nb-1]+1);
p.mul(r);
r.select(g4,2*w4[nb-1]+1);
p.mul(r);
for (i=nb-2;i>=0;i--) {
p.usqr();
r.select(g1,2*w1[i]+s1[i]);
p.mul(r);
r.select(g2,2*w2[i]+s2[i]);
p.mul(r);
r.select(g3,2*w3[i]+s3[i]);
p.mul(r);
r.select(g4,2*w4[i]+s4[i]);
p.mul(r);
}
// apply correction
r.copy(q[0]); r.conj();
r.mul(p);
p.cmove(r,pb1);
r.copy(q[4]); r.conj();
r.mul(p);
p.cmove(r,pb2);
r.copy(q[8]); r.conj();
r.mul(p);
p.cmove(r,pb3);
r.copy(q[12]); r.conj();
r.mul(p);
p.cmove(r,pb4);
p.reduce();
return p;
};
return FP48;
};
if (typeof module !== "undefined" && typeof module.exports !== "undefined") {
module.exports = {
FP48: FP48
};
}