circomlib/circuits/escalarmulfix.circom
2018-12-16 11:27:29 +01:00

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/*
Copyright 2018 0KIMS association.
This file is part of circom (Zero Knowledge Circuit Compiler).
circom is a free software: you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
circom is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
License for more details.
You should have received a copy of the GNU General Public License
along with circom. If not, see <https://www.gnu.org/licenses/>.
*/
include "mux3.circom";
include "montgomery.circom";
include "babyjub.circom";
/*
Window of 3 elements, it calculates
out = base + base*in[0] + 2*base*in[1] + 4*base*in[2]
out4 = 4*base
The result should be compensated.
*/
template WindowMulFix() {
signal input in[3];
signal input base[2];
signal output out[2];
signal output out8[2]; // Returns 8*Base (To be linked)
component mux = MultiMux3(2);
mux.s[0] <== in[0];
mux.s[1] <== in[1];
mux.s[2] <== in[2];
component dbl2 = MontgomeryDouble();
component adr3 = MontgomeryAdd();
component adr4 = MontgomeryAdd();
component adr5 = MontgomeryAdd();
component adr6 = MontgomeryAdd();
component adr7 = MontgomeryAdd();
component adr8 = MontgomeryAdd();
// in[0] -> 1*BASE
mux.c[0][0] <== base[0];
mux.c[1][0] <== base[1];
// in[1] -> 2*BASE
dbl2.in[0] <== base[0];
dbl2.in[1] <== base[1];
mux.c[0][1] <== dbl2.out[0];
mux.c[1][1] <== dbl2.out[1];
// in[2] -> 3*BASE
adr3.in1[0] <== base[0];
adr3.in1[1] <== base[1];
adr3.in2[0] <== dbl2.out[0];
adr3.in2[1] <== dbl2.out[1];
mux.c[0][2] <== adr3.out[0];
mux.c[1][2] <== adr3.out[1];
// in[3] -> 4*BASE
adr4.in1[0] <== base[0];
adr4.in1[1] <== base[1];
adr4.in2[0] <== adr3.out[0];
adr4.in2[1] <== adr3.out[1];
mux.c[0][3] <== adr4.out[0];
mux.c[1][3] <== adr4.out[1];
// in[4] -> 5*BASE
adr5.in1[0] <== base[0];
adr5.in1[1] <== base[1];
adr5.in2[0] <== adr4.out[0];
adr5.in2[1] <== adr4.out[1];
mux.c[0][4] <== adr5.out[0];
mux.c[1][4] <== adr5.out[1];
// in[5] -> 6*BASE
adr6.in1[0] <== base[0];
adr6.in1[1] <== base[1];
adr6.in2[0] <== adr5.out[0];
adr6.in2[1] <== adr5.out[1];
mux.c[0][5] <== adr6.out[0];
mux.c[1][5] <== adr6.out[1];
// in[6] -> 7*BASE
adr7.in1[0] <== base[0];
adr7.in1[1] <== base[1];
adr7.in2[0] <== adr6.out[0];
adr7.in2[1] <== adr6.out[1];
mux.c[0][6] <== adr7.out[0];
mux.c[1][6] <== adr7.out[1];
// in[7] -> 8*BASE
adr8.in1[0] <== base[0];
adr8.in1[1] <== base[1];
adr8.in2[0] <== adr7.out[0];
adr8.in2[1] <== adr7.out[1];
mux.c[0][7] <== adr8.out[0];
mux.c[1][7] <== adr8.out[1];
out8[0] <== adr8.out[0];
out8[1] <== adr8.out[1];
out[0] <== mux.out[0];
out[1] <== mux.out[1];
}
/*
This component does a multiplication of a escalar times a fix base
Signals:
e: The scalar in bits
base: the base point in edwards format
out: The result
dbl: Point in Edwards to be linked to the next segment.
*/
template SegmentMulFix(nWindows) {
signal input e[nWindows*3];
signal input base[2];
signal output out[2];
signal output dbl[2];
var i;
var j;
// Convert the base to montgomery
component e2m = Edwards2Montgomery();
e2m.in[0] <== base[0];
e2m.in[1] <== base[1];
component windows[nWindows];
component adders[nWindows-1];
component cadders[nWindows-1];
for (i=0; i<nWindows; i++) {
windows[i] = WindowMulFix();
if (i==0) {
windows[i].base[0] <== e2m.out[0];
windows[i].base[1] <== e2m.out[1];
} else {
windows[i].base[0] <== windows[i-1].out8[0];
windows[i].base[1] <== windows[i-1].out8[1];
adders[i-1] = MontgomeryAdd();
cadders[i-1] = MontgomeryAdd();
if (i==1) {
adders[i-1].in1[0] <== windows[0].out[0];
adders[i-1].in1[1] <== windows[0].out[1];
cadders[i-1].in1[0] <== e2m.out[0];
cadders[i-1].in1[1] <== e2m.out[1];
} else {
adders[i-1].in1[0] <== adders[i-2].out[0];
adders[i-1].in1[1] <== adders[i-2].out[1];
cadders[i-1].in1[0] <== cadders[i-2].out[0];
cadders[i-1].in1[1] <== cadders[i-2].out[1];
}
adders[i-1].in2[0] <== windows[i].out[0];
adders[i-1].in2[1] <== windows[i].out[1];
cadders[i-1].in2[0] <== windows[i-1].out8[0];
cadders[i-1].in2[1] <== windows[i-1].out8[1];
}
for (j=0; j<3; j++) {
windows[i].in[j] <== e[3*i+j];
}
}
component m2e = Montgomery2Edwards();
component cm2e = Montgomery2Edwards();
if (nWindows > 1) {
m2e.in[0] <== adders[nWindows-2].out[0];
m2e.in[1] <== adders[nWindows-2].out[1];
cm2e.in[0] <== cadders[nWindows-2].out[0];
cm2e.in[1] <== cadders[nWindows-2].out[1];
} else {
m2e.in[0] <== windows[0].out[0];
m2e.in[1] <== windows[0].out[1];
cm2e.in[0] <== e2m.out[0];
cm2e.in[1] <== e2m.out[1];
}
component cAdd = BabyAdd();
cAdd.x1 <== m2e.out[0];
cAdd.y1 <== m2e.out[1];
cAdd.x2 <== -cm2e.out[0];
cAdd.y2 <== cm2e.out[1];
cAdd.xout ==> out[0];
cAdd.yout ==> out[1];
windows[nWindows-1].out8[0] ==> dbl[0];
windows[nWindows-1].out8[1] ==> dbl[1];
}
/*
This component multiplies a escalar times a fixed point BASE (twisted edwards format)
Signals
e: The escalar in binary format
out: The output point in twisted edwards
*/
template EscalarMulFix(n, BASE) {
signal input e[n]; // Input in binary format
signal output out[2]; // Point (Twisted format)
var nsegments = (n-1)\249 +1;
var nlastsegment = n - (nsegments-1)*249;
component segments[nsegments];
component m2e[nsegments-1];
component adders[nsegments-1];
var s;
var i;
var nseg;
var nWindows
for (s=0; s<nsegments; s++) {
nseg = (s < nsegments-1) ? 249 : nlastsegment;
nWindows = ((nseg - 1)\3)+1;
segments[s] = SegmentMulFix(nWindows);
for (i=0; i<nseg; i++) {
segments[s].e[i] <== e[s*249+i];
}
for (i = nseg; i<nWindows*3; i++) {
segments[s].e[i] <== 0;
}
if (s==0) {
segments[s].base[0] <== BASE[0];
segments[s].base[1] <== BASE[1];
} else {
m2e[s-1] = Montgomery2Edwards();
adders[s-1] = BabyAdd();
segments[s-1].dbl[0] ==> m2e[s-1].in[0];
segments[s-1].dbl[1] ==> m2e[s-1].in[1];
m2e[s-1].out[0] ==> segments[s].base[0];
m2e[s-1].out[1] ==> segments[s].base[1];
if (s==1) {
segments[s-1].out[0] ==> adders[s-1].x1;
segments[s-1].out[1] ==> adders[s-1].y1;
} else {
adders[s-2].xout ==> adders[s-1].x1;
adders[s-2].yout ==> adders[s-1].y1;
}
segments[s].out[0] ==> adders[s-1].x2;
segments[s].out[1] ==> adders[s-1].y2;
}
}
if (nsegments == 1) {
segments[0].out[0] ==> out[0];
segments[0].out[1] ==> out[1];
} else {
adders[nsegments-2].xout ==> out[0];
adders[nsegments-2].yout ==> out[1];
}
}