circomlib/circuits/babyjub.circom

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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 "bitify.circom";
include "escalarmulfix.circom";
template BabyAdd() {
signal input x1;
signal input y1;
signal input x2;
signal input y2;
signal output xout;
signal output yout;
signal beta;
signal gamma;
signal delta;
signal tau;
var a = 168700;
var d = 168696;
beta <== x1*y2;
gamma <== y1*x2;
delta <== (-a*x1+y1)*(x2 + y2);
tau <== beta * gamma;
xout <-- (beta + gamma) / (1+ d*tau);
(1+ d*tau) * xout === (beta + gamma);
yout <-- (delta + a*beta - gamma) / (1-d*tau);
(1-d*tau)*yout === (delta + a*beta - gamma);
}
template BabyDbl() {
signal input x;
signal input y;
signal output xout;
signal output yout;
component adder = BabyAdd();
adder.x1 <== x;
adder.y1 <== y;
adder.x2 <== x;
adder.y2 <== y;
adder.xout ==> xout;
adder.yout ==> yout;
}
template BabyCheck() {
signal input x;
signal input y;
signal x2;
signal y2;
var a = 168700;
var d = 168696;
x2 <== x*x;
y2 <== y*y;
a*x2 + y2 === 1 + d*x2*y2;
}
// Extracts the public key from private key, as mentioned in https://tools.ietf.org/html/rfc8032
template BabyPbk() {
signal private input in;
signal output Ax;
signal output Ay;
var BASE8 = [
5299619240641551281634865583518297030282874472190772894086521144482721001553,
16950150798460657717958625567821834550301663161624707787222815936182638968203
];
component pvkBits = Num2Bits(253);
pvkBits.in <== in;
component mulFix = EscalarMulFix(253, BASE8);
var i;
for (i=0; i<253; i++) {
mulFix.e[i] <== pvkBits.out[i];
}
Ax <== mulFix.out[0];
Ay <== mulFix.out[1];
}