circomlib/circuits/binsub.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/>.
*/
/*
This component creates a binary substraction.
Main Constraint:
(in[0][0] * 2^0 + in[0][1] * 2^1 + ..... + in[0][n-1] * 2^(n-1)) +
+ 2^n
- (in[1][0] * 2^0 + in[1][1] * 2^1 + ..... + in[1][n-1] * 2^(n-1))
===
out[0] * 2^0 + out[1] * 2^1 + + out[n-1] *2^(n-1) + aux
out[0] * (out[0] - 1) === 0
out[1] * (out[0] - 1) === 0
.
.
.
out[n-1] * (out[n-1] - 1) === 0
aux * (aux-1) == 0
*/
template BinSub(n) {
signal input in[2][n];
signal output out[n];
signal aux;
var lin = 2**n;
var lout = 0;
for (var i=0; i<n; i++) {
lin = lin + in[0][i]*(2**i);
lin = lin - in[1][i]*(2**i);
}
for (var i=0; i<n; i++) {
out[i] <-- (lin >> i) & 1;
// Ensure out is binary
out[i] * (out[i] - 1) === 0;
lout = lout + out[i]*(2**i);
}
aux <-- (lin >> n) & 1;
aux*(aux-1) === 0;
lout = lout + aux*(2**n);
// Ensure the sum;
lin === lout;
}