circomlib/circuits/binsum.circom
2019-11-23 19:24:02 +02:00

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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/>.
*/
/*
Binary Sum
==========
This component creates a binary sum componet of ops operands and n bits each operand.
e is Number of carries: Depends on the number of operands in the input.
Main Constraint:
in[0][0] * 2^0 + in[0][1] * 2^1 + ..... + in[0][n-1] * 2^(n-1) +
+ in[1][0] * 2^0 + in[1][1] * 2^1 + ..... + in[1][n-1] * 2^(n-1) +
+ ..
+ in[ops-1][0] * 2^0 + in[ops-1][1] * 2^1 + ..... + in[ops-1][n-1] * 2^(n-1) +
===
out[0] * 2^0 + out[1] * 2^1 + + out[n+e-1] *2(n+e-1)
To waranty binary outputs:
out[0] * (out[0] - 1) === 0
out[1] * (out[0] - 1) === 0
.
.
.
out[n+e-1] * (out[n+e-1] - 1) == 0
*/
/*
This function calculates the number of extra bits in the output to do the full sum.
*/
/* a must be < Nq/2, where Nq is the number of elements in the scalar field */
function nbits(a) {
var n = 1;
var r = 0;
while (n-1<a) {
r++;
n *= 2;
}
return r;
}
/* n must be such that (2**(n+1) -2) < Nq/ops, where Nq is the number of bits in the scalar field */
template BinSum(n, ops) {
var nout = nbits((2**n -1)*ops);
signal input in[ops][n];
signal output out[nout];
var lin = 0;
var lout = 0;
var k;
var j;
for (k=0; k<n; k++) {
for (j=0; j<ops; j++) {
lin += in[j][k] * 2**k;
}
}
for (k=0; k<nout; k++) {
out[k] <-- (lin >> k) & 1;
// Ensure out is binary
out[k] * (out[k] - 1) === 0;
lout += out[k] * 2**k;
}
// Ensure the sum;
lin === lout;
}