72 lines
1.7 KiB
Plaintext
72 lines
1.7 KiB
Plaintext
/*
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Copyright 2018 0KIMS association.
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This file is part of circom (Zero Knowledge Circuit Compiler).
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circom is a free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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circom is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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License for more details.
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You should have received a copy of the GNU General Public License
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along with circom. If not, see <https://www.gnu.org/licenses/>.
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*/
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/*
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This component creates a binary substraction.
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Main Constraint:
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(in[0][0] * 2^0 + in[0][1] * 2^1 + ..... + in[0][n-1] * 2^(n-1)) +
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+ 2^n
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- (in[1][0] * 2^0 + in[1][1] * 2^1 + ..... + in[1][n-1] * 2^(n-1))
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===
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out[0] * 2^0 + out[1] * 2^1 + + out[n-1] *2^(n-1) + aux
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out[0] * (out[0] - 1) === 0
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out[1] * (out[0] - 1) === 0
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.
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.
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.
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out[n-1] * (out[n-1] - 1) === 0
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aux * (aux-1) == 0
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*/
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template BinSub(n) {
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signal input in[2][n];
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signal output out[n];
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signal aux;
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var lin = 2**n;
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var lout = 0;
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for (var i=0; i<n; i++) {
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lin = lin + in[0][i]*(2**i);
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lin = lin - in[1][i]*(2**i);
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}
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for (var i=0; i<n; i++) {
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out[i] <-- (lin >> i) & 1;
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// Ensure out is binary
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out[i] * (out[i] - 1) === 0;
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lout = lout + out[i]*(2**i);
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}
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aux <-- (lin >> n) & 1;
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aux*(aux-1) === 0;
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lout = lout + aux*(2**n);
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// Ensure the sum;
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lin === lout;
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}
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