1/*
  2    Copyright 2018 0KIMS association.
  3
  4    This file is part of circom (Zero Knowledge Circuit Compiler).
  5
  6    circom is a free software: you can redistribute it and/or modify it
  7    under the terms of the GNU General Public License as published by
  8    the Free Software Foundation, either version 3 of the License, or
  9    (at your option) any later version.
 10
 11    circom is distributed in the hope that it will be useful, but WITHOUT
 12    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 13    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
 14    License for more details.
 15
 16    You should have received a copy of the GNU General Public License
 17    along with circom. If not, see <https://www.gnu.org/licenses/>.
 18*/
 19
 20include "bitify.circom";
 21include "aliascheck.circom";
 22include "compconstant.circom";
 23include "babyjub.circom";
 24
 25
 26function sqrt(n) {
 27
 28    if (n == 0) {
 29        return 0;
 30    }
 31
 32    // Test that have solution
 33    var res = n ** ((-1) >> 1);
 34//        if (res!=1) assert(false, "SQRT does not exists");
 35    if (res!=1) return 0;
 36
 37    var m = 28;
 38    var c = 19103219067921713944291392827692070036145651957329286315305642004821462161904;
 39    var t = n ** 81540058820840996586704275553141814055101440848469862132140264610111;
 40    var r = n ** ((81540058820840996586704275553141814055101440848469862132140264610111+1)>>1);
 41    var sq;
 42    var i;
 43    var b;
 44    var j;
 45
 46    while ((r != 0)&&(t != 1)) {
 47        sq = t*t;
 48        i = 1;
 49        while (sq!=1) {
 50            i++;
 51            sq = sq*sq;
 52        }
 53
 54        // b = c ^ m-i-1
 55        b = c;
 56        for (j=0; j< m-i-1; j ++) b = b*b;
 57
 58        m = i;
 59        c = b*b;
 60        t = t*c;
 61        r = r*b;
 62    }
 63
 64    if (r > ((-1) >> 1)) {
 65        r = -r;
 66    }
 67
 68    return r;
 69}
 70
 71
 72template Bits2Point() {
 73    signal input in[256];
 74    signal output out[2];
 75}
 76
 77template Bits2Point_Strict() {
 78    signal input in[256];
 79    signal output out[2];
 80
 81    var i;
 82
 83    // Check aliasing
 84    component aliasCheckY = AliasCheck();
 85    for (i=0; i<254; i++) {
 86        aliasCheckY.in[i] <== in[i];
 87    }
 88    in[254] === 0;
 89
 90    component b2nY = Bits2Num(254);
 91    for (i=0; i<254; i++) {
 92        b2nY.in[i] <== in[i];
 93    }
 94
 95    out[1] <== b2nY.out;
 96
 97    var a = 168700;
 98    var d = 168696;
 99
100    var y2 = out[1] * out[1];
101
102    var x = sqrt(   (1-y2)/(a - d*y2)  );
103
104    if (in[255] == 1) x = -x;
105
106    out[0] <-- x;
107
108    component babyCheck = BabyCheck();
109    babyCheck.x <== out[0];
110    babyCheck.y <== out[1];
111
112    component n2bX = Num2Bits(254);
113    n2bX.in <== out[0];
114    component aliasCheckX = AliasCheck();
115    for (i=0; i<254; i++) {
116        aliasCheckX.in[i] <== n2bX.out[i];
117    }
118
119    component signCalc = CompConstant(10944121435919637611123202872628637544274182200208017171849102093287904247808);
120    for (i=0; i<254; i++) {
121        signCalc.in[i] <== n2bX.out[i];
122    }
123
124    signCalc.out === in[255];
125}
126
127
128template Point2Bits() {
129    signal input in[2];
130    signal output out[256];
131
132
133}
134
135template Point2Bits_Strict() {
136    signal input in[2];
137    signal output out[256];
138
139    var i;
140
141    component n2bX = Num2Bits(254);
142    n2bX.in <== in[0];
143    component n2bY = Num2Bits(254);
144    n2bY.in <== in[1];
145
146    component aliasCheckX = AliasCheck();
147    component aliasCheckY = AliasCheck();
148    for (i=0; i<254; i++) {
149        aliasCheckX.in[i] <== n2bX.out[i];
150        aliasCheckY.in[i] <== n2bY.out[i];
151    }
152
153    component signCalc = CompConstant(10944121435919637611123202872628637544274182200208017171849102093287904247808);
154    for (i=0; i<254; i++) {
155        signCalc.in[i] <== n2bX.out[i];
156    }
157
158    for (i=0; i<254; i++) {
159        out[i] <== n2bY.out[i];
160    }
161    out[254] <== 0;
162    out[255] <== signCalc.out;
163}