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*/
 19pragma circom 2.0.0;
 20
 21include "bitify.circom";
 22include "aliascheck.circom";
 23include "compconstant.circom";
 24include "babyjub.circom";
 25
 26
 27function sqrt(n) {
 28
 29    if (n == 0) {
 30        return 0;
 31    }
 32
 33    // Test that have solution
 34    var res = n ** ((-1) >> 1);
 35//        if (res!=1) assert(false, "SQRT does not exists");
 36    if (res!=1) return 0;
 37
 38    var m = 28;
 39    var c = 19103219067921713944291392827692070036145651957329286315305642004821462161904;
 40    var t = n ** 81540058820840996586704275553141814055101440848469862132140264610111;
 41    var r = n ** ((81540058820840996586704275553141814055101440848469862132140264610111+1)>>1);
 42    var sq;
 43    var i;
 44    var b;
 45    var j;
 46
 47    while ((r != 0)&&(t != 1)) {
 48        sq = t*t;
 49        i = 1;
 50        while (sq!=1) {
 51            i++;
 52            sq = sq*sq;
 53        }
 54
 55        // b = c ^ m-i-1
 56        b = c;
 57        for (j=0; j< m-i-1; j ++) b = b*b;
 58
 59        m = i;
 60        c = b*b;
 61        t = t*c;
 62        r = r*b;
 63    }
 64
 65    if (r < 0 ) {
 66        r = -r;
 67    }
 68
 69    return r;
 70}
 71
 72
 73template Bits2Point() {
 74    signal input in[256];
 75    signal output out[2];
 76}
 77
 78template Bits2Point_Strict() {
 79    signal input in[256];
 80    signal output out[2];
 81
 82    var i;
 83
 84    // Check aliasing
 85    component aliasCheckY = AliasCheck();
 86    for (i=0; i<254; i++) {
 87        aliasCheckY.in[i] <== in[i];
 88    }
 89    in[254] === 0;
 90
 91    component b2nY = Bits2Num(254);
 92    for (i=0; i<254; i++) {
 93        b2nY.in[i] <== in[i];
 94    }
 95
 96    out[1] <== b2nY.out;
 97
 98    var a = 168700;
 99    var d = 168696;
100
101    var y2 = out[1] * out[1];
102
103    var x = sqrt(   (1-y2)/(a - d*y2)  );
104
105    if (in[255] == 1) x = -x;
106
107    out[0] <-- x;
108
109    component babyCheck = BabyCheck();
110    babyCheck.x <== out[0];
111    babyCheck.y <== out[1];
112
113    component n2bX = Num2Bits(254);
114    n2bX.in <== out[0];
115    component aliasCheckX = AliasCheck();
116    for (i=0; i<254; i++) {
117        aliasCheckX.in[i] <== n2bX.out[i];
118    }
119
120    component signCalc = CompConstant(10944121435919637611123202872628637544274182200208017171849102093287904247808);
121    for (i=0; i<254; i++) {
122        signCalc.in[i] <== n2bX.out[i];
123    }
124
125    signCalc.out === in[255];
126}
127
128
129template Point2Bits() {
130    signal input in[2];
131    signal output out[256];
132
133
134}
135
136template Point2Bits_Strict() {
137    signal input in[2];
138    signal output out[256];
139
140    var i;
141
142    component n2bX = Num2Bits(254);
143    n2bX.in <== in[0];
144    component n2bY = Num2Bits(254);
145    n2bY.in <== in[1];
146
147    component aliasCheckX = AliasCheck();
148    component aliasCheckY = AliasCheck();
149    for (i=0; i<254; i++) {
150        aliasCheckX.in[i] <== n2bX.out[i];
151        aliasCheckY.in[i] <== n2bY.out[i];
152    }
153
154    component signCalc = CompConstant(10944121435919637611123202872628637544274182200208017171849102093287904247808);
155    for (i=0; i<254; i++) {
156        signCalc.in[i] <== n2bX.out[i];
157    }
158
159    for (i=0; i<254; i++) {
160        out[i] <== n2bY.out[i];
161    }
162    out[254] <== 0;
163    out[255] <== signCalc.out;
164}