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Combine mux constraints and use simplified bitstring algorithm for BigLessThan. #17

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Combine mux constraints and use simplified bitstring algorithm for BigLessThan. #17

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3f8b334
Remove unneeded manual signal setting.
BlakeMScurr Nov 29, 2022
447c589
Remove constraints by using standard mux pattern.
BlakeMScurr Nov 29, 2022
424f1c5
Simplify BigLessThan.
BlakeMScurr Nov 29, 2022
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50 changes: 14 additions & 36 deletions circuits/bigint.circom
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Original file line number Diff line number Diff line change
Expand Up @@ -300,45 +300,29 @@ template BigLessThan(n, k){
signal input b[k];
signal output out;

var a_lt = 0; // bit string representing registers where a > b
var b_lt = (1 << k) - 1;

component lt[k];
component eq[k];
for (var i = 0; i < k; i++) {
lt[i] = LessThan(n);
lt[i].in[0] <== a[i];
lt[i].in[1] <== b[i];

eq[i] = IsEqual();
eq[i].in[0] <== a[i];
eq[i].in[1] <== b[i];

var e = 1 << i;
a_lt += lt[i].out * e;
b_lt -= (eq[i].out + lt[i].out) * e;
}

// ors[i] holds (lt[k - 1] || (eq[k - 1] && lt[k - 2]) .. || (eq[k - 1] && .. && lt[i]))
// ands[i] holds (eq[k - 1] && .. && lt[i])
// eq_ands[i] holds (eq[k - 1] && .. && eq[i])
component ors[k - 1];
component ands[k - 1];
component eq_ands[k - 1];
for (var i = k - 2; i >= 0; i--) {
ands[i] = AND();
eq_ands[i] = AND();
ors[i] = OR();

if (i == k - 2) {
ands[i].a <== eq[k - 1].out;
ands[i].b <== lt[k - 2].out;
eq_ands[i].a <== eq[k - 1].out;
eq_ands[i].b <== eq[k - 2].out;
ors[i].a <== lt[k - 1].out;
ors[i].b <== ands[i].out;
} else {
ands[i].a <== eq_ands[i + 1].out;
ands[i].b <== lt[i].out;
eq_ands[i].a <== eq_ands[i + 1].out;
eq_ands[i].b <== eq[i].out;
ors[i].a <== ors[i + 1].out;
ors[i].b <== ands[i].out;
}
}
out <== ors[0].out;
component lt_bitstring = LessThan(k);
lt_bitstring.in[0] <== b_lt;
lt_bitstring.in[1] <== a_lt;
out <== lt_bitstring.out;
}

template BigIsEqual(k){
Expand Down Expand Up @@ -394,18 +378,14 @@ template BigMod(n, k) {
mul.b[k] <== 0;

component add = BigAdd(n, 2 * k + 2);
for (var i = 0; i < 2 * k; i++) {
for (var i = 0; i < 2 * k + 2; i++) {
add.a[i] <== mul.out[i];
if (i < k) {
add.b[i] <== mod[i];
} else {
add.b[i] <== 0;
}
}
add.a[2 * k] <== mul.out[2 * k];
add.a[2 * k + 1] <== mul.out[2 * k + 1];
add.b[2 * k] <== 0;
add.b[2 * k + 1] <== 0;

for (var i = 0; i < 2 * k; i++) {
add.out[i] === a[i];
Expand Down Expand Up @@ -471,10 +451,8 @@ template BigSubModP(n, k){
add.a[i] <== sub.out[i];
add.b[i] <== p[i];
}
signal tmp[k];
for (var i = 0; i < k; i++){
tmp[i] <== (1 - flag) * sub.out[i];
out[i] <== tmp[i] + flag * add.out[i];
out[i] <== sub.out[i] + flag * (add.out[i] - sub.out[i]);
}
}

Expand Down