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support long a and b values #30

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support long a and b values #30

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33 changes: 19 additions & 14 deletions circuits/curve.circom
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Original file line number Diff line number Diff line change
Expand Up @@ -64,16 +64,23 @@ template PointOnCurve(n, k, a, b, p){
for(var i=0; i<k; i++)
x_cu.b[i] <== in[0][i];

component ax = BigMultShortLong(n, k, 2*n + LOGK); // 2k-1 registers in [0, k*2^{2n})
for (var i=0; i<k; i++) {
ax.a[i] <== a[i];
ax.b[i] <== in[0][i];
}

// x_cu + a x + b has 3k-2 positive registers < k^2 * 2^{3n} + 2^{2n} + 2^n < (k^2 + 1) * 2^{3n}
component cu_red = PrimeReduce(n, k, 2*k-2, p, 4*n + 3*LOGK + 1);
for(var i=0; i<3*k-2; i++){
if(i == 0)
cu_red.in[i] <== x_cu.out[i] + a * in[0][i] + b;
else{
if(i < k)
cu_red.in[i] <== x_cu.out[i] + a * in[0][i];
else
if (i < k) {
cu_red.in[i] <== x_cu.out[i] + ax.out[i] + b[i];
} else {
if (i < 2*k-1) {
cu_red.in[i] <== x_cu.out[i] + ax.out[i];
} else {
cu_red.in[i] <== x_cu.out[i];
}
}
}
// cu_red has k registers < (k^2 + 1)*(2k-1)*2^{4n}
Expand Down Expand Up @@ -108,10 +115,11 @@ template PointOnTangent(n, k, a, p){
}
component right = BigMultShortLongUnequal(n, 2*k-1, k, 3*n + 2*LOGK + 3); // 3k-2 registers < (3*k+1)*k*2^{3n}
for(var i=0; i<2*k-1; i++){
if(i == 0)
right.a[i] <== 3 * x_sq.out[i] + a; // registers in [0, 3*k*2^{2n} + 2^n = (3k+2^{-n})*2^{2n})
else
right.a[i] <== 3 * x_sq.out[i];
if (i < k) {
right.a[i] <== 3 * x_sq.out[i] + a[i]; // registers in [0, 3*k*2^{2n} + 2^n = (3k+2^{-n})*2^{2n})
} else {
right.a[i] <== 3 * x_sq.out[i];
}
}
for(var i=0; i<k; i++){
right.b[i] <== in[0][0][i] - in[1][0][i];
Expand Down Expand Up @@ -248,17 +256,14 @@ template EllipticCurveDouble(n, k, a, b, p) {
signal input in[2][k];
signal output out[2][k];

var long_a[k];
var long_3[k];
long_a[0] = a;
long_3[0] = 3;
for (var i = 1; i < k; i++) {
long_a[i] = 0;
long_3[i] = 0;
}

// precompute lambda
var lamb_num[50] = long_add_mod(n, k, long_a, prod_mod(n, k, long_3, prod_mod(n, k, in[0], in[0], p), p), p);
var lamb_num[50] = long_add_mod(n, k, a, prod_mod(n, k, long_3, prod_mod(n, k, in[0], in[0], p), p), p);
var lamb_denom[50] = long_add_mod(n, k, in[1], in[1], p);
var lamb[50] = prod_mod(n, k, lamb_num, mod_inv(n, k, lamb_denom, p), p);

Expand Down