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/*
* ecgen, tool for generating Elliptic curve domain parameters
* Copyright (C) 2017-2018 J08nY
*/
#include "supersingular.h"
GENERATOR(supersingular_gen_equation) {
if (equalis(curve->field, 2)) {
return -2;
}
if (mod4(curve->field) == 3) {
curve->a = mkintmod(subis(curve->field, 1), curve->field);
curve->b = mkintmod(stoi(0), curve->field);
return 1;
}
GEN q = stoi(3);
while (!(mod4(q) == 3 && kronecker(curve->field, q) == -1)) {
q = nextprime(addis(q, 1));
}
if (equalis(q, 3)) {
curve->a = mkintmod(stoi(0), curve->field);
curve->b = mkintmod(stoi(1), curve->field);
return 1;
} else {
GEN H = polclass(negi(q), 0, 0);
GEN r = FpX_roots(H, curve->field);
GEN root = gel(r, 1);
curve->a = mkintmod(
Fp_div(Fp_mul(stoi(27), root, curve->field),
Fp_mul(stoi(4), Fp_sub(stoi(1728), root, curve->field),
curve->field),
curve->field),
curve->field);
curve->b = gneg(curve->a);
return 1;
}
}
GENERATOR(supersingular_gen_order) {
// copy field to order
curve->order = addis(curve->field, 1);
obj_insert(curve->curve, 1, curve->order);
return 1;
}
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