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/*
* ecgen, tool for generating Elliptic curve domain parameters
* Copyright (C) 2017 J08nY
*/
#include "custom.h"
#include "io/output.h"
#include "obj/curve.h"
#include "obj/point.h"
#include "obj/subgroup.h"
#include "util/bits.h"
static size_t custom_add_primes(GEN r, GEN order, GEN **primes,
size_t nprimes) {
size_t nalloc = nprimes;
if (nprimes == 0) {
nalloc = 10;
*primes = try_calloc(sizeof(GEN) * nalloc);
}
GEN logN = ground(glog(order, BIGDEFAULTPREC));
GEN rlog = mulii(r, logN);
GEN rplog = mulii(addis(r, 1), logN);
forprime_t iter;
forprime_init(&iter, rlog, rplog);
GEN prime;
while ((prime = forprime_next(&iter))) {
long k = kronecker(order, prime);
if (k == 1) {
GEN pstar = prime;
GEN ppow = divis(subis(prime, 1), 2);
if (mod2(ppow) == 1) {
pstar = negi(prime);
} else {
pstar = gcopy(pstar);
}
(*primes)[nprimes++] = pstar;
if (nprimes == nalloc) {
nalloc *= 2;
*primes = try_realloc(*primes, sizeof(GEN) * nalloc);
}
}
}
return nprimes;
}
static custom_quadr_t custom_quadr(GEN order) {
pari_sp ltop = avma;
custom_quadr_t result = {0};
GEN r = gen_0;
GEN *Sp;
size_t nprimes = custom_add_primes(r, order, &Sp, 0);
GEN logN = ground(glog(order, BIGDEFAULTPREC));
GEN rlog2 = sqri(mulii(r, logN));
GEN i = gen_0;
while (true) {
GEN imax = int2n(nprimes);
while (cmpii(i, imax) < 0) {
// debug_log("i %Pi", i);
pari_sp btop = avma;
GEN pprod = gen_1;
bits_t *ibits = bits_from_i_len(i, nprimes);
for (size_t j = 0; j < nprimes; ++j) {
if (GET_BIT(ibits->bits, j) == 1) {
// debug_log("multiplying %Pi", Sp[j]);
pprod = mulii(pprod, Sp[j]);
}
}
bits_free(&ibits);
if (cmpii(pprod, rlog2) < 0 && equalii(modis(pprod, 8), stoi(5))) {
// debug_log("candidate D = %Pi", pprod);
GEN x;
GEN y;
cornacchia2(negi(pprod), order, &x, &y);
GEN pp1 = addii(addis(order, 1), x);
GEN pp2 = subii(addis(order, 1), x);
if (isprime(pp1)) {
result.p = pp1;
result.D = pprod;
result.t = x;
result.v = gen_0;
gerepileall(ltop, 4, &result.p, &result.t, &result.v,
&result.D);
try_free(Sp);
return result;
}
if (isprime(pp2)) {
result.p = pp2;
result.D = pprod;
result.t = x;
result.v = gen_0;
gerepileall(ltop, 4, &result.p, &result.t, &result.v,
&result.D);
try_free(Sp);
return result;
}
}
avma = btop;
i = addis(i, 1);
}
r = addis(r, 1);
nprimes = custom_add_primes(r, order, &Sp, nprimes);
}
}
curve_t *custom_curve() {
GEN order = strtoi(cfg->cm_order);
if (!isprime(order)) {
fprintf(err, "Currently, order must be prime for CM to work.\n");
return NULL;
}
custom_quadr_t quadr = custom_quadr(order);
debug_log("order = %Pi", order);
debug_log("p = %Pi, t = %Pi, v = %Pi, D = %Pi, ", quadr.p, quadr.t, quadr.v,
quadr.D);
GEN H = polclass(quadr.D, 0, 0);
debug_log("H = %Ps", H);
GEN r = FpX_roots(H, quadr.p);
debug_log("roots = %Ps", r);
GEN a = NULL;
GEN e = NULL;
GEN g = NULL;
long rlen = glength(r);
for (long i = 1; i <= rlen; ++i) {
GEN root = gel(r, i);
a = Fp_div(Fp_mul(stoi(27), root, quadr.p),
Fp_mul(stoi(4), Fp_sub(stoi(1728), root, quadr.p), quadr.p),
quadr.p);
e = ellinit(mkvec2(a, negi(a)), quadr.p, 0);
g = genrand(e);
GEN gmul = ellmul(e, g, order);
if (gequal(gmul, gtovec(gen_0))) {
debug_log("YES %Ps", e);
break;
}
}
curve_t *result = curve_new();
result->field = quadr.p;
result->a = a;
result->b = negi(a);
result->curve = e;
result->order = order;
result->generators = subgroups_new(1);
result->generators[0] = subgroup_new();
result->generators[0]->generator = point_new();
result->generators[0]->generator->point = g;
result->generators[0]->generator->order = order;
result->generators[0]->generator->cofactor = stoi(1);
result->generators[0]->npoints = 0;
result->ngens = 1;
return result;
}
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