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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) {
debug_log("add_primes r = %Pi, nprimes = %lu", r, 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);
}
if (nprimes == nalloc) {
nalloc *= 2;
*primes = try_realloc(*primes, sizeof(GEN) * nalloc);
}
(*primes)[nprimes++] = pstar;
}
}
*primes = try_realloc(*primes, sizeof(GEN) * nprimes);
return nprimes;
}
static void custom_quadr_init(custom_quadr_t *quadr, GEN order) {
quadr->D = gen_0;
quadr->p = gen_0;
quadr->t = gen_0;
quadr->order = order;
quadr->r = gen_0;
quadr->i = gen_0;
quadr->Sp = NULL;
quadr->nprimes = 0;
}
static void custom_quadr_next(custom_quadr_t *quadr) {
// Ok I get some state in r, i, Sp and nprimes.
// Here I want to check if I want to generate more primes into Sp
// Then continue with i
GEN logN = ground(glog(quadr->order, BIGDEFAULTPREC));
GEN rlog2 = sqri(mulii(addis(quadr->r, 1), logN));
// When do I want more primes? If i == imax, or nprimes == 0
GEN imax = int2n(quadr->nprimes);
if (equalii(quadr->i, imax) || quadr->nprimes == 0) {
quadr->nprimes = custom_add_primes(quadr->r, quadr->order, &(quadr->Sp),
quadr->nprimes);
imax = int2n(quadr->nprimes);
}
pari_sp btop = avma;
while (true) {
while (cmpii(quadr->i, imax) < 0) {
// debug_log("i %Pi", quadr->i);
GEN pprod = gen_1;
bits_t *ibits = bits_from_i_len(quadr->i, quadr->nprimes);
for (size_t j = 0; j < quadr->nprimes; ++j) {
if (GET_BIT(ibits->bits, j) == 1) {
// debug_log("multiplying %Pi", quadr->Sp[j]);
pprod = mulii(pprod, quadr->Sp[j]);
}
}
bits_free(&ibits);
GEN absp = absi(pprod);
long m4 = mod4(absp);
if (cmpii(absp, rlog2) < 0 && equalii(modis(pprod, 8), stoi(5)) &&
m4 != 1 && m4 != 2) {
debug_log("candidate D = %Pi", pprod);
GEN x;
GEN y;
if (!cornacchia2(absp, quadr->order, &x, &y)) {
quadr->i = gerepileupto(btop, addis(quadr->i, 1));
// debug_log("Cornacchia fail");
continue;
}
GEN pp1 = addii(addis(quadr->order, 1), x);
GEN pp2 = subii(addis(quadr->order, 1), x);
if (isprime(pp1)) {
quadr->p = pp1;
quadr->D = pprod;
quadr->t = x;
quadr->i = addis(quadr->i, 1);
debug_log("good D %Pi", pprod);
return;
}
if (isprime(pp2)) {
quadr->p = pp2;
quadr->D = pprod;
quadr->t = x;
quadr->i = addis(quadr->i, 1);
debug_log("good D %Pi", pprod);
return;
}
}
quadr->i = gerepileupto(btop, addis(quadr->i, 1));
}
quadr->r = addis(quadr->r, 1);
quadr->nprimes = custom_add_primes(quadr->r, quadr->order, &(quadr->Sp),
quadr->nprimes);
rlog2 = sqri(mulii(addis(quadr->r, 1), logN));
imax = int2n(quadr->nprimes);
btop = avma;
}
}
static void custom_quadr_free(custom_quadr_t *quadr) { try_free(quadr->Sp); }
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;
}
GEN a = NULL;
GEN e = NULL;
GEN g = NULL;
custom_quadr_t quadr;
custom_quadr_init(&quadr, order);
while (true) {
custom_quadr_next(&quadr);
debug_log("order = %Pi", order);
debug_log("p = %Pi, t = %Pi, D = %Pi, ", quadr.p, quadr.t, 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);
if (gequal(r, gtovec(gen_0))) {
continue;
}
bool has_curve = false;
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);
pari_CATCH(e_TYPE) { continue; }
pari_TRY { checkell(e); };
pari_ENDCATCH{};
g = genrand(e);
GEN gmul = ellmul(e, g, order);
if (ell_is_inf(gmul)) {
debug_log("YES %Ps", e);
has_curve = true;
break;
}
}
if (has_curve) break;
}
custom_quadr_free(&quadr);
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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