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/*
* ecgen, tool for generating Elliptic curve domain parameters
* Copyright (C) 2017-2018 J08nY
*/
#include "cm_prime.h"
#include "cm_any.h"
#include "io/output.h"
#include "obj/curve.h"
#include "obj/point.h"
#include "obj/subgroup.h"
#include "util/bits.h"
static size_t 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 qdisc_init(cm_prime_qdisc_t *qdisc, GEN order) {
qdisc->D = gen_0;
qdisc->p = gen_0;
qdisc->t = gen_0;
qdisc->order = order;
qdisc->r = gen_0;
qdisc->i = gen_0;
qdisc->Sp = NULL;
qdisc->nprimes = 0;
}
static void qdisc_next(cm_prime_qdisc_t *qdisc) {
// 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(qdisc->order, BIGDEFAULTPREC));
GEN rlog2 = sqri(mulii(addis(qdisc->r, 1), logN));
// When do I want more primes? If i == imax, or nprimes == 0
GEN imax = int2n(qdisc->nprimes);
if (equalii(qdisc->i, imax) || qdisc->nprimes == 0) {
qdisc->nprimes =
add_primes(qdisc->r, qdisc->order, &(qdisc->Sp), qdisc->nprimes);
imax = int2n(qdisc->nprimes);
}
pari_sp btop = avma;
while (true) {
while (cmpii(qdisc->i, imax) < 0) {
// debug_log("i %Pi", qdisc->i);
GEN pprod = gen_1;
bits_t *ibits = bits_from_i_len(qdisc->i, qdisc->nprimes);
for (size_t j = 0; j < qdisc->nprimes; ++j) {
if (GET_BIT(ibits->bits, j) == 1) {
// debug_log("multiplying %Pi", qdisc->Sp[j]);
pprod = mulii(pprod, qdisc->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, qdisc->order, &x, &y)) {
qdisc->i = gerepileupto(btop, addis(qdisc->i, 1));
// debug_log("Cornacchia fail");
continue;
}
GEN pp1 = addii(addis(qdisc->order, 1), x);
GEN pp2 = subii(addis(qdisc->order, 1), x);
if (isprime(pp1)) {
qdisc->p = pp1;
qdisc->D = pprod;
qdisc->t = x;
qdisc->i = addis(qdisc->i, 1);
debug_log("good D %Pi", pprod);
return;
}
if (isprime(pp2)) {
qdisc->p = pp2;
qdisc->D = pprod;
qdisc->t = x;
qdisc->i = addis(qdisc->i, 1);
debug_log("good D %Pi", pprod);
return;
}
}
qdisc->i = gerepileupto(btop, addis(qdisc->i, 1));
}
qdisc->r = addis(qdisc->r, 1);
qdisc->nprimes =
add_primes(qdisc->r, qdisc->order, &(qdisc->Sp), qdisc->nprimes);
rlog2 = sqri(mulii(addis(qdisc->r, 1), logN));
imax = int2n(qdisc->nprimes);
btop = avma;
}
}
static void qdisc_free(cm_prime_qdisc_t *qdisc) { try_free(qdisc->Sp); }
curve_t *cm_prime_curve(GEN order) {
GEN e = NULL;
cm_prime_qdisc_t qdisc;
qdisc_init(&qdisc, order);
do {
qdisc_next(&qdisc);
e = cm_construct_curve(order, qdisc.D, qdisc.p, true);
} while (e == NULL);
qdisc_free(&qdisc);
curve_t *result = curve_new();
result->field = qdisc.p;
result->a = ell_get_a4(e);
result->b = ell_get_a6(e);
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 = genrand(e);
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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