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/*
* ecgen, tool for generating Elliptic curve domain parameters
* Copyright (C) 2017 J08nY
*/
#include "invalid.h"
#include "exhaustive/exhaustive.h"
#include "io/output.h"
#include "math/curve.h"
#include "math/equation.h"
#include "math/field.h"
#include "math/gens.h"
#include "math/order.h"
#include "math/point.h"
void invalid_ginit(gen_t *generators, config_t *cfg) {
generators[OFFSET_SEED] = &gen_skip;
if (cfg->random) {
generators[OFFSET_FIELD] = &field_random;
generators[OFFSET_A] = &a_random;
generators[OFFSET_B] = &b_random;
} else {
generators[OFFSET_FIELD] = &field_input;
generators[OFFSET_A] = &a_input;
generators[OFFSET_B] = &b_input;
}
generators[OFFSET_CURVE] = &curve_nonzero;
generators[OFFSET_ORDER] = &order_init;
}
size_t invalid_primes(GEN order, pari_ulong **primes) {
pari_sp ltop = avma;
GEN bound = sqri(order);
GEN product = gen_1;
pari_ulong last = 1;
size_t nprimes = 0;
size_t size = 10;
*primes = pari_malloc(size * sizeof(pari_ulong));
while (cmpii(bound, product) >= 0) {
product = mulis(product, last);
(*primes)[nprimes] = unextprime(last + 1);
last = (*primes)[nprimes];
nprimes++;
if (nprimes == size) {
pari_ulong *new_primes =
pari_realloc(*primes, size * 2 * sizeof(pari_ulong));
if (new_primes) {
*primes = new_primes;
size *= 2;
} else {
perror("Couldn't malloc.");
return 0;
}
}
}
// realloc to smaller size, to tightly fit all generated primes
pari_ulong *new_primes =
pari_realloc(*primes, nprimes * sizeof(pari_ulong));
if (new_primes) {
*primes = new_primes;
} else {
perror("Couldn't malloc.");
return 0;
}
avma = ltop;
return nprimes;
}
size_t invalid_curves(curve_t *curve, config_t *cfg, pari_ulong *primes,
size_t nprimes, curve_t ***curves) {
gen_t invalid_gen[OFFSET_END];
invalid_gen[OFFSET_FIELD] = &gen_skip;
invalid_gen[OFFSET_A] = &gen_skip;
invalid_gen[OFFSET_B] = &b_random;
invalid_gen[OFFSET_CURVE] = &curve_nonzero;
invalid_gen[OFFSET_ORDER] = &order_init;
invalid_gen[OFFSET_GENERATORS] = &gens_init;
invalid_gen[OFFSET_POINTS] = &points_primet;
arg_t *invalid_argss[OFFSET_END];
// We will have nprimes curves in the end
*curves = pari_malloc(nprimes * sizeof(curve_t *));
if (!(*curves)) {
perror("Couldn't malloc.");
return 0;
}
memset(*curves, 0, nprimes * sizeof(curve_t *));
// Alloc a curve, and only alloc a new one when this pointer is saved into
// **curves
curve_t *invalid = curve_new();
// copy field + a from curve to invalid
invalid->field = gcopy(curve->field);
invalid->a = gcopy(curve->a);
size_t ncurves = 0;
while (ncurves < nprimes) {
pari_sp btop = avma;
// generate a curve with random b
exhaustive_gen(invalid, cfg, invalid_gen, NULL, OFFSET_B,
OFFSET_GENERATORS);
// does some small prime from our array divide the curve order?
// if so how many?
size_t total = 0;
for (size_t i = nprimes; i-- > 0;) {
if ((*curves)[i] == NULL && dvdis(invalid->order, primes[i])) {
// whoo we have a new invalid curve
if (!total && cfg->verbose) {
fprintf(
debug,
"we have a new one, calculating prime order points.\n");
}
total++;
}
}
if (total > 0) {
// only pass small primes that divide the curve order and those
// where we dont have a curve yet.
// this is passed to points_primet which uses trial division to find
// a point with given prime order.
size_t j = 0;
pari_ulong dprimes[total];
for (size_t i = 0; i < nprimes; ++i) {
if ((*curves)[i] == NULL && dvdis(invalid->order, primes[i])) {
if (cfg->verbose) {
fprintf(debug, "prime %lu divides curve order.\n",
primes[i]);
}
dprimes[j++] = primes[i];
}
}
arg_t prime_divisors = {dprimes, total};
invalid_argss[OFFSET_POINTS] = &prime_divisors;
// generate prime order points, this is expensive (order needs to be
// factorised, so only do it if we want the curve)
exhaustive_gen(invalid, cfg, invalid_gen, invalid_argss,
OFFSET_GENERATORS, OFFSET_END);
size_t count = 0;
for (size_t i = nprimes; i-- > 0;) {
if ((*curves)[i] == NULL && dvdis(invalid->order, primes[i])) {
if (count == 0) {
// save a copy on first prime divisor from range
(*curves)[i] = invalid;
} else {
// copy if pointer already assigned
(*curves)[i] = curve_new();
(*curves)[i] = curve_copy(invalid, (*curves)[i]);
}
output_o((*curves)[i], cfg);
ncurves++;
count++;
}
}
// copy the curve params that stay into a new curve, since this
// curve pointer got assigned
// this is for performance reasons. As it only copies the curve
// and mallocs memory if this curve is saved.
invalid = curve_new();
invalid->field = gcopy(curve->field);
invalid->a = gcopy(curve->a);
if (cfg->verbose) {
fprintf(debug,
"curve saved: %lu primes from range divide order.\n",
total);
fprintf(debug, "curves done: %lu out of %lu needed. %.0f%% \n",
ncurves, nprimes, ((float)(ncurves) / nprimes) * 100);
}
} else {
// here, we generated the curve but didn't use it, because no
// primes from range divided order. Thus remove it
// like it never existed.
points_free_deep(&invalid->points, invalid->npoints);
avma = btop;
}
}
return ncurves;
}
int invalid_do(config_t *cfg) {
// create the curve to invalidate
// Either from input or random with -r
curve_t *curve = curve_new();
gen_t gen[OFFSET_END];
arg_t *argss[OFFSET_END];
invalid_ginit(gen, cfg);
// actually generate the curve
if (!exhaustive_gen(curve, cfg, gen, argss, OFFSET_FIELD, OFFSET_POINTS)) {
curve_free(&curve);
return 1;
}
output_o(curve, cfg);
// now, generate primes upto order^2
pari_ulong *primes;
size_t nprimes = invalid_primes(curve->order, &primes);
if (cfg->verbose) {
fprintf(debug, "primes upto: p_max = %lu, n = %lu\n",
primes[nprimes - 1], nprimes);
}
curve_t **curves;
size_t ncurves = invalid_curves(curve, cfg, primes, nprimes, &curves);
for (size_t i = 0; i < ncurves; ++i) {
curve_free(&curves[i]);
}
pari_free(curves);
pari_free(primes);
curve_free(&curve);
return 0;
}
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