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vec.c
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/* Copyright 2008-2019 Douglas Wikstrom
*
* This file is part of Verificatum Elliptic Curve library (VEC).
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use, copy,
* modify, merge, publish, distribute, sublicense, and/or sell copies
* of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include <time.h>
#include <string.h>
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <gmp.h>
#include "vec.h"
#define DEFAULT_TEST_TIME 500
#define DEFAULT_SPEED_TIME 2000
/*
* We use compiler flags that enforce that unused variables are
* flagged as errors. Sometimes we need to declare an exception
* explicitly state explicitly.
*/
#define VEC_UNUSED(x) ((void)(x))
/* LCOV_EXCL_START */
void
fail(char *str)
{
fprintf(stderr, "FAILED!\n");
fprintf(stderr, "%s", str);
exit(-1);
}
/* LCOV_EXCL_STOP */
void
test_dbl_add(vec_curve *curve)
{
int t;
mpz_t tx;
mpz_t ty;
mpz_t rx1;
mpz_t ry1;
mpz_t rx2;
mpz_t ry2;
mpz_t Ox;
mpz_t Oy;
vec_scratch_mpz_t scratch;
mpz_init(tx);
mpz_init(ty);
mpz_init(rx1);
mpz_init(ry1);
mpz_init(rx2);
mpz_init(ry2);
mpz_init(Ox);
mpz_init(Oy);
vec_scratch_init_mpz_t(scratch);
mpz_set_si(Ox, -1);
mpz_set_si(Oy, -1);
t = clock();
/* Test doubling unit element. */
vec_dbl(scratch,
rx1, ry1,
curve,
Ox, Oy);
assert(vec_eq(rx1, ry1, Ox, Oy));
/* Test adding unit element. */
vec_add(scratch,
rx1, ry1,
curve,
curve->gx, curve->gy,
Ox, Oy);
assert(vec_eq(rx1, ry1, curve->gx, curve->gy));
vec_add(scratch,
rx1, ry1,
curve,
Ox, Oy,
curve->gx, curve->gy);
assert(vec_eq(rx1, ry1, curve->gx, curve->gy));
/* Test adding point to its negation. */
mpz_sub(rx2, curve->modulus, curve->gy);
vec_add(scratch,
rx1, ry1,
curve,
curve->gx, rx2,
curve->gx, curve->gy);
assert(vec_eq(rx1, ry1, Ox, Oy));
/* Test processing of general elements. */
mpz_set(tx, curve->gx);
mpz_set(ty, curve->gy);
do
{
/* 4 * (tx, ty) */
vec_dbl(scratch,
rx1, ry1,
curve,
tx, ty);
vec_dbl(scratch,
rx1, ry1,
curve,
rx1, ry1);
/* 2 * (tx, ty) + (tx, ty) + (tx, ty) */
vec_dbl(scratch,
rx2, ry2,
curve,
tx, ty);
vec_add(scratch,
rx2, ry2,
curve,
rx2, ry2,
tx, ty);
vec_add(scratch,
rx2, ry2,
curve,
rx2, ry2,
tx, ty);
assert(vec_eq(rx1, ry1, rx2, ry2));
mpz_set(tx, rx1);
mpz_set(ty, ry1);
}
while (!vec_done(t, DEFAULT_TEST_TIME));
vec_scratch_clear_mpz_t(scratch);
mpz_clear(Ox);
mpz_clear(Oy);
mpz_clear(ry2);
mpz_clear(rx2);
mpz_clear(ry1);
mpz_clear(rx1);
mpz_clear(ty);
mpz_clear(tx);
}
void
test_mul(vec_curve *curve) {
int t;
mpz_t rx1;
mpz_t ry1;
mpz_t rx2;
mpz_t ry2;
mpz_t rx3;
mpz_t ry3;
mpz_t rx4;
mpz_t ry4;
vec_scratch_mpz_t scratch;
mpz_t Ox;
mpz_t Oy;
mpz_t scalar1;
mpz_t scalar2;
mpz_t scalar3;
mpz_init(rx1);
mpz_init(ry1);
mpz_init(rx2);
mpz_init(ry2);
mpz_init(rx3);
mpz_init(ry3);
mpz_init(rx4);
mpz_init(ry4);
mpz_init(Ox);
mpz_init(Oy);
vec_scratch_init_mpz_t(scratch);
mpz_init(scalar1);
mpz_init(scalar2);
mpz_init(scalar3);
mpz_set_si(Ox, -1);
mpz_set_si(Oy, -1);
/* Generate "random" scalar1. */
mpz_set_ui(scalar1, 1);
mpz_mul_2exp(scalar1, scalar1, 1000);
mpz_mod(scalar1, scalar1, curve->n);
/* Test multiplying unit element. */
vec_mul(rx1, ry1,
curve,
Ox, Oy,
scalar1);
assert(vec_eq(rx1, ry1, Ox, Oy));
/* Test general multiplication. */
mpz_set_ui(scalar2, 1);
mpz_mul_2exp(scalar2, scalar2, 1000);
mpz_mod(scalar2, scalar2, curve->n);
t = clock();
do
{
vec_mul(rx1, ry1,
curve,
curve->gx, curve->gy,
scalar1);
vec_mul(rx2, ry2,
curve,
curve->gx, curve->gy,
scalar2);
mpz_add(scalar3, scalar1, scalar2);
vec_mul(rx3, ry3,
curve,
curve->gx, curve->gy,
scalar3);
vec_add(scratch,
rx4, ry4,
curve,
rx1, ry1,
rx2, ry2);
assert(vec_eq(rx4, ry4, rx3, ry3));
mpz_add(scalar1, scalar1, scalar2);
mpz_mod(scalar1, scalar1, curve->n);
mpz_mul(scalar2, scalar2, scalar2);
mpz_mod(scalar2, scalar2, curve->n);
}
while (!vec_done(t, DEFAULT_TEST_TIME));
mpz_clear(scalar2);
mpz_clear(scalar1);
vec_scratch_clear_mpz_t(scratch);
mpz_clear(Ox);
mpz_clear(Oy);
mpz_clear(ry4);
mpz_clear(rx4);
mpz_clear(ry3);
mpz_clear(rx3);
mpz_clear(ry2);
mpz_clear(rx2);
mpz_clear(ry1);
mpz_clear(rx1);
}
void
test_smul(vec_curve *curve) {
int t;
size_t len;
size_t i;
mpz_t rx1;
mpz_t ry1;
mpz_t rx2;
mpz_t ry2;
mpz_t *basesx;
mpz_t *basesy;
mpz_t *scalars;
mpz_t scalar;
vec_scratch_mpz_t scratch;
mpz_init(rx1);
mpz_init(ry1);
mpz_init(rx2);
mpz_init(ry2);
mpz_init(scalar);
vec_scratch_init_mpz_t(scratch);
mpz_set_ui(scalar, 1);
mpz_mul_2exp(scalar, scalar, 100000);
mpz_mod(scalar, scalar, curve->n);
len = 1;
t = clock();
do
{
/* Generate "random" bases and scalars. */
basesx = vec_array_alloc_init(len);
basesy = vec_array_alloc_init(len);
scalars = vec_array_alloc_init(len);
for (i = 0; i < len; i++) {
vec_mul(basesx[i], basesy[i],
curve,
curve->gx, curve->gy,
scalar);
mpz_mul(scalar, scalar, scalar);
mpz_mod(scalar, scalar, curve->n);
mpz_set(scalars[i], scalar);
}
/* Compute simultaneous multiplication naively. */
mpz_set_si(rx1, -1);
mpz_set_si(ry1, -1);
for (i = 0; i < len; i++) {
vec_mul(rx2, ry2,
curve,
basesx[i], basesy[i],
scalars[i]);
vec_add(scratch,
rx1, ry1,
curve,
rx1, ry1,
rx2, ry2);
}
vec_smul(rx2, ry2,
curve,
basesx, basesy,
scalars,
len);
assert(vec_eq(rx2, ry2, rx1, ry1));
vec_array_clear_free(scalars, len);
vec_array_clear_free(basesy, len);
vec_array_clear_free(basesx, len);
len <<= 1;
}
while (!vec_done(t, DEFAULT_TEST_TIME));
vec_scratch_clear_mpz_t(scratch);
mpz_clear(scalar);
mpz_clear(ry2);
mpz_clear(rx2);
mpz_clear(ry1);
mpz_clear(rx1);
}
void
test_jdbl(vec_curve *curve)
{
int t;
mpz_t rx1;
mpz_t ry1;
mpz_t rx2;
mpz_t ry2;
vec_scratch_mpz_t scratch;
mpz_t Ox;
mpz_t Oy;
mpz_init(rx1);
mpz_init(ry1);
mpz_init(rx2);
mpz_init(ry2);
mpz_init(Ox);
mpz_init(Oy);
vec_scratch_init_mpz_t(scratch);
t = clock();
mpz_set_si(Ox, -1);
mpz_set_si(Oy, -1);
/* Test processing of unit element. */
vec_jdbl_aff(scratch,
rx1, ry1,
curve,
Ox, Oy);
assert(vec_eq(rx1, ry1, Ox, Oy));
/* Test processing of general elements. */
mpz_set(rx1, curve->gx);
mpz_set(ry1, curve->gy);
mpz_set(rx2, curve->gx);
mpz_set(ry2, curve->gy);
do
{
vec_dbl(scratch,
rx1, ry1,
curve,
rx1, ry1);
vec_jdbl_aff(scratch,
rx2, ry2,
curve,
rx2, ry2);
assert(vec_eq(rx1, ry1, rx2, ry2));
}
while (!vec_done(t, DEFAULT_TEST_TIME));
vec_scratch_init_mpz_t(scratch);
mpz_clear(Oy);
mpz_clear(Ox);
mpz_clear(ry2);
mpz_clear(rx2);
mpz_clear(ry1);
mpz_clear(rx1);
}
void
test_jadd(vec_curve *curve)
{
int t;
mpz_t rx1;
mpz_t ry1;
mpz_t rx2;
mpz_t ry2;
vec_scratch_mpz_t scratch;
mpz_t Ox;
mpz_t Oy;
mpz_t bx;
mpz_t by;
mpz_init(rx1);
mpz_init(ry1);
mpz_init(rx2);
mpz_init(ry2);
mpz_init(Ox);
mpz_init(Oy);
mpz_init(bx);
mpz_init(by);
vec_scratch_init_mpz_t(scratch);
t = clock();
mpz_set_si(Ox, -1);
mpz_set_si(Oy, -1);
/* Test processing of unit element. */
vec_jadd_aff(scratch,
rx1, ry1,
curve,
Ox, Oy,
Ox, Oy);
assert(vec_eq(rx1, ry1, Ox, Oy));
vec_jadd_aff(scratch,
rx1, ry1,
curve,
curve->gx, curve->gy,
Ox, Oy);
assert(vec_eq(rx1, ry1, curve->gx, curve->gy));
vec_jadd_aff(scratch,
rx1, ry1,
curve,
Ox, Oy,
curve->gx, curve->gy);
assert(vec_eq(rx1, ry1, curve->gx, curve->gy));
/* Test adding point to its negation. */
mpz_sub(rx2, curve->modulus, curve->gy);
vec_jadd_aff(scratch,
rx1, ry1,
curve,
curve->gx, rx2,
curve->gx, curve->gy);
assert(vec_eq(rx1, ry1, Ox, Oy));
/* Test processing of general elements. */
mpz_set(rx1, curve->gx);
mpz_set(ry1, curve->gy);
mpz_set(rx2, curve->gx);
mpz_set(ry2, curve->gy);
mpz_set(bx, curve->gx);
mpz_set(by, curve->gy);
do
{
vec_add(scratch,
rx1, ry1,
curve,
rx1, ry1,
bx, by);
vec_jadd_aff(scratch,
rx2, ry2,
curve,
rx2, ry2,
bx, by);
vec_dbl(scratch,
bx, by,
curve,
bx, by);
vec_add(scratch,
bx, by,
curve,
bx, by,
curve->gx, curve->gy);
assert(vec_eq(rx1, ry1, rx2, ry2));
}
while (!vec_done(t, DEFAULT_TEST_TIME));
vec_scratch_clear_mpz_t(scratch);
mpz_clear(by);
mpz_clear(bx);
mpz_clear(Oy);
mpz_clear(Ox);
mpz_clear(ry2);
mpz_clear(rx2);
mpz_clear(ry1);
mpz_clear(rx1);
}
void
test_jmul(vec_curve *curve)
{
int t;
mpz_t rx1;
mpz_t ry1;
mpz_t rx2;
mpz_t ry2;
vec_scratch_mpz_t scratch;
mpz_t Ox;
mpz_t Oy;
mpz_t bx;
mpz_t by;
mpz_t scalar;
mpz_init(rx1);
mpz_init(ry1);
mpz_init(rx2);
mpz_init(ry2);
vec_scratch_init_mpz_t(scratch);
mpz_init(Ox);
mpz_init(Oy);
mpz_init(bx);
mpz_init(by);
mpz_init(scalar);
t = clock();
mpz_set_si(Ox, -1);
mpz_set_si(Oy, -1);
/* Test multiplication with unit element. */
mpz_set_ui(scalar, 1);
mpz_mul_2exp(scalar, scalar, 100000);
mpz_mod(scalar, scalar, curve->n);
vec_jmul_aff(rx1, ry1,
curve,
Ox, Oy,
scalar);
assert(vec_eq(rx1, ry1, Ox, Oy));
mpz_set(bx, curve->gx);
mpz_set(by, curve->gy);
/* Test general multiplication. */
do
{
vec_mul(rx1, ry1,
curve,
bx, by,
scalar);
vec_jmul_aff(rx2, ry2,
curve,
bx, by,
scalar);
assert(vec_eq(rx1, ry1, rx2, ry2));
mpz_set(bx, rx1);
mpz_set(by, ry1);
mpz_mul(scalar, scalar, scalar);
mpz_mod(scalar, scalar, curve->n);
}
while (!vec_done(t, DEFAULT_TEST_TIME));
mpz_clear(bx);
mpz_clear(by);
mpz_clear(Ox);
mpz_clear(Oy);
vec_scratch_clear_mpz_t(scratch);
mpz_clear(ry2);
mpz_clear(rx2);
mpz_clear(ry1);
mpz_clear(rx1);
}
void
test_jsmul(vec_curve *curve)
{
int t;
size_t len;
size_t i;
mpz_t rx1;
mpz_t ry1;
mpz_t rx2;
mpz_t ry2;
mpz_t *basesx;
mpz_t *basesy;
mpz_t *scalars;
mpz_t scalar;
mpz_init(rx1);
mpz_init(ry1);
mpz_init(rx2);
mpz_init(ry2);
mpz_init(scalar);
mpz_set_ui(scalar, 1);
mpz_mul_2exp(scalar, scalar, 100000);
mpz_mod(scalar, scalar, curve->n);
len = 1;
t = clock();
do
{
/* Generate "random" bases and scalars. */
basesx = vec_array_alloc_init(len);
basesy = vec_array_alloc_init(len);
scalars = vec_array_alloc_init(len);
for (i = 0; i < len; i++) {
vec_mul(basesx[i], basesy[i],
curve,
curve->gx, curve->gy,
scalar);
mpz_mul(scalar, scalar, scalar);
mpz_mod(scalar, scalar, curve->n);
mpz_set(scalars[i], scalar);
}
/* Compute simultaneous multiplication affinely. */
vec_smul(rx1, ry1,
curve,
basesx, basesy,
scalars,
len);
/* Compute simultaneous multiplication Jacobi. */
vec_jsmul_aff(rx2, ry2,
curve,
basesx, basesy,
scalars,
len);
assert(vec_eq(rx2, ry2, rx1, ry1));
vec_array_clear_free(scalars, len);
vec_array_clear_free(basesy, len);
vec_array_clear_free(basesx, len);
len <<= 1;
}
while (!vec_done(t, DEFAULT_TEST_TIME));
mpz_clear(scalar);
mpz_clear(ry2);
mpz_clear(rx2);
mpz_clear(ry1);
mpz_clear(rx1);
}
void
test_jfmul(vec_curve *curve)
{
int t;
mpz_t rx1;
mpz_t ry1;
mpz_t rx2;
mpz_t ry2;
vec_scratch_mpz_t scratch;
vec_jfmul_tab_ptr table_ptr;
mpz_t scalar;
mpz_init(rx1);
mpz_init(ry1);
mpz_init(rx2);
mpz_init(ry2);
vec_scratch_init_mpz_t(scratch);
mpz_init(scalar);
t = clock();
table_ptr = vec_jfmul_precomp_aff(curve, curve->gx, curve->gy, 1000);
/* Test multiplication with unit element. */
mpz_set_ui(scalar, 0);
vec_mul(rx1, ry1,
curve,
curve->gx, curve->gy,
scalar);
vec_jfmul_aff(rx2, ry2,
curve,
table_ptr,
scalar);
assert(vec_eq(rx1, ry1, rx2, ry2));
/* Test general multiplication. */
mpz_set_ui(scalar, 1);
mpz_mul_2exp(scalar, scalar, 100000);
mpz_mod(scalar, scalar, curve->n);
do
{
vec_mul(rx1, ry1,
curve,
curve->gx, curve->gy,
scalar);
vec_jfmul_aff(rx2, ry2,
curve,
table_ptr,
scalar);
assert(vec_eq(rx1, ry1, rx2, ry2));
mpz_mul(scalar, scalar, scalar);
mpz_mod(scalar, scalar, curve->n);
}
while (!vec_done(t, DEFAULT_TEST_TIME));
vec_jfmul_free_aff(curve, table_ptr);
mpz_clear(scalar);
vec_scratch_clear_mpz_t(scratch);
mpz_clear(ry2);
mpz_clear(rx2);
mpz_clear(ry1);
mpz_clear(rx1);
}
void
test_sqrt(mpz_t p) {
int t;
mpz_t a;
mpz_t z;
mpz_t res;
mpz_init(a);
mpz_init(z);
mpz_init(res);
t = clock();
mpz_set_si(a, 1);
mpz_mul_2exp(a, a, 1000);
mpz_mod(a, a, p);
mpz_set_si(z, 2);
while (mpz_legendre(z, p) == 1)
{
mpz_add_ui(z, z, 1);
}
mpz_mul(a, a, a);
mpz_mod(a, a, p);
do
{
vec_sqrt(res, a, p);
mpz_mul(res, res, res);
mpz_mod(res, res, p);
assert(mpz_cmp(res, a) == 0);
/* Randomize a new square */
mpz_powm(a, a, a, p);
mpz_mul(a, a, a);
mpz_mod(a, a, p);
}
while (!vec_done(t, DEFAULT_TEST_TIME));
mpz_clear(res);
mpz_clear(z);
mpz_clear(a);
}
/* These are timing routines and not tested beyond using them. */
/* LCOV_EXCL_START */
void
print_time()
{
time_t timer;
char buffer[25];
struct tm* tm_info;
time(&timer);
tm_info = localtime(&timer);
strftime(buffer, 25, "%Y:%m:%d%H:%M:%S\n", tm_info);
fprintf(stderr, "%s", buffer);
}
void
print_doublings(char *prefix, long ops)
{
printf("%12ld %s doublings\n", ops, prefix);
fflush(stdout);
}
void
print_additions(char *prefix, long ops)
{
printf("%12ld %s additions\n", ops, prefix);
fflush(stdout);
}
void
print_multiplications(char *prefix, long ops)
{
printf("%12ld %s multiplications\n", ops, prefix);
fflush(stdout);
}
void
print_test(char *str)
{
printf("%s\n", str);
fflush(stdout);
}
long
time_dbl(vec_curve *curve, jdbl_func jdbl, long millisecs)
{
long i;
int t;
vec_scratch_mpz_t scratch;
mpz_t x;
mpz_t y;
vec_scratch_init_mpz_t(scratch);
mpz_init(x);
mpz_init(y);
mpz_set(x, curve->gx);
mpz_set(y, curve->gy);
t = clock();
i = 0;
do
{
if (jdbl != NULL)
{
vec_jdbl_aff(scratch,
x, y,
curve,
x, y);
}
else
{
vec_dbl(scratch,
x, y,
curve,
x, y);
}
i++;
}
while (!vec_done(t, millisecs));
mpz_clear(y);
mpz_clear(x);
vec_scratch_clear_mpz_t(scratch);
return i;
}