+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Elliptic curves over prime fields
- *
- * (c) 2001 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include <mLib/sub.h>
-
-#include "ec.h"
-
-/*----- Simple prime curves -----------------------------------------------*/
-
-static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops;
-
-static ec *ecneg(ec_curve *c, ec *d, const ec *p)
-{
- EC_COPY(d, p);
- if (d->y)
- d->y = F_NEG(c->f, d->y, d->y);
- return (d);
-}
-
-static ec *ecfind(ec_curve *c, ec *d, mp *x)
-{
- mp *p, *q;
- field *f = c->f;
-
- q = F_SQR(f, MP_NEW, x);
- p = F_MUL(f, MP_NEW, x, q);
- q = F_MUL(f, q, x, c->a);
- p = F_ADD(f, p, p, q);
- p = F_ADD(f, p, p, c->b);
- MP_DROP(q);
- p = F_SQRT(f, p, p);
- if (!p)
- return (0);
- EC_DESTROY(d);
- d->x = MP_COPY(x);
- d->y = p;
- d->z = MP_COPY(f->one);
- return (d);
-}
-
-static ec *ecdbl(ec_curve *c, ec *d, const ec *a)
-{
- if (EC_ATINF(a) || F_ZEROP(c->f, a->y))
- EC_SETINF(d);
- else {
- field *f = c->f;
- mp *lambda;
- mp *dy, *dx;
-
- dx = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */
- dy = F_DBL(f, MP_NEW, a->y); /* %$2 y$% */
- dx = F_TPL(f, dx, dx); /* %$3 x^2$% */
- dx = F_ADD(f, dx, dx, c->a); /* %$3 x^2 + A$% */
- dy = F_INV(f, dy, dy); /* %$(2 y)^{-1}$% */
- lambda = F_MUL(f, MP_NEW, dx, dy); /* %$\lambda = (3 x^2 + A)/(2 y)$% */
-
- dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
- dy = F_DBL(f, dy, a->x); /* %$2 x$% */
- dx = F_SUB(f, dx, dx, dy); /* %$x' = \lambda^2 - 2 x */
- dy = F_SUB(f, dy, a->x, dx); /* %$x - x'$% */
- dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x - x')$% */
- dy = F_SUB(f, dy, dy, a->y); /* %$y' = \lambda (x - x') - y$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = 0;
- MP_DROP(lambda);
- }
- return (d);
-}
-
-static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a)
-{
- if (EC_ATINF(a) || F_ZEROP(c->f, a->y))
- EC_SETINF(d);
- else {
- field *f = c->f;
- mp *p, *q, *m, *s, *dx, *dy, *dz;
-
- p = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */
- q = F_SQR(f, MP_NEW, p); /* %$z^4$% */
- p = F_MUL(f, p, q, c->a); /* %$A z^4$% */
- m = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */
- m = F_TPL(f, m, m); /* %$3 x^2$% */
- m = F_ADD(f, m, m, p); /* %$m = 3 x^2 + A z^4$% */
-
- q = F_DBL(f, q, a->y); /* %$2 y$% */
- dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */
-
- p = F_SQR(f, p, q); /* %$4 y^2$% */
- s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */
- q = F_SQR(f, q, p); /* %$16 y^4$% */
- q = F_HLV(f, q, q); /* %$t = 8 y^4$% */
-
- p = F_DBL(f, p, s); /* %$2 s$% */
- dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */
- dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */
-
- s = F_SUB(f, s, s, dx); /* %$s - x'$% */
- dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */
- dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = dz;
- MP_DROP(m);
- MP_DROP(q);
- MP_DROP(s);
- }
- return (d);
-}
-
-static ec *ecprojxdbl(ec_curve *c, ec *d, const ec *a)
-{
- if (EC_ATINF(a) || F_ZEROP(c->f, a->y))
- EC_SETINF(d);
- else {
- field *f = c->f;
- mp *p, *q, *m, *s, *dx, *dy, *dz;
-
- m = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */
- p = F_SUB(f, MP_NEW, a->x, m); /* %$x - z^2$% */
- q = F_ADD(f, MP_NEW, a->x, m); /* %$x + z^2$% */
- m = F_MUL(f, m, p, q); /* %$x^2 - z^4$% */
- m = F_TPL(f, m, m); /* %$m = 3 x^2 - 3 z^4$% */
-
- q = F_DBL(f, q, a->y); /* %$2 y$% */
- dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */
-
- p = F_SQR(f, p, q); /* %$4 y^2$% */
- s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */
- q = F_SQR(f, q, p); /* %$16 y^4$% */
- q = F_HLV(f, q, q); /* %$t = 8 y^4$% */
-
- p = F_DBL(f, p, s); /* %$2 s$% */
- dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */
- dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */
-
- s = F_SUB(f, s, s, dx); /* %$s - x'$% */
- dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */
- dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = dz;
- MP_DROP(m);
- MP_DROP(q);
- MP_DROP(s);
- }
- return (d);
-}
-
-static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b)
-{
- if (a == b)
- ecdbl(c, d, a);
- else if (EC_ATINF(a))
- EC_COPY(d, b);
- else if (EC_ATINF(b))
- EC_COPY(d, a);
- else {
- field *f = c->f;
- mp *lambda;
- mp *dy, *dx;
-
- if (!MP_EQ(a->x, b->x)) {
- dy = F_SUB(f, MP_NEW, a->y, b->y); /* %$y_0 - y_1$% */
- dx = F_SUB(f, MP_NEW, a->x, b->x); /* %$x_0 - x_1$% */
- dx = F_INV(f, dx, dx); /* %$(x_0 - x_1)^{-1}$% */
- lambda = F_MUL(f, MP_NEW, dy, dx);
- /* %$\lambda = (y_0 - y1)/(x_0 - x_1)$% */
- } else if (F_ZEROP(c->f, a->y) || !MP_EQ(a->y, b->y)) {
- EC_SETINF(d);
- return (d);
- } else {
- dx = F_SQR(f, MP_NEW, a->x); /* %$x_0^2$% */
- dx = F_TPL(f, dx, dx); /* %$3 x_0^2$% */
- dx = F_ADD(f, dx, dx, c->a); /* %$3 x_0^2 + A$% */
- dy = F_DBL(f, MP_NEW, a->y); /* %$2 y_0$% */
- dy = F_INV(f, dy, dy); /* %$(2 y_0)^{-1}$% */
- lambda = F_MUL(f, MP_NEW, dx, dy);
- /* %$\lambda = (3 x_0^2 + A)/(2 y_0)$% */
- }
-
- dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
- dx = F_SUB(f, dx, dx, a->x); /* %$\lambda^2 - x_0$% */
- dx = F_SUB(f, dx, dx, b->x); /* %$x' = \lambda^2 - x_0 - x_1$% */
- dy = F_SUB(f, dy, b->x, dx); /* %$x_1 - x'$% */
- dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x_1 - x')$% */
- dy = F_SUB(f, dy, dy, b->y); /* %$y' = \lambda (x_1 - x') - y_1$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = 0;
- MP_DROP(lambda);
- }
- return (d);
-}
-
-static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b)
-{
- if (a == b)
- c->ops->dbl(c, d, a);
- else if (EC_ATINF(a))
- EC_COPY(d, b);
- else if (EC_ATINF(b))
- EC_COPY(d, a);
- else {
- field *f = c->f;
- mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz;
-
- q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */
- u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */
- p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */
- s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */
-
- q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */
- uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/
- p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */
- ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */
-
- w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */
- r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */
- if (F_ZEROP(f, w)) {
- MP_DROP(w);
- MP_DROP(u);
- MP_DROP(s);
- MP_DROP(uu);
- MP_DROP(ss);
- if (F_ZEROP(f, r)) {
- MP_DROP(r);
- return (c->ops->dbl(c, d, a));
- } else {
- MP_DROP(r);
- EC_SETINF(d);
- return (d);
- }
- }
- u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */
- s = F_ADD(f, s, s, ss); /* %$m = ss + r$% */
-
- uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */
- dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */
-
- p = F_SQR(f, uu, w); /* %$w^2$% */
- q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */
- u = F_MUL(f, u, p, w); /* %$w^3$% */
- p = F_MUL(f, p, u, s); /* %$m w^3$% */
-
- dx = F_SQR(f, u, r); /* %$r^2$% */
- dx = F_SUB(f, dx, dx, q); /* %$x' = r^2 - t w^2$% */
-
- s = F_DBL(f, s, dx); /* %$2 x'$% */
- q = F_SUB(f, q, q, s); /* %$v = t w^2 - 2 x'$% */
- dy = F_MUL(f, s, q, r); /* %$v r$% */
- dy = F_SUB(f, dy, dy, p); /* %$v r - m w^3$% */
- dy = F_HLV(f, dy, dy); /* %$y' = (v r - m w^3)/2$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = dz;
- MP_DROP(p);
- MP_DROP(q);
- MP_DROP(r);
- MP_DROP(w);
- }
- return (d);
-}
-
-static int eccheck(ec_curve *c, const ec *p)
-{
- field *f = c->f;
- mp *l, *x, *r;
- int rc;
- if (EC_ATINF(p)) return (0);
- l = F_SQR(f, MP_NEW, p->y);
- x = F_SQR(f, MP_NEW, p->x);
- r = F_MUL(f, MP_NEW, x, p->x);
- x = F_MUL(f, x, c->a, p->x);
- r = F_ADD(f, r, r, x);
- r = F_ADD(f, r, r, c->b);
- rc = MP_EQ(l, r) ? 0 : -1;
- mp_drop(l);
- mp_drop(x);
- mp_drop(r);
- return (rc);
-}
-
-static int ecprojcheck(ec_curve *c, const ec *p)
-{
- ec t = EC_INIT;
- int rc;
-
- c->ops->fix(c, &t, p);
- rc = eccheck(c, &t);
- EC_DESTROY(&t);
- return (rc);
-}
-
-static void ecdestroy(ec_curve *c)
-{
- MP_DROP(c->a);
- MP_DROP(c->b);
- DESTROY(c);
-}
-
-/* --- @ec_prime@, @ec_primeproj@ --- *
- *
- * Arguments: @field *f@ = the underlying field for this elliptic curve
- * @mp *a, *b@ = the coefficients for this curve
- *
- * Returns: A pointer to the curve, or null.
- *
- * Use: Creates a curve structure for an elliptic curve defined over
- * a prime field. The @primeproj@ variant uses projective
- * coordinates, which can be a win.
- */
-
-extern ec_curve *ec_prime(field *f, mp *a, mp *b)
-{
- ec_curve *c = CREATE(ec_curve);
- c->ops = &ec_primeops;
- c->f = f;
- c->a = F_IN(f, MP_NEW, a);
- c->b = F_IN(f, MP_NEW, b);
- return (c);
-}
-
-extern ec_curve *ec_primeproj(field *f, mp *a, mp *b)
-{
- ec_curve *c = CREATE(ec_curve);
- mp *ax;
-
- ax = mp_add(MP_NEW, a, MP_THREE);
- ax = F_IN(f, ax, ax);
- if (F_ZEROP(f, ax))
- c->ops = &ec_primeprojxops;
- else
- c->ops = &ec_primeprojops;
- MP_DROP(ax);
- c->f = f;
- c->a = F_IN(f, MP_NEW, a);
- c->b = F_IN(f, MP_NEW, b);
- return (c);
-}
-
-static const ec_ops ec_primeops = {
- "prime",
- ecdestroy, ec_stdsamep, ec_idin, ec_idout, ec_idfix,
- ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck
-};
-
-static const ec_ops ec_primeprojops = {
- "primeproj",
- ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix,
- ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
-};
-
-static const ec_ops ec_primeprojxops = {
- "primeproj",
- ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix,
- ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck
-};
-
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-#define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
-
-int main(int argc, char *argv[])
-{
- field *f;
- ec_curve *c;
- ec g = EC_INIT, d = EC_INIT;
- mp *p, *a, *b, *r;
- int i, n = argc == 1 ? 1 : atoi(argv[1]);
-
- printf("ec-prime: ");
- fflush(stdout);
- a = MP(-3);
- b = MP(0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef);
- p = MP(39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319);
- r = MP(39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942642);
-
- f = field_niceprime(p);
- c = ec_primeproj(f, a, b);
-
- g.x = MP(0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7);
- g.y = MP(0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f);
-
- for (i = 0; i < n; i++) {
- ec_mul(c, &d, &g, r);
- if (EC_ATINF(&d)) {
- fprintf(stderr, "zero too early\n");
- return (1);
- }
- ec_add(c, &d, &d, &g);
- if (!EC_ATINF(&d)) {
- fprintf(stderr, "didn't reach zero\n");
- MP_EPRINT("d.x", d.x);
- MP_EPRINT("d.y", d.y);
- return (1);
- }
- ec_destroy(&d);
- }
- ec_destroy(&g);
- ec_destroycurve(c);
- F_DESTROY(f);
- MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r);
- assert(!mparena_count(&mparena_global));
- printf("ok\n");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff