+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Arithmetic for elliptic curves over binary fields
- *
- * (c) 2004 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"
-#include "ec-guts.h"
-
-/*----- Main code ---------------------------------------------------------*/
-
-static const ec_ops ec_binops, ec_binprojops;
-
-static ec *ecneg(ec_curve *c, ec *d, const ec *p)
-{
- EC_COPY(d, p);
- if (d->x)
- d->y = F_ADD(c->f, d->y, d->y, d->x);
- return (d);
-}
-
-static ec *ecprojneg(ec_curve *c, ec *d, const ec *p)
-{
- EC_COPY(d, p);
- if (d->x) {
- mp *t = F_MUL(c->f, MP_NEW, d->x, d->z);
- d->y = F_ADD(c->f, d->y, d->y, t);
- MP_DROP(t);
- }
- return (d);
-}
-
-static ec *ecfind(ec_curve *c, ec *d, mp *x)
-{
- field *f = c->f;
- mp *y, *u, *v;
-
- if (F_ZEROP(f, x))
- y = F_SQRT(f, MP_NEW, c->b);
- else {
- u = F_SQR(f, MP_NEW, x); /* %$x^2$% */
- y = F_MUL(f, MP_NEW, u, c->a); /* %$a x^2$% */
- y = F_ADD(f, y, y, c->b); /* %$a x^2 + b$% */
- v = F_MUL(f, MP_NEW, u, x); /* %$x^3$% */
- y = F_ADD(f, y, y, v); /* %$A = x^3 + a x^2 + b$% */
- if (!F_ZEROP(f, y)) {
- u = F_INV(f, u, u); /* %$x^{-2}$% */
- v = F_MUL(f, v, u, y); /* %$B = A x^{-2} = x + a + b x^{-2}$% */
- y = F_QUADSOLVE(f, y, v); /* %$z^2 + z = B$% */
- if (y) y = F_MUL(f, y, y, x); /* %$y = z x$% */
- }
- MP_DROP(u);
- MP_DROP(v);
- }
- if (!y) return (0);
- EC_DESTROY(d);
- d->x = MP_COPY(x);
- d->y = y;
- 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->x))
- EC_SETINF(d);
- else {
- field *f = c->f;
- mp *lambda;
- mp *dx, *dy;
-
- dx = F_INV(f, MP_NEW, a->x); /* %$x^{-1}$% */
- dy = F_MUL(f, MP_NEW, dx, a->y); /* %$y/x$% */
- lambda = F_ADD(f, dy, dy, a->x); /* %$\lambda = x + y/x$% */
-
- dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
- dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
- dx = F_ADD(f, dx, dx, c->a); /* %$x' = a + \lambda^2 + \lambda$% */
-
- dy = F_ADD(f, MP_NEW, a->x, dx); /* %$ x + x' $% */
- dy = F_MUL(f, dy, dy, lambda); /* %$ (x + x') \lambda$% */
- dy = F_ADD(f, dy, dy, a->y); /* %$ (x + x') \lambda + y$% */
- dy = F_ADD(f, dy, dy, dx); /* %$ y' = (x + x') \lambda + y + x'$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = 0;
- MP_DROP(lambda);
- }
- return (d);
-}
-
-static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a)
-{
- if (EC_ATINF(a) || F_ZEROP(c->f, a->x))
- EC_SETINF(d);
- else {
- field *f = c->f;
- ecctx_bin *cc = (ecctx_bin *)c;
- mp *dx, *dy, *dz, *u, *v;
-
- dy = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */
- dx = F_MUL(f, MP_NEW, dy, cc->bb); /* %$c z^2$% */
- dx = F_ADD(f, dx, dx, a->x); /* %$x + c z^2$% */
- dz = F_SQR(f, MP_NEW, dx); /* %$(x + c z^2)^2$% */
- dx = F_SQR(f, dx, dz); /* %$x' = (x + c z^2)^4$% */
-
- dz = F_MUL(f, dz, dy, a->x); /* %$z' = x z^2$% */
-
- dy = F_SQR(f, dy, a->x); /* %$x^2$% */
- u = F_MUL(f, MP_NEW, a->y, a->z); /* %$y z$% */
- u = F_ADD(f, u, u, dz); /* %$z' + y z$% */
- u = F_ADD(f, u, u, dy); /* %$u = z' + x^2 + y z$% */
-
- v = F_SQR(f, MP_NEW, dy); /* %$x^4$% */
- dy = F_MUL(f, dy, v, dz); /* %$x^4 z'$% */
- v = F_MUL(f, v, u, dx); /* %$u x'$% */
- dy = F_ADD(f, dy, dy, v); /* %$y' = x^4 z' + u x'$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = dz;
- MP_DROP(u);
- MP_DROP(v);
- }
- return (d);
-}
-
-static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b)
-{
- if (a == b)
- ecdbl(c, d, a);
- else if (EC_ATINF(a))
- EC_COPY(d, b);
- else if (EC_ATINF(b))
- EC_COPY(d, a);
- else {
- field *f = c->f;
- mp *lambda;
- mp *dx, *dy;
-
- if (!MP_EQ(a->x, b->x)) {
- dx = F_ADD(f, MP_NEW, a->x, b->x); /* %$x_0 + x_1$% */
- dy = F_INV(f, MP_NEW, dx); /* %$(x_0 + x_1)^{-1}$% */
- dx = F_ADD(f, dx, a->y, b->y); /* %$y_0 + y_1$% */
- lambda = F_MUL(f, MP_NEW, dy, dx);
- /* %$\lambda = (y_0 + y_1)/(x_0 + x_1)$% */
-
- dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
- dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
- dx = F_ADD(f, dx, dx, c->a); /* %$a + \lambda^2 + \lambda$% */
- dx = F_ADD(f, dx, dx, a->x); /* %$a + \lambda^2 + \lambda + x_0$% */
- dx = F_ADD(f, dx, dx, b->x);
- /* %$x' = a + \lambda^2 + \lambda + x_0 + x_1$% */
- } else if (!MP_EQ(a->y, b->y) || F_ZEROP(f, a->x)) {
- EC_SETINF(d);
- return (d);
- } else {
- dx = F_INV(f, MP_NEW, a->x); /* %$x^{-1}$% */
- dy = F_MUL(f, MP_NEW, dx, a->y); /* %$y/x$% */
- lambda = F_ADD(f, dy, dy, a->x); /* %$\lambda = x + y/x$% */
-
- dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
- dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
- dx = F_ADD(f, dx, dx, c->a); /* %$x' = a + \lambda^2 + \lambda$% */
- dy = MP_NEW;
- }
-
- dy = F_ADD(f, dy, a->x, dx); /* %$ x + x' $% */
- dy = F_MUL(f, dy, dy, lambda); /* %$ (x + x') \lambda$% */
- dy = F_ADD(f, dy, dy, a->y); /* %$ (x + x') \lambda + y$% */
- dy = F_ADD(f, dy, dy, dx); /* %$ y' = (x + x') \lambda + y + x'$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = 0;
- MP_DROP(lambda);
- }
- return (d);
-}
-
-static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b)
-{
- if (a == b)
- c->ops->dbl(c, d, a);
- else if (EC_ATINF(a))
- EC_COPY(d, b);
- else if (EC_ATINF(b))
- EC_COPY(d, a);
- else {
- field *f = c->f;
- mp *dx, *dy, *dz, *u, *uu, *v, *t, *s, *ss, *r, *w, *l;
-
- dz = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */
- u = F_MUL(f, MP_NEW, dz, a->x); /* %$u_0 = x_0 z_1^2$% */
- t = F_MUL(f, MP_NEW, dz, b->z); /* %$z_1^3$% */
- s = F_MUL(f, MP_NEW, t, a->y); /* %$s_0 = y_0 z_1^3$% */
-
- dz = F_SQR(f, dz, a->z); /* %$z_0^2$% */
- uu = F_MUL(f, MP_NEW, dz, b->x); /* %$u_1 = x_1 z_0^2$% */
- t = F_MUL(f, t, dz, a->z); /* %$z_0^3$% */
- ss = F_MUL(f, MP_NEW, t, b->y); /* %$s_1 = y_1 z_0^3$% */
-
- w = F_ADD(f, u, u, uu); /* %$r = u_0 + u_1$% */
- r = F_ADD(f, s, s, ss); /* %$w = s_0 + s_1$% */
- if (F_ZEROP(f, w)) {
- MP_DROP(w);
- MP_DROP(uu);
- MP_DROP(ss);
- MP_DROP(t);
- MP_DROP(dz);
- if (F_ZEROP(f, r)) {
- MP_DROP(r);
- return (c->ops->dbl(c, d, a));
- } else {
- MP_DROP(r);
- EC_SETINF(d);
- return (d);
- }
- }
-
- l = F_MUL(f, t, a->z, w); /* %$l = z_0 w$% */
-
- dz = F_MUL(f, dz, l, b->z); /* %$z' = l z_1$% */
-
- ss = F_MUL(f, ss, r, b->x); /* %$r x_1$% */
- t = F_MUL(f, uu, l, b->y); /* %$l y_1$% */
- v = F_ADD(f, ss, ss, t); /* %$v = r x_1 + l y_1$% */
-
- t = F_ADD(f, t, r, dz); /* %$t = r + z'$% */
-
- uu = F_SQR(f, MP_NEW, dz); /* %$z'^2$% */
- dx = F_MUL(f, MP_NEW, uu, c->a); /* %$a z'^2$% */
- uu = F_MUL(f, uu, t, r); /* %$t r$% */
- dx = F_ADD(f, dx, dx, uu); /* %$a z'^2 + t r$% */
- r = F_SQR(f, r, w); /* %$w^2$% */
- uu = F_MUL(f, uu, r, w); /* %$w^3$% */
- dx = F_ADD(f, dx, dx, uu); /* %$x' = a z'^2 + t r + w^3$% */
-
- r = F_SQR(f, r, l); /* %$l^2$% */
- dy = F_MUL(f, uu, v, r); /* %$v l^2$% */
- l = F_MUL(f, l, t, dx); /* %$t x'$% */
- dy = F_ADD(f, dy, dy, l); /* %$y' = t x' + v l^2$% */
-
- EC_DESTROY(d);
- d->x = dx;
- d->y = dy;
- d->z = dz;
- MP_DROP(l);
- MP_DROP(r);
- MP_DROP(w);
- MP_DROP(t);
- MP_DROP(v);
- }
- return (d);
-}
-
-static int eccheck(ec_curve *c, const ec *p)
-{
- field *f = c->f;
- int rc;
- mp *u, *v;
-
- if (EC_ATINF(p)) return (0);
- v = F_SQR(f, MP_NEW, p->x);
- u = F_MUL(f, MP_NEW, v, p->x);
- v = F_MUL(f, v, v, c->a);
- u = F_ADD(f, u, u, v);
- u = F_ADD(f, u, u, c->b);
- v = F_MUL(f, v, p->x, p->y);
- u = F_ADD(f, u, u, v);
- v = F_SQR(f, v, p->y);
- u = F_ADD(f, u, u, v);
- rc = F_ZEROP(f, u) ? 0 : -1;
- mp_drop(u);
- mp_drop(v);
- 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)
-{
- ecctx_bin *cc = (ecctx_bin *)c;
- MP_DROP(cc->c.a);
- MP_DROP(cc->c.b);
- if (cc->bb) MP_DROP(cc->bb);
- DESTROY(cc);
-}
-
-/* --- @ec_bin@, @ec_binproj@ --- *
- *
- * 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 binary field. The @binproj@ variant uses projective
- * coordinates, which can be a win.
- */
-
-ec_curve *ec_bin(field *f, mp *a, mp *b)
-{
- ecctx_bin *cc = CREATE(ecctx_bin);
- cc->c.ops = &ec_binops;
- cc->c.f = f;
- cc->c.a = F_IN(f, MP_NEW, a);
- cc->c.b = F_IN(f, MP_NEW, b);
- cc->bb = 0;
- return (&cc->c);
-}
-
-ec_curve *ec_binproj(field *f, mp *a, mp *b)
-{
- ecctx_bin *cc = CREATE(ecctx_bin);
- int i;
- mp *c, *d;
-
- cc->c.ops = &ec_binprojops;
- cc->c.f = f;
- cc->c.a = F_IN(f, MP_NEW, a);
- cc->c.b = F_IN(f, MP_NEW, b);
-
- c = MP_COPY(cc->c.b);
- for (i = 0; i < f->nbits - 2; i++)
- c = F_SQR(f, c, c);
- d = F_SQR(f, MP_NEW, c); d = F_SQR(f, d, d);
- if (!MP_EQ(d, cc->c.b)) {
- MP_DROP(c);
- MP_DROP(d);
- MP_DROP(cc->c.a);
- MP_DROP(cc->c.b);
- DESTROY(cc);
- return (0);
- }
- cc->bb = c;
- MP_DROP(d);
- return (&cc->c);
-}
-
-static const ec_ops ec_binops = {
- "bin",
- ecdestroy, ec_stdsamep, ec_idin, ec_idout, ec_idfix,
- ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck
-};
-
-static const ec_ops ec_binprojops = {
- "binproj",
- ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix,
- ecfind, ecprojneg, ecprojadd, ec_stdsub, ecprojdbl, 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, *beta;
- int i, n = argc == 1 ? 1 : atoi(argv[1]);
-
- printf("ec-bin: ");
- fflush(stdout);
- a = MP(0x7ffffffffffffffffffffffffffffffffffffffff);
- b = MP(0x6645f3cacf1638e139c6cd13ef61734fbc9e3d9fb);
- p = MP(0x800000000000000000000000000000000000000c9);
- beta = MP(0x715169c109c612e390d347c748342bcd3b02a0bef);
- r = MP(0x040000000000000000000292fe77e70c12a4234c32);
-
- f = field_binnorm(p, beta);
- c = ec_binproj(f, a, b);
- g.x = MP(0x0311103c17167564ace77ccb09c681f886ba54ee8);
- g.y = MP(0x333ac13c6447f2e67613bf7009daf98c87bb50c7f);
-
- 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_EPRINTX("d.x", d.x);
- MP_EPRINTX("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); MP_DROP(beta);
- assert(!mparena_count(&mparena_global));
- printf("ok\n");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff