X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/f46efa79cd2bb9adc81541f1218965f85a6b2eef..78614e02310dbe879d55f0a68e47349db074ff61:/ec-prime.c diff --git a/ec-prime.c b/ec-prime.c index 7712bbf..52815e4 100644 --- a/ec-prime.c +++ b/ec-prime.c @@ -1,13 +1,13 @@ /* -*-c-*- * - * $Id: ec-prime.c,v 1.7 2004/03/27 00:04:46 mdw Exp $ + * $Id$ * * Elliptic curves over prime fields * * (c) 2001 Straylight/Edgeware */ -/*----- Licensing notice --------------------------------------------------* +/*----- Licensing notice --------------------------------------------------* * * This file is part of Catacomb. * @@ -15,68 +15,24 @@ * 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. */ -/*----- Revision history --------------------------------------------------* - * - * $Log: ec-prime.c,v $ - * Revision 1.7 2004/03/27 00:04:46 mdw - * Implement efficient reduction for pleasant-looking primes. - * - * Revision 1.6 2004/03/23 15:19:32 mdw - * Test elliptic curves more thoroughly. - * - * Revision 1.5 2004/03/22 02:19:10 mdw - * Rationalise the sliding-window threshold. Drop guarantee that right - * arguments to EC @add@ are canonical, and fix up projective implementations - * to cope. - * - * Revision 1.4 2004/03/21 22:52:06 mdw - * Merge and close elliptic curve branch. - * - * Revision 1.3.4.3 2004/03/21 22:39:46 mdw - * Elliptic curves on binary fields work. - * - * Revision 1.3.4.2 2004/03/20 00:13:31 mdw - * Projective coordinates for prime curves - * - * Revision 1.3.4.1 2003/06/10 13:43:53 mdw - * Simple (non-projective) curves over prime fields now seem to work. - * - * Revision 1.3 2003/05/15 23:25:59 mdw - * Make elliptic curve stuff build. - * - * Revision 1.2 2002/01/13 13:48:44 mdw - * Further progress. - * - * Revision 1.1 2001/04/29 18:12:33 mdw - * Prototype version. - * - */ - /*----- Header files ------------------------------------------------------*/ #include #include "ec.h" -/*----- Data structures ---------------------------------------------------*/ - -typedef struct ecctx { - ec_curve c; - mp *a, *b; -} ecctx; - /*----- Simple prime curves -----------------------------------------------*/ static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops; @@ -92,14 +48,13 @@ static ec *ecneg(ec_curve *c, ec *d, const ec *p) static ec *ecfind(ec_curve *c, ec *d, mp *x) { mp *p, *q; - ecctx *cc = (ecctx *)c; 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, cc->a); + q = F_MUL(f, q, x, c->a); p = F_ADD(f, p, p, q); - p = F_ADD(f, p, p, cc->b); + p = F_ADD(f, p, p, c->b); MP_DROP(q); p = F_SQRT(f, p, p); if (!p) @@ -113,20 +68,17 @@ static ec *ecfind(ec_curve *c, ec *d, mp *x) static ec *ecdbl(ec_curve *c, ec *d, const ec *a) { - if (EC_ATINF(a)) + if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) EC_SETINF(d); - else if (F_ZEROP(c->f, a->y)) - EC_COPY(d, a); else { field *f = c->f; - ecctx *cc = (ecctx *)c; 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, cc->a); /* %$3 x^2 + A$% */ + 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); /* %$\lambda = (3 x^2 + A)/(2 y)$% */ @@ -148,18 +100,15 @@ static ec *ecdbl(ec_curve *c, ec *d, const ec *a) static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) { - if (EC_ATINF(a)) + if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) EC_SETINF(d); - else if (F_ZEROP(c->f, a->y)) - EC_COPY(d, a); else { field *f = c->f; - ecctx *cc = (ecctx *)c; 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, cc->a); /* %$A z^4$% */ + 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); /* %$m = 3 x^2 + A z^4$% */ @@ -193,10 +142,8 @@ static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) static ec *ecprojxdbl(ec_curve *c, ec *d, const ec *a) { - if (EC_ATINF(a)) + if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) EC_SETINF(d); - else if (F_ZEROP(c->f, a->y)) - EC_COPY(d, a); else { field *f = c->f; mp *p, *q, *m, *s, *dx, *dy, *dz; @@ -257,10 +204,9 @@ static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) EC_SETINF(d); return (d); } else { - ecctx *cc = (ecctx *)c; 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, cc->a); /* %$3 x_0^2 + A$% */ + 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); @@ -332,7 +278,7 @@ static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) 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); /* %$x' = r^2 - t w^2$% */ @@ -356,15 +302,16 @@ static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) static int eccheck(ec_curve *c, const ec *p) { - ecctx *cc = (ecctx *)c; field *f = c->f; + mp *l, *x, *r; int rc; - mp *l = F_SQR(f, MP_NEW, p->y); - mp *x = F_SQR(f, MP_NEW, p->x); - mp *r = F_MUL(f, MP_NEW, x, p->x); - x = F_MUL(f, x, cc->a, p->x); + 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, cc->b); + r = F_ADD(f, r, r, c->b); rc = MP_EQ(l, r) ? 0 : -1; mp_drop(l); mp_drop(x); @@ -376,7 +323,7 @@ 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); @@ -385,10 +332,9 @@ static int ecprojcheck(ec_curve *c, const ec *p) static void ecdestroy(ec_curve *c) { - ecctx *cc = (ecctx *)c; - MP_DROP(cc->a); - MP_DROP(cc->b); - DESTROY(cc); + MP_DROP(c->a); + MP_DROP(c->b); + DESTROY(c); } /* --- @ec_prime@, @ec_primeproj@ --- * @@ -396,7 +342,7 @@ static void ecdestroy(ec_curve *c) * Arguments: @field *f@ = the underlying field for this elliptic curve * @mp *a, *b@ = the coefficients for this curve * - * Returns: A pointer to the 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 @@ -405,44 +351,47 @@ static void ecdestroy(ec_curve *c) extern ec_curve *ec_prime(field *f, mp *a, mp *b) { - ecctx *cc = CREATE(ecctx); - cc->c.ops = &ec_primeops; - cc->c.f = f; - cc->a = F_IN(f, MP_NEW, a); - cc->b = F_IN(f, MP_NEW, b); - return (&cc->c); + 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) { - ecctx *cc = CREATE(ecctx); + 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)) - cc->c.ops = &ec_primeprojxops; + c->ops = &ec_primeprojxops; else - cc->c.ops = &ec_primeprojops; + c->ops = &ec_primeprojops; MP_DROP(ax); - cc->c.f = f; - cc->a = F_IN(f, MP_NEW, a); - cc->b = F_IN(f, MP_NEW, b); - return (&cc->c); + 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 = { - ecdestroy, ec_idin, ec_idout, ec_idfix, + "prime", + ecdestroy, ec_stdsamep, ec_idin, ec_idout, ec_idfix, ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck }; static const ec_ops ec_primeprojops = { - ecdestroy, ec_projin, ec_projout, ec_projfix, + "primeproj", + ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck }; static const ec_ops ec_primeprojxops = { - ecdestroy, ec_projin, ec_projout, ec_projfix, + "primeproj", + ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck }; @@ -463,17 +412,17 @@ int main(int argc, char *argv[]) printf("ec-prime: "); fflush(stdout); a = MP(-3); - b = MP(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1); - p = MP(6277101735386680763835789423207666416083908700390324961279); - r = MP(6277101735386680763835789423176059013767194773182842284080); + b = MP(0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef); + p = MP(39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319); + r = MP(39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942642); f = field_niceprime(p); c = ec_primeproj(f, a, b); - - g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012); - g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811); - for (i = 0; i < n; i++) { + 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");