X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/41cb1beba35c8a69ee7ae1298f51711995011b5c..78614e02310dbe879d55f0a68e47349db074ff61:/ec-prime.c diff --git a/ec-prime.c b/ec-prime.c index 4611855..52815e4 100644 --- a/ec-prime.c +++ b/ec-prime.c @@ -1,13 +1,13 @@ /* -*-c-*- * - * $Id: ec-prime.c,v 1.3 2003/05/15 23:25:59 mdw Exp $ + * $Id$ * * Elliptic curves over prime fields * * (c) 2001 Straylight/Edgeware */ -/*----- Licensing notice --------------------------------------------------* +/*----- Licensing notice --------------------------------------------------* * * This file is part of Catacomb. * @@ -15,81 +15,79 @@ * 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 1.3 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 -----------------------------------------------*/ -/*----- Main code ---------------------------------------------------------*/ - -static const ec_ops ec_primeops; +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); - d->y = F_NEG(c->f, d->y, d->y); + 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)) + if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) EC_SETINF(d); - else if (!MP_LEN(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); - dy = F_DBL(f, MP_NEW, a->y); - dx = F_TPL(f, dx, dx); - dx = F_ADD(f, dx, dx, cc->a); - dy = F_INV(f, dy, dy); - lambda = F_MUL(f, MP_NEW, dx, dy); + 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); - dy = F_DBL(f, dy, a->x); - dx = F_SUB(f, dx, dx, dy); - dy = F_SUB(f, dy, a->x, dx); - dy = F_MUL(f, dy, lambda, dy); - dy = F_SUB(f, dy, dy, a->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$% */ EC_DESTROY(d); d->x = dx; @@ -100,6 +98,89 @@ static ec *ecdbl(ec_curve *c, ec *d, const ec *a) return (d); } +static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) +{ + if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) + EC_SETINF(d); + else { + field *f = c->f; + mp *p, *q, *m, *s, *dx, *dy, *dz; + + p = F_SQR(f, MP_NEW, a->z); /* %$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) @@ -114,29 +195,30 @@ static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) mp *dy, *dx; if (!MP_EQ(a->x, b->x)) { - dy = F_SUB(f, MP_NEW, a->y, b->y); - dx = F_SUB(f, MP_NEW, a->x, b->x); - dx = F_INV(f, dx, dx); + 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); - } else if (!MP_LEN(a->y) || !MP_EQ(a->y, b->y)) { + /* %$\lambda = (y_0 - y1)/(x_0 - x_1)$% */ + } else if (F_ZEROP(c->f, a->y) || !MP_EQ(a->y, b->y)) { EC_SETINF(d); return (d); } else { - ecctx *cc = (ecctx *)c; - dx = F_SQR(f, MP_NEW, a->x); - dx = F_TPL(f, dx, dx); - dx = F_ADD(f, dx, dx, cc->a); - dy = F_DBL(f, MP_NEW, a->y); - dy = F_INV(f, dy, dy); + 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); - dx = F_SUB(f, dx, dx, a->x); - dx = F_SUB(f, dx, dx, b->x); - dy = F_SUB(f, dy, b->x, dx); - dy = F_MUL(f, dy, lambda, dy); - dy = F_SUB(f, dy, dy, b->y); + 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; @@ -147,20 +229,120 @@ static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) 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) { - 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@ --- * * - * Arguments: @field *f@ = the underyling field for this elliptic curve + * 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 @@ -169,16 +351,48 @@ 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 = MP_COPY(a); - cc->b = MP_COPY(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) +{ + 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 = { - ecdestroy, ec_idin, ec_idout, 0, ecneg, ecadd, ec_stdsub, ecdbl + "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 ----------------------------------------------------------*/ @@ -187,33 +401,48 @@ static const ec_ops ec_primeops = { #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) -int main(void) +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(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1); - p = MP(6277101735386680763835789423207666416083908700390324961279); - r = MP(6277101735386680763835789423176059013767194773182842284081); + b = MP(0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef); + p = MP(39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319); + r = MP(39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942642); - f = field_prime(p); - c = ec_prime(f, a, b); - - g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012); - g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811); + f = field_niceprime(p); + c = ec_primeproj(f, a, b); - ec_mul(c, &d, &g, r); - MP_PRINT("d.x", d.x); - MP_PRINT("d.y", d.y); + g.x = MP(0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7); + g.y = MP(0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f); - ec_destroy(&d); + 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); }