X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/e9926004f7caf25abbfb87ebd921a01e6bf865dc..c3caa2face1cda7002eb58245ad75865bf437455:/ec-bin.c diff --git a/ec-bin.c b/ec-bin.c new file mode 100644 index 0000000..3e85e65 --- /dev/null +++ b/ec-bin.c @@ -0,0 +1,431 @@ +/* -*-c-*- + * + * $Id: ec-bin.c,v 1.2 2004/03/21 22:52:06 mdw Exp $ + * + * 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. + */ + +/*----- Revision history --------------------------------------------------* + * + * $Log: ec-bin.c,v $ + * Revision 1.2 2004/03/21 22:52:06 mdw + * Merge and close elliptic curve branch. + * + * Revision 1.1.2.1 2004/03/21 22:39:46 mdw + * Elliptic curves on binary fields work. + * + */ + +/*----- Header files ------------------------------------------------------*/ + +#include + +#include "ec.h" + +/*----- Data structures ---------------------------------------------------*/ + +typedef struct ecctx { + ec_curve c; + mp *a, *b; + mp *bb; +} ecctx; + +/*----- 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) +{ + /* write me */ + return (0); +} + +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; + ecctx *cc = (ecctx *)c; + 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, cc->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'$% */ + + EC_DESTROY(d); + d->x = dx; + d->y = dy; + d->z = 0; + MP_DROP(lambda); + } + return (d); +} + +static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) +{ + if (EC_ATINF(a) || F_ZEROP(c->f, a->x)) + EC_SETINF(d); + else { + field *f = c->f; + ecctx *cc = (ecctx *)c; + mp *dx, *dy, *dz, *u, *v; + + dy = F_SQR(f, MP_NEW, a->z); /* %$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'$% */ + + EC_DESTROY(d); + d->x = dx; + d->y = dy; + d->z = dz; + MP_DROP(u); + MP_DROP(v); + assert(!(d->x->f & MP_DESTROYED)); + assert(!(d->y->f & MP_DESTROYED)); + assert(!(d->z->f & MP_DESTROYED)); + } + return (d); +} + +static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) +{ + if (a == b) + ecdbl(c, d, a); + else if (EC_ATINF(a)) + EC_COPY(d, b); + else if (EC_ATINF(b)) + EC_COPY(d, a); + else { + field *f = c->f; + ecctx *cc = (ecctx *)c; + mp *lambda; + mp *dx, *dy; + + if (!MP_EQ(a->x, b->x)) { + dx = F_ADD(f, MP_NEW, a->x, b->x); /* %$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$% */ + dx = F_ADD(f, dx, dx, cc->a); /* %$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$% */ + dx = F_ADD(f, dx, dx, cc->a); /* %$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'$% */ + + EC_DESTROY(d); + d->x = dx; + d->y = dy; + d->z = 0; + MP_DROP(lambda); + } + return (d); +} + +static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) +{ + if (a == b) + c->ops->dbl(c, d, a); + else if (EC_ATINF(a)) + EC_COPY(d, b); + else if (EC_ATINF(b)) + EC_COPY(d, a); + else { + field *f = c->f; + ecctx *cc = (ecctx *)c; + mp *dx, *dy, *dz, *u, *uu, *v, *t, *s, *ss, *r, *w, *l; + + dz = F_SQR(f, MP_NEW, b->z); /* %$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$% */ + dx = F_MUL(f, MP_NEW, uu, cc->a); /* %$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) +{ + ecctx *cc = (ecctx *)c; + field *f = c->f; + int rc; + mp *u, *v; + + v = F_SQR(f, MP_NEW, p->x); + u = F_MUL(f, MP_NEW, v, p->x); + v = F_MUL(f, v, v, cc->a); + u = F_ADD(f, u, u, v); + u = F_ADD(f, u, u, cc->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); + 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 *cc = (ecctx *)c; + MP_DROP(cc->a); + MP_DROP(cc->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. + * + * 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 *cc = CREATE(ecctx); + cc->c.ops = &ec_binops; + cc->c.f = f; + cc->a = F_IN(f, MP_NEW, a); + cc->b = F_IN(f, MP_NEW, b); + cc->bb = 0; + return (&cc->c); +} + +ec_curve *ec_binproj(field *f, mp *a, mp *b) +{ + ecctx *cc = CREATE(ecctx); + cc->c.ops = &ec_binprojops; + cc->c.f = f; + cc->a = F_IN(f, MP_NEW, a); + cc->b = F_IN(f, MP_NEW, b); + cc->bb = F_SQRT(f, MP_NEW, b); + cc->bb = F_SQRT(f, cc->bb, cc->bb); + return (&cc->c); +} + +static const ec_ops ec_binops = { + ecdestroy, ec_idin, ec_idout, ec_idfix, + 0, ecneg, ecadd, ec_stdsub, ecdbl, eccheck +}; + +static const ec_ops ec_binprojops = { + ecdestroy, ec_projin, ec_projout, ec_projfix, + 0, 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; + int i, n = argc == 1 ? 1 : atoi(argv[1]); + + printf("ec-bin: "); + fflush(stdout); + a = MP(1); + b = MP(0x066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad); + p = MP(0x20000000000000000000000000000000000000004000000000000000001); + r = + MP(6901746346790563787434755862277025555839812737345013555379383634485462); + + f = field_binpoly(p); + c = ec_binproj(f, a, b); + + g.x = MP(0x0fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b); + g.y = MP(0x1006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052); + + 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); + MP_EPRINTX("d.z", 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 -------------------------------------------------*/