X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/math/ec-bin.c

diff --git a/math/ec-bin.c b/math/ec-bin.c
new file mode 100644
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--- /dev/null
+++ b/math/ec-bin.c
@@ -0,0 +1,445 @@
+/* -*-c-*-
+ *
+ * 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 -------------------------------------------------*/