X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/4edc47b89bc56cd4041fdb0f4e8e892acd589ed8..1d6d3b01cb40e0cfaeb816c87c513695aea0816a:/ec-info.c

diff --git a/ec-info.c b/ec-info.c
index bcc0ab8..0e225a7 100644
--- a/ec-info.c
+++ b/ec-info.c
@@ -1,13 +1,13 @@
 /* -*-c-*-
  *
- * $Id: ec-info.c,v 1.3 2004/04/01 21:28:41 mdw Exp $
+ * $Id$
  *
  * Elliptic curve information management
  *
  * (c) 2004 Straylight/Edgeware
  */
 
-/*----- Licensing notice --------------------------------------------------* 
+/*----- Licensing notice --------------------------------------------------*
  *
  * This file is part of Catacomb.
  *
@@ -15,38 +15,18 @@
  * 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-info.c,v $
- * Revision 1.3  2004/04/01 21:28:41  mdw
- * Normal basis support (translates to poly basis internally).  Rewrite
- * EC and prime group table generators in awk, so that they can reuse data
- * for repeated constants.
- *
- * Revision 1.2  2004/04/01 12:50:09  mdw
- * Add cyclic group abstraction, with test code.  Separate off exponentation
- * functions for better static linking.  Fix a buttload of bugs on the way.
- * Generally ensure that negative exponents do inversion correctly.  Add
- * table of standard prime-field subgroups.  (Binary field subgroups are
- * currently unimplemented but easy to add if anyone ever finds a good one.)
- *
- * Revision 1.1  2004/03/27 17:54:11  mdw
- * Standard curves and curve checking.
- *
- */
-
 /*----- Header files ------------------------------------------------------*/
 
 #include "ec.h"
@@ -54,6 +34,7 @@
 #include "gf.h"
 #include "pgen.h"
 #include "mprand.h"
+#include "mpint.h"
 #include "rabin.h"
 
 /*----- Main code ---------------------------------------------------------*/
@@ -67,7 +48,7 @@
  * Use:		Parses an elliptic curve description, which has the form
  *
  *		  * a field description
- *		  * an optional `/'
+ *		  * an optional `;'
  *		  * `prime', `primeproj', `bin', or `binproj'
  *		  * an optional `:'
  *		  * the %$a$% parameter
@@ -82,7 +63,7 @@ ec_curve *ec_curveparse(qd_parse *qd)
   field *f;
 
   if ((f = field_parse(qd)) == 0) goto fail;
-  qd_delim(qd, '/');
+  qd_delim(qd, ';');
   switch (qd_enum(qd, "prime,primeproj,bin,binproj")) {
     case 0:
       if (F_TYPE(f) != FTY_PRIME) {
@@ -131,6 +112,10 @@ ec_curve *ec_curveparse(qd_parse *qd)
     default:
       goto fail;
   }
+  if (!c) {
+    qd->e = "bad curve parameters";
+    goto fail;
+  }
   if (a) MP_DROP(a);
   if (b) MP_DROP(b);
   return (c);
@@ -179,7 +164,7 @@ fail:
   return (0);
 }
 
-/* --- @getinfo@ --- *
+/* --- @ec_infofromdata@ --- *
  *
  * Arguments:	@ec_info *ei@ = where to write the information
  *		@ecdata *ed@ = raw data
@@ -190,7 +175,7 @@ fail:
  *		curves.
  */
 
-static void getinfo(ec_info *ei, ecdata *ed)
+void ec_infofromdata(ec_info *ei, ecdata *ed)
 {
   field *f;
 
@@ -215,6 +200,7 @@ static void getinfo(ec_info *ei, ecdata *ed)
       abort();
   }
 
+  assert(f); assert(ei->c);
   EC_CREATE(&ei->g); ei->g.x = &ed->gx; ei->g.y = &ed->gy; ei->g.z = 0;
   ei->r = &ed->r; ei->h = &ed->h;
 }
@@ -232,7 +218,7 @@ static void getinfo(ec_info *ei, ecdata *ed)
  *		curve, or it has the form
  *
  *		  * elliptic curve description
- *		  * optional `/'
+ *		  * optional `;'
  *		  * common point
  *		  * optional `:'
  *		  * group order
@@ -250,12 +236,13 @@ int ec_infoparse(qd_parse *qd, ec_info *ei)
 
   for (ee = ectab; ee->name; ee++) {
     if (qd_enum(qd, ee->name) >= 0) {
-      getinfo(ei, ee->data);
+      ec_infofromdata(ei, ee->data);
       goto found;
     }
   }
+
   if ((c = ec_curveparse(qd)) == 0) goto fail;
-  qd_delim(qd, '/'); if (!ec_ptparse(qd, &g)) goto fail;
+  qd_delim(qd, ';'); if (!ec_ptparse(qd, &g)) goto fail;
   qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail;
   qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail;
   ei->c = c; ei->g = g; ei->r = r; ei->h = h;
@@ -341,46 +328,17 @@ void ec_freeinfo(ec_info *ei)
  * Use:		Checks an elliptic curve according to the rules in SEC1.
  */
 
-static int primeeltp(mp *x, field *f)
-{
-  return (!MP_ISNEG(x) && MP_CMP(x, <, f->m));
-}
-
-static const char *primecheck(const ec_info *ei, grand *gr)
+static const char *gencheck(const ec_info *ei, grand *gr, mp *q)
 {
   ec_curve *c = ei->c;
   field *f = c->f;
-  int i;
+  int i, j, n;
+  mp *qq;
+  mp *nn;
   mp *x, *y;
   ec p;
   int rc;
 
-  /* --- Check %$p$% is an odd prime --- */
-
-  if (!pgen_primep(f->m, gr)) return ("p not prime");
-
-  /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
-
-  if (!primeeltp(c->a, f)) return ("a out of range");
-  if (!primeeltp(c->b, f)) return ("b out of range");
-  if (!primeeltp(ei->g.x, f)) return ("G_x out of range");
-  if (!primeeltp(ei->g.x, f)) return ("G_y out of range");
-
-  /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
-
-  x = F_SQR(f, MP_NEW, c->a);
-  x = F_MUL(f, x, x, c->a);
-  x = F_QDL(f, x, x);
-  y = F_SQR(f, MP_NEW, c->b);
-  y = F_TPL(f, y, y);
-  y = F_TPL(f, y, y);
-  y = F_TPL(f, y, y);
-  x = F_ADD(f, x, x, y);
-  rc = F_ZEROP(f, x);
-  MP_DROP(x);
-  MP_DROP(y);
-  if (rc) return ("not an elliptic curve");
-
   /* --- Check %$G \in E$% --- */
 
   if (EC_ATINF(&ei->g)) return ("generator at infinity");
@@ -390,29 +348,54 @@ static const char *primecheck(const ec_info *ei, grand *gr)
 
   if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
 
-  /* --- Check %$0 < h \le 4$% --- */
-
-  if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
-    return ("cofactor out of range");
-
-  /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
+  /* --- Check that the cofactor is correct --- *
+   *
+   * Let %$q$% be the size of the field, and let %$n = h r = \#E(\gf{q})$% be
+   * the number of %$\gf{q}$%-rational points on our curve.  Hasse's theorem
+   * tells us that
+   *
+   *   %$|q + 1 - n| \le 2\sqrt{q}$%
+   *
+   * or, if we square both sides,
+   *
+   *   %$(q + 1 - n)^2 \le 4 q$%.
+   *
+   * We'd like the cofactor to be uniquely determined by this equation, which
+   * is possible as long as it's not too big.  (If it is, we have to mess
+   * about with Weil pairings, which is no fun.)  For this, we need the
+   * following inequalities:
+   *
+   *   * %$A = (q + 1 - n)^2 \le 4 q$% (both lower and upper bounds from
+   *	 Hasse's theorem);
    *
-   * This seems to work with the approximate-sqrt in the library, but might
-   * not be so good in some cases.  Throw in some extra significate figures
-   * for good measure.
+   *   * %$B = (q + 1 - n - r)^2 > 4 q$% (check %$h - 1$% isn't possible);
+   *	 and
+   *
+   *   * %$C = (q + 1 - n + r)^2 > 4 q$% (check %$h + 1$% isn't possible).
    */
 
-  x = mp_lsl(MP_NEW, f->m, 128);
-  x = mp_sqrt(x, x);
-  y = mp_lsl(MP_NEW, MP_ONE, 64);
-  x = mp_add(x, x, y);
-  x = mp_sqr(x, x);
-  mp_div(&x, 0, x, ei->r);
-  x = mp_lsr(x, x, 128);
-  rc = MP_EQ(x, ei->h);
+  rc = 1;
+  qq = mp_add(MP_NEW, q, MP_ONE);
+  nn = mp_mul(MP_NEW, ei->r, ei->h);
+  nn = mp_sub(nn, qq, nn);
+  qq = mp_lsl(qq, q, 2);
+
+  y = mp_sqr(MP_NEW, nn);
+  if (MP_CMP(y, >, qq)) rc = 0;
+
+  x = mp_sub(MP_NEW, nn, ei->r);
+  y = mp_sqr(y, x);
+  if (MP_CMP(y, <=, qq)) rc = 0;
+
+  x = mp_add(x, nn, ei->r);
+  y = mp_sqr(y, x);
+  if (MP_CMP(y, <=, qq)) rc = 0;
+
   MP_DROP(x);
   MP_DROP(y);
-  if (!rc) return ("incorrect cofactor");
+  MP_DROP(nn);
+  MP_DROP(qq);
+  if (!rc) return ("incorrect or ambiguous cofactor");
 
   /* --- Check %$n G = O$% --- */
 
@@ -422,110 +405,111 @@ static const char *primecheck(const ec_info *ei, grand *gr)
   EC_DESTROY(&p);
   if (!rc) return ("incorrect group order");
 
-  /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
+  /* --- Check %$q^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
    *
-   * The spec says %$q$%, not %$p$%, but I think that's a misprint.
+   * Actually, give up if %$q^B \ge 2^{2000}$% because that's probably
+   * good enough for jazz.
    */
 
   x = MP_NEW;
-  mp_div(0, &x, f->m, ei->r);
-  i = 20;
-  while (i) {
-    if (MP_EQ(x, MP_ONE)) break;
+  mp_div(0, &x, q, ei->r);
+  n = mp_bits(ei->r) - 1;
+  for (i = 0, j = n; i < 20; i++, j += n) {
+    if (j >= 2000)
+      break;
+    if (MP_EQ(x, MP_ONE)) {
+      MP_DROP(x);
+      return("curve embedding degree too low");
+    }
     x = mp_mul(x, x, f->m);
     mp_div(0, &x, x, ei->r);
-    i--;
   }
   MP_DROP(x);
-  if (i) return ("curve is weak");
 
   /* --- Done --- */
 
   return (0);
 }
 
-static const char *bincheck(const ec_info *ei, grand *gr)
+static int primeeltp(mp *x, field *f)
+  { return (!MP_NEGP(x) && MP_CMP(x, <, f->m)); }
+
+static const char *primecheck(const ec_info *ei, grand *gr)
 {
   ec_curve *c = ei->c;
   field *f = c->f;
-  int i;
   mp *x, *y;
-  ec p;
   int rc;
+  const char *err;
 
-  /* --- Check that %$p$% is irreducible --- */
+  /* --- Check %$p$% is an odd prime --- */
 
-  if (!gf_irreduciblep(f->m)) return ("p not irreducible");
+  if (!pgen_primep(f->m, gr)) return ("p not prime");
 
-  /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
+  /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
 
-  if (mp_bits(c->a) > f->nbits) return ("a out of range");
-  if (mp_bits(c->b) > f->nbits) return ("a out of range");
-  if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range");
-  if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range");
+  if (!primeeltp(c->a, f)) return ("a out of range");
+  if (!primeeltp(c->b, f)) return ("b out of range");
+  if (!primeeltp(ei->g.x, f)) return ("G_x out of range");
+  if (!primeeltp(ei->g.x, f)) return ("G_y out of range");
 
-  /* --- Check that %$b \ne 0$% --- */
+  /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
 
-  if (F_ZEROP(f, c->b)) return ("b is zero");
+  x = F_SQR(f, MP_NEW, c->a);
+  x = F_MUL(f, x, x, c->a);
+  x = F_QDL(f, x, x);
+  y = F_SQR(f, MP_NEW, c->b);
+  y = F_TPL(f, y, y);
+  y = F_TPL(f, y, y);
+  y = F_TPL(f, y, y);
+  x = F_ADD(f, x, x, y);
+  rc = F_ZEROP(f, x);
+  MP_DROP(x);
+  MP_DROP(y);
+  if (rc) return ("not an elliptic curve");
 
-  /* --- Check that %$G \in E$% --- */
+  /* --- Now do the general checks --- */
 
-  if (EC_ATINF(&ei->g)) return ("generator at infinity");
-  if (ec_check(c, &ei->g)) return ("generator not on curve");
+  err = gencheck(ei, gr, f->m);
+  return (err);
+}
 
-  /* --- Check %$r$% is prime --- */
+static const char *bincheck(const ec_info *ei, grand *gr)
+{
+  ec_curve *c = ei->c;
+  field *f = c->f;
+  mp *x;
+  int rc;
+  const char *err;
 
-  if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
+  /* --- Check that %$m$% is prime --- */
 
-  /* --- Check %$0 < h \le 4$% --- */
+  x = mp_fromuint(MP_NEW, f->nbits);
+  rc = pfilt_smallfactor(x);
+  mp_drop(x);
+  if (rc != PGEN_DONE) return ("degree not prime");
 
-  if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
-    return ("cofactor out of range");
+  /* --- Check that %$p$% is irreducible --- */
 
-  /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
-   *
-   * This seems to work with the approximate-sqrt in the library, but might
-   * not be so good in some cases.  Throw in some extra significate figures
-   * for good measure.
-   */     
-
-  x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128);
-  x = mp_sqrt(x, x);
-  y = mp_lsl(MP_NEW, MP_ONE, 64);
-  x = mp_add(x, x, y);
-  x = mp_sqr(x, x);
-  mp_div(&x, 0, x, ei->r);
-  x = mp_lsr(x, x, 128);
-  rc = MP_EQ(x, ei->h);
-  MP_DROP(x);
-  MP_DROP(y);
-  if (!rc) return ("incorrect cofactor");
+  if (!gf_irreduciblep(f->m)) return ("p not irreducible");
 
-  /* --- Check %$n G = O$% --- */
+  /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
 
-  EC_CREATE(&p);
-  ec_mul(c, &p, &ei->g, ei->r);
-  rc = EC_ATINF(&p);
-  EC_DESTROY(&p);
-  if (!rc) return ("incorrect group order");
+  if (mp_bits(c->a) > f->nbits) return ("a out of range");
+  if (mp_bits(c->b) > f->nbits) return ("a out of range");
+  if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range");
+  if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range");
 
-  /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
+  /* --- Check that %$b \ne 0$% --- */
 
-  x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
-  mp_div(0, &x, x, ei->r);
-  i = 20;
-  while (i) {
-    if (MP_EQ(x, MP_ONE)) break;
-    x = mp_mul(x, x, f->m);
-    mp_div(0, &x, x, ei->r);
-    i--;
-  }
-  MP_DROP(x);
-  if (i) return ("curve is weak");
+  if (F_ZEROP(f, c->b)) return ("b is zero");
 
-  /* --- Done --- */
+  /* --- Now do the general checks --- */
 
-  return (0);
+  x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
+  err = gencheck(ei, gr, x);
+  mp_drop(x);
+  return (err);
 }
 
 const char *ec_checkinfo(const ec_info *ei, grand *gr)
@@ -543,29 +527,51 @@ const char *ec_checkinfo(const ec_info *ei, grand *gr)
 
 #include "fibrand.h"
 
-int main(void)
+int main(int argc, char *argv[])
 {
   const ecentry *ee;
   const char *e;
   int ok = 1;
+  int i;
   grand *gr;
 
   gr = fibrand_create(0);
-  fputs("checking standard curves: ", stdout);
-  for (ee = ectab; ee->name; ee++) {
-    ec_info ei;
-    getinfo(&ei, ee->data);
-    e = ec_checkinfo(&ei, gr);
-    ec_freeinfo(&ei);
-    if (e) {
-      fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e);
-      ok = 0;
+  if (argc > 1) {
+    for (i = 1; i < argc; i++) {
+      ec_info ei;
+      if ((e = ec_getinfo(&ei, argv[i])) != 0)
+	fprintf(stderr, "bad curve spec `%s': %s", argv[i], e);
+      else {
+	e = ec_checkinfo(&ei, gr);
+	ec_freeinfo(&ei);
+	if (!e)
+	  printf("OK %s\n", argv[i]);
+	else {
+	  printf("BAD %s: %s\n", argv[i], e);
+	  ok = 0;
+	}
+      }
+      assert(mparena_count(MPARENA_GLOBAL) == 0);
     }
-    putchar('.');
+  } else {
+    fputs("checking standard curves:", stdout);
     fflush(stdout);
+    for (ee = ectab; ee->name; ee++) {
+      ec_info ei;
+      ec_infofromdata(&ei, ee->data);
+      e = ec_checkinfo(&ei, gr);
+      ec_freeinfo(&ei);
+      if (e) {
+	printf(" [%s fails: %s]", ee->name, e);
+	ok = 0;
+      } else
+	printf(" %s", ee->name);
+      fflush(stdout);
+      assert(mparena_count(MPARENA_GLOBAL) == 0);
+    }
+    fputs(ok ? " ok\n" : " failed\n", stdout);
   }
   gr->ops->destroy(gr);
-  fputs(ok ? " ok\n" : " failed\n", stdout);
   return (!ok);
 }