Raw I/O of elliptic curve points and group elements.

diff --git a/Makefile.m4 b/Makefile.m4
index e15b5eb..bd832ab 100644 (file)
--- a/Makefile.m4
+++ b/Makefile.m4
@@ -1,6 +1,6 @@
 ## -*-m4-*-
 ##
-## $Id: Makefile.m4,v 1.77 2004/04/01 21:28:41 mdw Exp $
+## $Id: Makefile.m4,v 1.78 2004/04/04 19:04:11 mdw Exp $
 ##
 ## Makefile for Catacomb
 ##
@@ -29,6 +29,9 @@
 ##----- Revision history ----------------------------------------------------
 ##
 ## $Log: Makefile.m4,v $
+## Revision 1.78  2004/04/04 19:04:11  mdw
+## Raw I/O of elliptic curve points and group elements.
+##
 ## Revision 1.77  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
@@ -394,7 +397,7 @@ pkginclude_HEADERS = \
        oaep.h pkcs1.h pss.h tlsprf.h sslprf.h \
        gfshare.h share.h \
        rho.h \
-       field.h ec.h ec-exp.h ec-test.h ectab.h ec-keys.h \
+       field.h ec.h ec-exp.h ec-test.h ectab.h ec-keys.h ec-raw.h \
        ptab.h group.h \
        allwithsuffix(`ciphers', `cipher_modes', `.h') \
        allwithsuffix(`hashes', `hash_modes', `.h') \
@@ -423,7 +426,7 @@ define(`GF_SOURCES',
 define(`EC_SOURCES',
        `field.c field-parse.c f-prime.c f-niceprime.c f-binpoly.c \
        ec.c ec-exp.c ec-prime.c ec-bin.c ec-test.c ec-info.c ectab.c \
-       ec-fetch.c g-ec.c')
+       ec-fetch.c ec-raw.c g-ec.c')
 
 define(`PGEN_SOURCES',
        `pfilt.c rabin.c \

diff --git a/ec-raw.c b/ec-raw.c
new file mode 100644 (file)
index 0000000..ad9b583
--- /dev/null
+++ b/ec-raw.c
@@ -0,0 +1,104 @@
+/* -*-c-*-
+ *
+ * $Id: ec-raw.c,v 1.1 2004/04/04 19:04:11 mdw Exp $
+ *
+ * Raw formatting of elliptic curve points
+ *
+ * (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-raw.c,v $
+ * Revision 1.1  2004/04/04 19:04:11  mdw
+ * Raw I/O of elliptic curve points and group elements.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "ec.h"
+#include "ec-raw.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @ec_putraw@ --- *
+ *
+ * Arguments:  @ec_curve *c@ = elliptic curve
+ *             @buf *b@ = pointer to a buffer
+ *             @const ec *p@ = an elliptic curve point
+ *
+ * Returns:    Zero on success, nonzero on failure.
+ *
+ * Use:                Puts an elliptic curve point to the given buffer using the
+ *             standard uncompressed format described in P1383 and SEC1.
+ *             This requires at most @1 + 2 * c->f->noctets@ space in the
+ *             buffer.  We don't do point compression.
+ */
+
+int ec_putraw(ec_curve *c, buf *b, const ec *p)
+{
+  octet *q;
+  size_t n;
+
+  if (EC_ATINF(p)) return (buf_putbyte(b, 0));
+  buf_putbyte(b, 4);
+  n = c->f->noctets;
+  if ((q = buf_get(b, n * 2)) == 0) return (-1);
+  mp_storeb(p->x, q, n);
+  mp_storeb(p->y, q + n, n);
+  return (0);
+}
+
+/* --- @ec_getraw@ --- *
+ *
+ * Arguments:  @ec_curve *c@ = elliptic curve
+ *             @buf *b@ = pointer to a buffer
+ *             @ec *d@ = an elliptic curve point
+ *
+ * Returns:    Zero on success, nonzero on failure.
+ *
+ * Use:                Reads an elliptic curve point from the given buffer using the
+ *             standard uncompressed format described in P1383 and SEC1.
+ *             We don't do point compression.
+ */
+
+int ec_getraw(ec_curve *c, buf *b, ec *d)
+{
+  const octet *q;
+  size_t n;
+  int u;
+
+  if ((u = buf_getbyte(b)) < 0) return (-1);
+  if (!u) { EC_SETINF(d); return (0); }
+  if (!(u & 4)) return (-1);
+  n = c->f->noctets;
+  if ((q = buf_get(b, n * 2)) == 0) return (-1);
+  EC_DESTROY(d);
+  d->x = mp_loadb(MP_NEW, q, n);
+  d->y = mp_loadb(MP_NEW, q + n, n);
+  d->z = 0;
+  return (0);
+}
+
+/*----- That's all, folks -------------------------------------------------*/

diff --git a/ec-raw.h b/ec-raw.h
new file mode 100644 (file)
index 0000000..e0fde75
--- /dev/null
+++ b/ec-raw.h
@@ -0,0 +1,93 @@
+/* -*-c-*-
+ *
+ * $Id: ec-raw.h,v 1.1 2004/04/04 19:04:11 mdw Exp $
+ *
+ * Raw formatting of elliptic curve points
+ *
+ * (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-raw.h,v $
+ * Revision 1.1  2004/04/04 19:04:11  mdw
+ * Raw I/O of elliptic curve points and group elements.
+ *
+ */
+
+#ifndef CATACOMB_EC_RAW_H
+#define CATACOMB_EC_RAW_H
+
+#ifdef __cplusplus
+  extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#ifndef CATACOMB_BUF_H
+#  include "buf.h"
+#endif
+
+#ifndef CATACOMB_EC_H
+#  include "ec.h"
+#endif
+
+/*----- Data formatting ---------------------------------------------------*/
+
+/* --- @ec_putraw@ --- *
+ *
+ * Arguments:  @ec_curve *c@ = elliptic curve
+ *             @buf *b@ = pointer to a buffer
+ *             @const ec *p@ = an elliptic curve point
+ *
+ * Returns:    Zero on success, nonzero on failure.
+ *
+ * Use:                Puts an elliptic curve point to the given buffer using the
+ *             standard uncompressed format described in P1383 and SEC1.
+ *             We don't do point compression.
+ */
+
+extern int ec_putraw(ec_curve */*c*/, buf */*b*/, const ec */*p*/);
+
+/* --- @ec_getraw@ --- *
+ *
+ * Arguments:  @ec_curve *c@ = elliptic curve
+ *             @buf *b@ = pointer to a buffer
+ *             @ec *d@ = an elliptic curve point
+ *
+ * Returns:    Zero on success, nonzero on failure.
+ *
+ * Use:                Reads an elliptic curve point from the given buffer using the
+ *             standard uncompressed format described in P1383 and SEC1.
+ *             We don't do point compression.
+ */
+
+extern int ec_getraw(ec_curve */*c*/, buf */*b*/, ec */*d*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+  }
+#endif
+
+#endif

diff --git a/g-ec.c b/g-ec.c
index 91583bb..dcf8a10 100644 (file)
--- a/g-ec.c
+++ b/g-ec.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: g-ec.c,v 1.2 2004/04/03 03:32:05 mdw Exp $
+ * $Id: g-ec.c,v 1.3 2004/04/04 19:04:11 mdw Exp $
  *
  * Abstraction for elliptic curve groups
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: g-ec.c,v $
+ * Revision 1.3  2004/04/04 19:04:11  mdw
+ * Raw I/O of elliptic curve points and group elements.
+ *
  * Revision 1.2  2004/04/03 03:32:05  mdw
  * General robustification.
  *
@@ -50,6 +53,7 @@
 
 #define ge ec
 #include "group.h"
+#include "ec-raw.h"
 
 /*----- Data structures ---------------------------------------------------*/
 
@@ -182,6 +186,19 @@ static int gfrombuf(group *gg, buf *b, ec *d) {
   if (!rc) EC_COPY(d, &t); EC_DESTROY(&t); return (rc);
 }
 
+static int gtoraw(group *gg, buf *b, ec *x) {
+  gctx *g = (gctx *)gg; ec t = EC_INIT; int rc;
+  EC_OUT(g->ei.c, &t, x); rc = ec_putraw(g->ei.c, b, &t);
+  EC_DESTROY(&t); return (rc);
+}
+
+static int gfromraw(group *gg, buf *b, ec *d) {
+  gctx *g = (gctx *)gg; ec t = EC_INIT; int rc;
+  if (ec_getraw(g->ei.c, b, &t)) return (-1);
+  EC_IN(g->ei.c, &t, &t); rc = EC_CHECK(g->ei.c, &t);
+  if (!rc) EC_COPY(d, &t); EC_DESTROY(&t); return (rc);
+}
+
 /* --- @group_ec@ --- *
  *
  * Arguments:  @const ec_info *ei@ = elliptic curve parameters
@@ -202,7 +219,7 @@ static const group_ops gops = {
   gcheck,
   gmul, gsqr, ginv, gdiv, gexp, gmexp,
   gread, gwrite,
-  gtoint, gfromint, gtoec, gfromec, gtobuf, gfrombuf
+  gtoint, gfromint, gtoec, gfromec, gtobuf, gfrombuf, gtoraw, gfromraw
 };
 
 group *group_ec(const ec_info *ei)
@@ -211,7 +228,7 @@ group *group_ec(const ec_info *ei)
 
   g->g.ops = &gops;
   g->g.nbits = ei->c->f->nbits * 2;
-  g->g.noctets = ei->c->f->noctets * 2;
+  g->g.noctets = ei->c->f->noctets * 2 + 1;
   g->ei = *ei;
   EC_CREATE(&g->id);
   g->g.i = &g->id;

diff --git a/g-prime.c b/g-prime.c
index 03cce55..97f455f 100644 (file)
--- a/g-prime.c
+++ b/g-prime.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: g-prime.c,v 1.2 2004/04/03 03:32:05 mdw Exp $
+ * $Id: g-prime.c,v 1.3 2004/04/04 19:04:11 mdw Exp $
  *
  * Abstraction for prime groups
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: g-prime.c,v $
+ * Revision 1.3  2004/04/04 19:04:11  mdw
+ * Raw I/O of elliptic curve points and group elements.
+ *
  * Revision 1.2  2004/04/03 03:32:05  mdw
  * General robustification.
  *
@@ -149,6 +152,20 @@ static int gfrombuf(group *gg, buf *b, mp **d) {
   *d = mpmont_mul(&g->mm, x, x, g->mm.r2); return(0);
 }
 
+static int gtoraw(group *gg, buf *b, mp **x) {
+  gctx *g = (gctx *)gg; octet *q; mp *t = mpmont_reduce(&g->mm, MP_NEW, *x);
+  if ((q = buf_get(b, g->g.noctets)) == 0) { MP_DROP(t); return (-1); }
+  mp_storeb(t, q, g->g.noctets); MP_DROP(t); return (0);
+}
+
+static int gfromraw(group *gg, buf *b, mp **d) {
+  gctx * g = (gctx *)gg; mp *x; octet *q;
+  if ((q = buf_get(b, g->g.noctets)) == 0) return (-1);
+  x = mp_loadb(MP_NEW, q, g->g.noctets);
+  mp_div(0, &x, x, g->mm.m); mp_drop(*d);
+  *d = mpmont_mul(&g->mm, x, x, g->mm.r2); return(0);
+}
+
 /* --- @group_prime@ --- *
  *
  * Arguments:  @const gprime_param *gp@ = group parameters
@@ -166,7 +183,8 @@ static const group_ops gops = {
   gcheck,
   gmul, gsqr, ginv, group_stddiv, gexp, gmexp,
   gread, gwrite,
-  gtoint, gfromint, group_stdtoec, group_stdfromec, gtobuf, gfrombuf
+  gtoint, gfromint, group_stdtoec, group_stdfromec, gtobuf, gfrombuf,
+  gtoraw, gfromraw
 };
 
 group *group_prime(const gprime_param *gp)

diff --git a/group-file.c b/group-file.c
index 64e0e4b..a819f92 100644 (file)
--- a/group-file.c
+++ b/group-file.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: group-file.c,v 1.1 2004/04/01 12:50:09 mdw Exp $
+ * $Id: group-file.c,v 1.2 2004/04/04 19:04:11 mdw Exp $
  *
  * File I/O for group elements
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: group-file.c,v $
+ * Revision 1.2  2004/04/04 19:04:11  mdw
+ * Raw I/O of elliptic curve points and group elements.
+ *
  * Revision 1.1  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.
@@ -71,6 +74,6 @@ int group_readfile(group *g, ge *d, FILE *fp)
  */
 
 int group_writefile(group *g, ge *x, FILE *fp)
-  { return (G_WRITE(g, x, &mptext_stringops, fp)); }
+  { return (G_WRITE(g, x, &mptext_fileops, fp)); }
 
 /*----- That's all, folks -------------------------------------------------*/

diff --git a/group-test.c b/group-test.c
index 5fdf147..7c1936b 100644 (file)
--- a/group-test.c
+++ b/group-test.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: group-test.c,v 1.1 2004/04/01 12:50:09 mdw Exp $
+ * $Id: group-test.c,v 1.2 2004/04/04 19:04:11 mdw Exp $
  *
  * Testing group operations
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: group-test.c,v $
+ * Revision 1.2  2004/04/04 19:04:11  mdw
+ * Raw I/O of elliptic curve points and group elements.
+ *
  * Revision 1.1  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.
@@ -450,6 +453,71 @@ static int vfrombuf(dstr *v)
   return (ok);
 }
 
+static int vtoraw(dstr *v)
+{
+  group *g = getgroup(v[0].buf);
+  ge *x = getge(g, v[1].buf);
+  int ir = *(int *)v[2].buf;
+  dstr c = DSTR_INIT;
+  int ic;
+  buf b;
+  int ok = 1;
+
+  dstr_ensure(&c, v[3].len);
+  buf_init(&b, c.buf, v[3].len);
+  ic = G_TORAW(g, &b, x);
+  c.len = BLEN(&b);
+  if (ic != ir || (!ic && (c.len != v[3].len ||
+                          memcmp(c.buf, v[3].buf, c.len)))) {
+    ok = 0;
+    fprintf(stderr, "*** toraw failed\n");
+    fprintf(stderr, "*** group: %s\n", v[0].buf);
+    show(g, "x", x);
+    if (ir) fprintf(stderr, "*** expected failure\n");
+    else {
+      fprintf(stderr, "*** expected: "); type_hex.dump(&v[3], stderr);
+      fprintf(stderr, "\n*** computed: "); type_hex.dump(&c, stderr);
+      fputc('\n', stderr);
+    }
+  }
+  G_DESTROY(g, x); dstr_destroy(&c);
+  G_DESTROYGROUP(g);
+  assert(mparena_count(MPARENA_GLOBAL) == 0);
+  return (ok);
+}
+
+static int vfromraw(dstr *v)
+{
+  group *g = getgroup(v[0].buf);
+  int ir = *(int *)v[2].buf;
+  ge *r = getge(g, v[3].buf);
+  int ic;
+  ge *c = G_CREATE(g);
+  buf b;
+  int ok = 1;
+
+  buf_init(&b, v[1].buf, v[1].len);
+  ic = G_FROMRAW(g, &b, c);
+  if ((ic < 0) != (ir < 0) || (ir >= 0 &&
+                              (ir != BLEN(&b) || !G_EQ(g, r, c)))) {
+    ok = 0;
+    fprintf(stderr, "*** fromraw failed\n");
+    fprintf(stderr, "*** group: %s\n", v[0].buf);
+    fprintf(stderr, "*** input string: "); type_hex.dump(&v[1], stderr);
+    fputc('\n', stderr);
+    if (ir < 0) fprintf(stderr, "*** expected failure\n");
+    else {
+      show(g, "expected", r); show(g, "computed", c);
+      fprintf(stderr, "*** expected used = %d\n", ir);
+      fprintf(stderr, "*** computed used = %lu\n", (unsigned long)BLEN(&b));
+    }
+  }
+  G_DESTROY(g, r); G_DESTROY(g, c);
+  G_DESTROYGROUP(g);
+  assert(mparena_count(MPARENA_GLOBAL) == 0);
+  return (ok);
+}
+
 static const test_chunk tests[] = {
   { "check",   vcheck,         { &type_string, &type_string } },
   { "checkelt",        vcheckelt,      { &type_string, &type_string, &type_int } },
@@ -493,6 +561,10 @@ static const test_chunk tests[] = {
                                  &type_int, &type_hex } },
   { "frombuf", vfrombuf,       { &type_string, &type_hex,
                                  &type_int, &type_string } },
+  { "toraw",   vtoraw,         { &type_string, &type_string,
+                                 &type_int, &type_hex } },
+  { "fromraw", vfromraw,       { &type_string, &type_hex,
+                                 &type_int, &type_string } },
   { 0 }
 };
 

diff --git a/group.h b/group.h
index d099a8f..0e32de6 100644 (file)
--- a/group.h
+++ b/group.h
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: group.h,v 1.2 2004/04/03 03:32:05 mdw Exp $
+ * $Id: group.h,v 1.3 2004/04/04 19:04:11 mdw Exp $
  *
  * General cyclic group abstraction
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: group.h,v $
+ * Revision 1.3  2004/04/04 19:04:11  mdw
+ * Raw I/O of elliptic curve points and group elements.
+ *
  * Revision 1.2  2004/04/03 03:32:05  mdw
  * General robustification.
  *
@@ -82,7 +85,7 @@
 typedef struct group_ {
   const struct group_ops *ops;         /* Operations table */
   size_t nbits;                                /* Size of an element in bits */
-  size_t noctets;                      /* Size of an element in octets */
+  size_t noctets;                      /* Size of raw element in octets */
   ge *i;                               /* Identity element */
   ge *g;                               /* Generator element */
   mp *r;                               /* Order of the generator */
@@ -140,6 +143,8 @@ typedef struct group_ops {
   int (*fromec)(group */*g*/, ge */*d*/, ec */*p*/);
   int (*tobuf)(group */*h*/, buf */*b*/, ge */*x*/);
   int (*frombuf)(group */*h*/, buf */*b*/, ge */*d*/);
+  int (*toraw)(group */*h*/, buf */*b*/, ge */*x*/);
+  int (*fromraw)(group */*h*/, buf */*b*/, ge */*d*/);
 
 } group_ops;
 
@@ -177,6 +182,8 @@ enum {
 #define G_FROMEC(g, d, p)      (g)->ops->fromec((g), (d), (p))
 #define G_TOBUF(g, b, x)       (g)->ops->tobuf((g), (b), (x))
 #define G_FROMBUF(g, b, d)     (g)->ops->frombuf((g), (b), (d))
+#define G_TORAW(g, b, x)       (g)->ops->toraw((g), (b), (x))
+#define G_FROMRAW(g, b, d)     (g)->ops->fromraw((g), (b), (d))
 
 /*----- Handy functions ---------------------------------------------------*/
 

diff --git a/tests/group b/tests/group
index eb9c1fa..0c2035a 100644 (file)
--- a/tests/group
+++ b/tests/group
@@ -1,4 +1,4 @@
-# $Id: group,v 1.1 2004/04/01 12:50:41 mdw Exp $
+# $Id: group,v 1.2 2004/04/04 19:04:11 mdw Exp $
 #
 # Test group abstraction, and a bunch of other things.
 
@@ -282,3 +282,39 @@ frombuf {
     "00010000188497a9fa119ff34c9c24a156ed0d44a0c5f5d1f19fc9f0eddead"
     29, "0, 0x8497a9fa119ff34c9c24a156ed0d44a0c5f5d1f19fc9f0ed";
 }
+
+toraw {
+  "prime { 29, 7, 16}" 22 -1 "";
+  "prime { 29, 7, 16}" 22 0 "16";
+  "prime { 29, 7, 16}" 0 -1 "";
+  "prime { 29, 7, 16}" 0 0 "00";
+  "prime { 4294967311, 364289, 18767 }" 4285559121 0 "00ff707151";
+  "prime { 4294967311, 364289, 18767 }" 4285559121 -1 "ff707151";
+
+  "ec { secp112r1 }" inf 0 "00";
+  "ec { secp112r1 }"
+    "0x09487239995a5ee76b55f9c2f098, 0xa89ce5af8724c0a23e0e0ff77500"
+    0 "0409487239995a5ee76b55f9c2f098a89ce5af8724c0a23e0e0ff77500";      
+  "ec { nist-p192 }"
+    "0, 0x8497a9fa119ff34c9c24a156ed0d44a0c5f5d1f19fc9f0ed"
+    0 "040000000000000000000000000000000000000000000000008497a9fa119ff34c9c24a156ed0d44a0c5f5d1f19fc9f0ed";
+}
+
+fromraw {
+  "prime { 29, 7, 16}" "" -1 0;
+  "prime { 29, 7, 16}" "160bad" 1 22;
+  "prime { 29, 7, 16}" "00" 1 0;
+  "prime { 4294967311, 364289, 18767 }" "00ff707151e7c0" 5 4285559121;
+  "prime { 4294967311, 364289, 18767 }" "ff707151" -1 0;
+
+  "ec { secp112r1 }" "" -1 inf;
+  "ec { secp112r1 }" "00" 1 inf;
+  "ec { secp112r1 }"
+    "0409487239995a5ee76b55f9c2f098a89ce5af8724c0a23e0e0ff775" -1 inf;
+  "ec { secp112r1 }"
+    "0409487239995a5ee76b55f9c2f098a89ce5af8724c0a23e0e0ff77500"
+    29 "0x09487239995a5ee76b55f9c2f098, 0xa89ce5af8724c0a23e0e0ff77500";
+  "ec { nist-p192 }"
+    "070000000000000000000000000000000000000000000000008497a9fa119ff34c9c24a156ed0d44a0c5f5d1f19fc9f0ed00deadbeef"
+    49 "0, 0x8497a9fa119ff34c9c24a156ed0d44a0c5f5d1f19fc9f0ed";
+}