X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/f1140c41e9297d14386ee18fbed7a9686d223024..813390c45f438f411662b1a55678e63f11681eb4:/mp-modsqrt.c

diff --git a/mp-modsqrt.c b/mp-modsqrt.c
index 6c21dc4..1791185 100644
--- a/mp-modsqrt.c
+++ b/mp-modsqrt.c
@@ -1,13 +1,13 @@
 /* -*-c-*-
  *
- * $Id: mp-modsqrt.c,v 1.3 2001/02/03 12:00:29 mdw Exp $
+ * $Id: mp-modsqrt.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
  *
  * Compute square roots modulo a prime
  *
  * (c) 2000 Straylight/Edgeware
  */
 
-/*----- Licensing notice --------------------------------------------------* 
+/*----- Licensing notice --------------------------------------------------*
  *
  * This file is part of Catacomb.
  *
@@ -15,33 +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: mp-modsqrt.c,v $
- * Revision 1.3  2001/02/03 12:00:29  mdw
- * Now @mp_drop@ checks its argument is non-NULL before attempting to free
- * it.  Note that the macro version @MP_DROP@ doesn't do this.
- *
- * Revision 1.2  2000/10/08 12:02:21  mdw
- * Use @MP_EQ@ instead of @MP_CMP@.
- *
- * Revision 1.1  2000/06/22 19:01:31  mdw
- * Compute square roots in a prime field.
- *
- */
-
 /*----- Header files ------------------------------------------------------*/
 
 #include "fibrand.h"
@@ -66,6 +51,9 @@
  *		work if %$p$% is composite: you must factor the modulus, take
  *		a square root mod each factor, and recombine the results
  *		using the Chinese Remainder Theorem.
+ *
+ *		We guarantee that the square root returned is the smallest
+ *		one (i.e., the `positive' square root).
  */
 
 mp *mp_modsqrt(mp *d, mp *a, mp *p)
@@ -100,9 +88,8 @@ mp *mp_modsqrt(mp *d, mp *a, mp *p)
 
   /* --- Find the inverse of %$a$% --- */
 
-  ainv = MP_NEW;
-  mp_gcd(0, &ainv, 0, a, p);
-  
+  ainv = mp_modinv(MP_NEW, a, p);
+
   /* --- Split %$p - 1$% into a power of two and an odd number --- */
 
   t = mp_sub(MP_NEW, p, MP_ONE);
@@ -111,10 +98,13 @@ mp *mp_modsqrt(mp *d, mp *a, mp *p)
   /* --- Now to really get going --- */
 
   mpmont_create(&mm, p);
+  b = mpmont_mul(&mm, b, b, mm.r2);
   c = mpmont_expr(&mm, b, b, t);
   t = mp_add(t, t, MP_ONE);
   t = mp_lsr(t, t, 1);
-  r = mpmont_expr(&mm, t, a, t);
+  dd = mpmont_mul(&mm, MP_NEW, a, mm.r2);
+  r = mpmont_expr(&mm, t, dd, t);
+  mp_drop(dd);
   ainv = mpmont_mul(&mm, ainv, ainv, mm.r2);
 
   mone = mp_sub(MP_NEW, p, mm.r);
@@ -129,7 +119,7 @@ mp *mp_modsqrt(mp *d, mp *a, mp *p)
     dd = mpmont_reduce(&mm, dd, dd);
     dd = mpmont_mul(&mm, dd, dd, ainv);
 
-    /* --- Now %$d = d_0^{s - i - 1}$% --- */
+    /* --- Now %$d = d_0^{2^{s - i - 1}}$% --- */
 
     for (j = i; j < s - 1; j++) {
       dd = mp_sqr(dd, dd);
@@ -144,9 +134,14 @@ mp *mp_modsqrt(mp *d, mp *a, mp *p)
     c = mpmont_reduce(&mm, c, c);
   }
 
-  /* --- Done, so tidy up --- */
+  /* --- Done, so tidy up --- *
+   *
+   * Canonify the answer.
+   */
 
   d = mpmont_reduce(&mm, d, r);
+  r = mp_sub(r, p, d);
+  if (MP_CMP(r, <, d)) { mp *tt = r; r = d; d = tt; }
   mp_drop(ainv);
   mp_drop(r); mp_drop(c);
   mp_drop(dd);
@@ -174,22 +169,17 @@ static int verify(dstr *v)
     ok = 0;
   else if (MP_EQ(r, rr))
     ok = 1;
-  else {
-    r = mp_sub(r, p, r);
-    if (MP_EQ(r, rr))
-      ok = 1;
-  }
 
   if (!ok) {
     fputs("\n*** fail\n", stderr);
     fputs("a  = ", stderr); mp_writefile(a, stderr, 10); fputc('\n', stderr);
     fputs("p  = ", stderr); mp_writefile(p, stderr, 10); fputc('\n', stderr);
     if (r) {
-      fputs("r  = ", stderr);
+      fputs("r	= ", stderr);
       mp_writefile(r, stderr, 10);
       fputc('\n', stderr);
     } else
-      fputs("r  = <undef>\n", stderr);
+      fputs("r	= <undef>\n", stderr);
     fputs("rr = ", stderr); mp_writefile(rr, stderr, 10); fputc('\n', stderr);
     ok = 0;
   }