From 6f80d39fee0e2c8756d0e57fee709d9deffd9503 Mon Sep 17 00:00:00 2001
From: mdw <mdw>
Date: Sat, 29 Jul 2000 09:57:42 +0000
Subject: [PATCH] Improve primitive-element testing a lot.  Now much more
 sensible and orthogonal: you can find a generator for any given subgroup
 order by putting in the appropriate parameters.

---
 prim.c | 43 +++++++++++++++++++++++++++++--------------
 prim.h | 19 ++++++++++++++++---
 2 files changed, 45 insertions(+), 17 deletions(-)

diff --git a/prim.c b/prim.c
index bdad98b..31ef919 100644
--- a/prim.c
+++ b/prim.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: prim.c,v 1.1 1999/12/22 15:58:59 mdw Exp $
+ * $Id: prim.c,v 1.2 2000/07/29 09:57:42 mdw Exp $
  *
  * Finding primitive elements
  *
@@ -30,6 +30,11 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: prim.c,v $
+ * Revision 1.2  2000/07/29 09:57:42  mdw
+ * Improve primitive-element testing a lot.  Now much more sensible and
+ * orthogonal: you can find a generator for any given subgroup order by
+ * putting in the appropriate parameters.
+ *
  * Revision 1.1  1999/12/22 15:58:59  mdw
  * Search for primitive elements using prime-search equipment.
  *
@@ -57,27 +62,37 @@ int prim_test(int rq, pgen_event *ev, void *p)
     case PGEN_BEGIN:
       return (PGEN_TRY);
     case PGEN_TRY: {
-      mp *x = MP_NEW;
-      mp *f = c->f;
+      mp *x;
       rc = PGEN_FAIL;
 
-      x = mpmont_exp(&c->mm, x, ev->m, f);
-      if (MP_CMP(x, ==, MP_ONE))
-	goto done;
-      if (c->n == 0) {
-	mp_drop(ev->m);
-	ev->m = MP_COPY(x);
-      } else {
-	size_t n = c->n - 1;
-	f++;
+      if (!c->exp)
+        x = mp_copy(ev->m);
+      else {
+	x = mpmont_exp(&c->mm, MP_NEW, ev->m, c->exp);
+	if (MP_CMP(x, ==, MP_ONE))
+	  goto done;
+      }
+      if (c->n == 0)
+        goto ok;
+      else {
+	size_t n = c->n;
+	mp **f = c->f;
+	mp *y = MP_NEW;
 	while (n) {
-	  x = mpmont_exp(&c->mm, x, ev->m, f);
-	  if (MP_CMP(x, ==, MP_ONE))
+	  y = mpmont_exp(&c->mm, y, x, *f);
+	  if (MP_CMP(y, ==, MP_ONE)) {
+	    mp_drop(y);
 	    goto done;
+	  }
 	  n--; f++;
 	}
+	mp_drop(y);
       }
+    ok:
       rc = PGEN_DONE;
+      mp_drop(ev->m);
+      ev->m = x;
+      break;
     done:
       mp_drop(x);
     } break;
diff --git a/prim.h b/prim.h
index 30392cd..90b1156 100644
--- a/prim.h
+++ b/prim.h
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: prim.h,v 1.1 1999/12/22 15:58:59 mdw Exp $
+ * $Id: prim.h,v 1.2 2000/07/29 09:57:42 mdw Exp $
  *
  * Finding primitive elements
  *
@@ -30,6 +30,11 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: prim.h,v $
+ * Revision 1.2  2000/07/29 09:57:42  mdw
+ * Improve primitive-element testing a lot.  Now much more sensible and
+ * orthogonal: you can find a generator for any given subgroup order by
+ * putting in the appropriate parameters.
+ *
  * Revision 1.1  1999/12/22 15:58:59  mdw
  * Search for primitive elements using prime-search equipment.
  *
@@ -64,12 +69,20 @@
  *
  * All fields must be configured by the client.  Set @n@ to zero to discover
  * generators of the subgroup of order %$m / f$%.
+ *
+ * Let %$p = \prod q_i + 1$% be a prime number.  In order to find an element
+ * %$g$% with order %$o$%, we choose elements %$h_j$% from %$\gf{p}^*$%,
+ * compute $%g_j = h_j^{p/o}$%, rejecting %$h_j$% where %$g_j = 1$%, and then
+ * for each proper prime factor %$q_i$% of %$p/o$% we check that
+ * %$g^{f_i} \ne 1$%, where the %$f_i$% are cofactors of the %$q_i$%
+ * (%$f_i q_i = p/o$%).
  */
 
 typedef struct prim_ctx {
   mpmont mm;				/* Montgomery context for modulus */
-  mp *f;				/* Array of factors */
-  size_t n;				/* Number of factors */
+  mp *exp;				/* Exponent (%$p/o$%; may be zero) */
+  size_t n;				/* Number of cofactors */
+  mp **f;				/* Array of cofactors */
 } prim_ctx;
 
 /*----- Functions provided ------------------------------------------------*/
-- 
2.11.0