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

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+/* -*-c-*-
+ *
+ * Finding primitive elements
+ *
+ * (c) 1999 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.
+ */
+
+#ifndef CATACOMB_PRIM_H
+#define CATACOMB_PRIM_H
+
+#ifdef __cplusplus
+  extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#include <stddef.h>
+
+#ifndef CATACOMB_MP_H
+#  include "mp.h"
+#endif
+
+#ifndef CATACOMB_MPMONT_H
+#  include "mpmont.h"
+#endif
+
+#ifndef CATACOMB_PGEN_H
+#  include "pgen.h"
+#endif
+
+/*----- Data structures ---------------------------------------------------*/
+
+/* --- @prim_ctx@ --- *
+ *
+ * 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 *exp;				/* Exponent (%$p/o$%; may be zero) */
+  size_t n;				/* Number of cofactors */
+  mp **f;				/* Array of cofactors */
+} prim_ctx;
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @prim_test@ --- */
+
+extern pgen_proc prim_test;
+
+/* --- @prim_step@ --- */
+
+extern pgen_proc prim_step;
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+  }
+#endif
+
+#endif