/* -*-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
*
/*----- 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.
*
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;
/* -*-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
*
/*----- 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.
*
*
* 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 ------------------------------------------------*/