/* -*-c-*-
*
- * $Id: f-binpoly.c,v 1.5 2004/03/27 17:54:11 mdw Exp $
+ * $Id: f-binpoly.c,v 1.8 2004/04/02 01:03:49 mdw Exp $
*
* Binary fields with polynomial basis representation
*
/*----- Revision history --------------------------------------------------*
*
* $Log: f-binpoly.c,v $
+ * Revision 1.8 2004/04/02 01:03:49 mdw
+ * Miscellaneous constification.
+ *
+ * Revision 1.7 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
+ * for repeated constants.
+ *
+ * Revision 1.6 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.
+ * Generally ensure that negative exponents do inversion correctly. Add
+ * table of standard prime-field subgroups. (Binary field subgroups are
+ * currently unimplemented but easy to add if anyone ever finds a good one.)
+ *
* Revision 1.5 2004/03/27 17:54:11 mdw
* Standard curves and curve checking.
*
#include "gf.h"
#include "gfreduce.h"
#include "mprand.h"
+#include "gfn.h"
-/*----- Data structures ---------------------------------------------------*/
+/*----- Polynomial basis --------------------------------------------------*/
typedef struct fctx {
field f;
gfreduce r;
} fctx;
-/*----- Main code ---------------------------------------------------------*/
-
/* --- Field operations --- */
static void fdestroy(field *ff)
-{
- fctx *f = (fctx *)ff;
- gfreduce_destroy(&f->r);
- DESTROY(f);
-}
+ { fctx *f = (fctx *)ff; gfreduce_destroy(&f->r); DESTROY(f); }
static mp *frand(field *f, mp *d, grand *r)
-{
- return (mprand(d, f->nbits, r, 0));
-}
+ { return (mprand(d, f->nbits, r, 0)); }
-static int fzerop(field *ff, mp *x)
-{
- return (!MP_LEN(x));
-}
+static int fzerop(field *ff, mp *x) { return (!MP_LEN(x)); }
-static mp *fadd(field *ff, mp *d, mp *x, mp *y)
-{
- return (gf_add(d, x, y));
-}
+static mp *fadd(field *ff, mp *d, mp *x, mp *y) { return (gf_add(d, x, y)); }
-static mp *fmul(field *ff, mp *d, mp *x, mp *y)
-{
- fctx *f = (fctx *)ff;
- d = gf_mul(d, x, y);
+static mp *fmul(field *ff, mp *d, mp *x, mp *y) {
+ fctx *f = (fctx *)ff; d = gf_mul(d, x, y);
return (gfreduce_do(&f->r, d, d));
}
-static mp *fsqr(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- d = gf_sqr(d, x);
+static mp *fsqr(field *ff, mp *d, mp *x) {
+ fctx *f = (fctx *)ff; d = gf_sqr(d, x);
return (gfreduce_do(&f->r, d, d));
}
static mp *finv(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- gf_gcd(0, 0, &d, f->r.p, x);
- return (d);
-}
+ { fctx *f = (fctx *)ff; gf_gcd(0, 0, &d, f->r.p, x); return (d); }
static mp *freduce(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- return (gfreduce_do(&f->r, d, x));
-}
+ { fctx *f = (fctx *)ff; return (gfreduce_do(&f->r, d, x)); }
static mp *fsqrt(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- return (gfreduce_sqrt(&f->r, d, x));
-}
+ { fctx *f = (fctx *)ff; return (gfreduce_sqrt(&f->r, d, x)); }
static mp *fquadsolve(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- return (gfreduce_quadsolve(&f->r, d, x));
-}
+ { fctx *f = (fctx *)ff; return (gfreduce_quadsolve(&f->r, d, x)); }
/* --- Field operations table --- */
-static field_ops fops = {
+static const field_ops fops = {
FTY_BINARY, "binpoly",
- fdestroy, frand,
+ fdestroy, frand, field_stdsamep,
freduce, field_id,
fzerop, field_id, fadd, fadd, fmul, fsqr, finv, freduce, fsqrt,
fquadsolve,
return (&f->f);
}
+/*----- Normal basis ------------------------------------------------------*/
+
+typedef struct fnctx {
+ fctx f;
+ gfn ntop, pton;
+} fnctx;
+
+/* --- Field operations --- */
+
+static void fndestroy(field *ff) {
+ fnctx *f = (fnctx *)ff; gfreduce_destroy(&f->f.r);
+ gfn_destroy(&f->ntop); gfn_destroy(&f->pton);
+ DESTROY(f);
+}
+
+static int fnsamep(field *ff, field *gg) {
+ fnctx *f = (fnctx *)ff, *g = (fnctx *)gg;
+ return (MP_EQ(f->ntop.r[0], g->ntop.r[0]) && field_stdsamep(ff, gg));
+}
+
+static mp *fnin(field *ff, mp *d, mp *x)
+ { fnctx *f = (fnctx *)ff; return (gfn_transform(&f->ntop, d, x)); }
+
+static mp *fnout(field *ff, mp *d, mp *x)
+ { fnctx *f = (fnctx *)ff; return (gfn_transform(&f->pton, d, x)); }
+
+/* --- Field operations table --- */
+
+static const field_ops fnops = {
+ FTY_BINARY, "binnorm",
+ fndestroy, frand, fnsamep,
+ fnin, fnout,
+ fzerop, field_id, fadd, fadd, fmul, fsqr, finv, freduce, fsqrt,
+ fquadsolve,
+ 0, 0, 0, 0
+};
+
+/* --- @field_binnorm@ --- *
+ *
+ * Arguments: @mp *p@ = the reduction polynomial
+ * @mp *beta@ = representation of normal point
+ *
+ * Returns: A pointer to the field.
+ *
+ * Use: Creates a field structure for a binary field mod @p@ which
+ * uses a normal basis representation externally. Computations
+ * are still done on a polynomial-basis representation.
+ */
+
+field *field_binnorm(mp *p, mp *beta)
+{
+ fnctx *f = CREATE(fnctx);
+ f->f.f.ops = &fnops;
+ f->f.f.zero = MP_ZERO;
+ f->f.f.one = MP_ONE;
+ f->f.f.nbits = mp_bits(p) - 1;
+ f->f.f.noctets = (f->f.f.nbits + 7) >> 3;
+ gfreduce_create(&f->f.r, p);
+ f->f.f.m = f->f.r.p;
+ gfn_create(p, beta, &f->ntop, &f->pton);
+ return (&f->f.f);
+}
+
/*----- That's all, folks -------------------------------------------------*/