/* -*-c-*-
*
- * $Id: f-prime.c,v 1.3.4.1 2003/06/10 13:43:53 mdw Exp $
+ * $Id: f-prime.c,v 1.9 2004/04/01 21:28:41 mdw Exp $
*
* Prime fields with Montgomery arithmetic
*
/*----- Revision history --------------------------------------------------*
*
* $Log: f-prime.c,v $
+ * Revision 1.9 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 1.8 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 1.7 2004/03/27 17:54:11 mdw
+ * Standard curves and curve checking.
+ *
+ * Revision 1.6 2004/03/23 15:19:32 mdw
+ * Test elliptic curves more thoroughly.
+ *
+ * Revision 1.5 2004/03/23 12:08:26 mdw
+ * Random field-element selection.
+ *
+ * Revision 1.4 2004/03/21 22:52:06 mdw
+ * Merge and close elliptic curve branch.
+ *
+ * Revision 1.3.4.3 2004/03/21 22:39:46 mdw
+ * Elliptic curves on binary fields work.
+ *
+ * Revision 1.3.4.2 2004/03/20 00:13:31 mdw
+ * Projective coordinates for prime curves
+ *
* Revision 1.3.4.1 2003/06/10 13:43:53 mdw
* Simple (non-projective) curves over prime fields now seem to work.
*
#include "field.h"
#include "mpmont.h"
+#include "mprand.h"
-/*----- Data structures ---------------------------------------------------*/
+/*----- Main code ---------------------------------------------------------*/
typedef struct fctx {
field f;
mpmont mm;
} fctx;
-/*----- Main code ---------------------------------------------------------*/
-
/* --- Field operations --- */
static void fdestroy(field *ff)
-{
- fctx *f = (fctx *)ff;
- mpmont_destroy(&f->mm);
- DESTROY(f);
-}
+ { fctx *f = (fctx *)ff; mpmont_destroy(&f->mm); DESTROY(f); }
-static mp *fin(field *ff, mp *d, mp *x)
-{
+static mp *frand(field *ff, mp *d, grand *r)
+ { fctx *f = (fctx *)ff; return (mprand_range(d, f->mm.m, r, 0)); }
+
+static mp *fin(field *ff, mp *d, mp *x) {
fctx *f = (fctx *)ff;
mp_div(0, &d, x, f->mm.m);
return (mpmont_mul(&f->mm, d, d, f->mm.r2));
}
static mp *fout(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- return (mpmont_reduce(&f->mm, d, x));
-}
+ { fctx *f = (fctx *)ff; return (mpmont_reduce(&f->mm, d, x)); }
+
+static int fzerop(field *ff, mp *x) { return (!MP_LEN(x)); }
static mp *fneg(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- return (mp_sub(d, f->mm.m, x));
-}
+ { fctx *f = (fctx *)ff; return (mp_sub(d, f->mm.m, x)); }
-static mp *fadd(field *ff, mp *d, mp *x, mp *y)
-{
- fctx *f = (fctx *)ff;
- d = mp_add(d, x, y);
- if (d->f & MP_NEG)
- d = mp_add(d, d, f->mm.m);
- else if (MP_CMP(d, >, f->mm.m))
- d = mp_sub(d, d, f->mm.m);
+static mp *fadd(field *ff, mp *d, mp *x, mp *y) {
+ fctx *f = (fctx *)ff; d = mp_add(d, x, y);
+ if (d->f & MP_NEG) d = mp_add(d, d, f->mm.m);
+ else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
return (d);
}
-static mp *fsub(field *ff, mp *d, mp *x, mp *y)
-{
- fctx *f = (fctx *)ff;
- d = mp_sub(d, x, y);
- if (d->f & MP_NEG)
- d = mp_add(d, d, f->mm.m);
- else if (MP_CMP(d, >, f->mm.m))
- d = mp_sub(d, d, f->mm.m);
+static mp *fsub(field *ff, mp *d, mp *x, mp *y) {
+ fctx *f = (fctx *)ff; d = mp_sub(d, x, y);
+ if (d->f & MP_NEG) d = mp_add(d, d, f->mm.m);
+ else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
return (d);
}
static mp *fmul(field *ff, mp *d, mp *x, mp *y)
-{
- fctx *f = (fctx *)ff;
- return (mpmont_mul(&f->mm, d, x, y));
-}
+ { fctx *f = (fctx *)ff; return (mpmont_mul(&f->mm, d, x, y)); }
-static mp *fsqr(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- d = mp_sqr(d, x);
+static mp *fsqr(field *ff, mp *d, mp *x) {
+ fctx *f = (fctx *)ff; d = mp_sqr(d, x);
return (mpmont_reduce(&f->mm, d, d));
}
-static mp *finv(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- d = mpmont_reduce(&f->mm, d, x);
- mp_gcd(0, 0, &d, f->mm.m, d);
- return (mpmont_mul(&f->mm, d, d, f->mm.r2));
+static mp *finv(field *ff, mp *d, mp *x) {
+ fctx *f = (fctx *)ff; d = mpmont_reduce(&f->mm, d, x);
+ mp_gcd(0, 0, &d, f->mm.m, d); return (mpmont_mul(&f->mm, d, d, f->mm.r2));
}
static mp *freduce(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- mp_div(0, &d, x, f->mm.m);
- return (d);
+ { fctx *f = (fctx *)ff; mp_div(0, &d, x, f->mm.m); return (d); }
+
+static mp *fsqrt(field *ff, mp *d, mp *x) {
+ fctx *f = (fctx *)ff; d = mpmont_reduce(&f->mm, d, x);
+ d = mp_modsqrt(d, d, f->mm.m); if (!d) return (d);
+ return (mpmont_mul(&f->mm, d, d, f->mm.r2));
}
-static mp *fdbl(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- d = mp_lsl(d, x, 1);
- if (MP_CMP(d, >, f->mm.m))
- d = mp_sub(d, d, f->mm.m);
+static mp *fdbl(field *ff, mp *d, mp *x) {
+ fctx *f = (fctx *)ff; d = mp_lsl(d, x, 1);
+ if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
return (d);
}
-static mp *ftpl(field *ff, mp *d, mp *x)
-{
- fctx *f = (fctx *)ff;
- MP_DEST(d, MP_LEN(x) + 1, x->f);
+static mp *ftpl(field *ff, mp *d, mp *x) {
+ fctx *f = (fctx *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f);
MPX_UMULN(d->v, d->vl, x->v, x->vl, 3);
- while (MP_CMP(d, >, f->mm.m))
- d = mp_sub(d, d, f->mm.m);
+ while (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
return (d);
}
-static mp *fsqrt(field *ff, mp *d, mp *x)
-{
+static mp *fqdl(field *ff, mp *d, mp *x) {
+ fctx *f = (fctx *)ff; d = mp_lsl(d, x, 2);
+ while (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
+ return (d);
+}
+
+static mp *fhlv(field *ff, mp *d, mp *x) {
fctx *f = (fctx *)ff;
- d = mpmont_reduce(&f->mm, d, x);
- d = mp_modsqrt(d, d, f->mm.m);
- return (mpmont_mul(&f->mm, d, d, f->mm.r2));
+ if (!MP_LEN(x)) { MP_COPY(x); MP_DROP(d); return (x); }
+ if (x->v[0] & 1) { d = mp_add(d, x, f->mm.m); x = d; }
+ return (mp_lsr(d, x, 1));
}
/* --- Field operations table --- */
static field_ops fops = {
- fdestroy,
+ FTY_PRIME, "prime",
+ fdestroy, frand, field_stdsamep,
fin, fout,
- fneg, fadd, fsub, fmul, fsqr, finv, freduce,
- fdbl, ftpl, fsqrt
+ fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
+ 0,
+ fdbl, ftpl, fqdl, fhlv
};
/* --- @field_prime@ --- *
mpmont_create(&f->mm, p);
f->f.zero = MP_ZERO;
f->f.one = f->mm.r;
+ f->f.m = f->mm.m;
+ f->f.nbits = mp_bits(p);
+ f->f.noctets = (f->f.nbits + 7) >> 3;
return (&f->f);
}