Commit f51f6335 authored by Niels Möller's avatar Niels Möller

Implemented point doubling for Edwards curves.

parent ff2c93c0
2014-07-11 Niels Möller <nisse@lysator.liu.se>
* ecc-dup-eh.c (ecc_dup_eh, ecc_dup_eh_itch): New file, new functions.
* ecc-eh-to-a.c (ecc_eh_to_a, ecc_eh_to_a_itch): New file, new
functions.
* ecc.h: Declare new functions.
* ecc-internal.h (ECC_EH_TO_A_ITCH, ECC_DUP_EH_ITCH): New macros.
* Makefile.in (hogweed_SOURCES): Added ecc-dup-eh.c and
ecc-eh-to-a.c.
* ecc-internal.h (struct ecc_curve): New constant edwards_root.
* ecc-192.c (nettle_secp_192r1): Updated accordingly, additional
NULL pointer.
......
......@@ -167,6 +167,7 @@ hogweed_SOURCES = sexp.c sexp-format.c \
ecc-25519.c \
ecc-size.c ecc-j-to-a.c ecc-a-to-j.c \
ecc-dup-jj.c ecc-add-jja.c ecc-add-jjj.c \
ecc-dup-eh.c ecc-eh-to-a.c \
ecc-mul-g.c ecc-mul-a.c ecc-hash.c ecc-random.c \
ecc-point.c ecc-scalar.c ecc-point-mul.c ecc-point-mul-g.c \
ecc-ecdsa-sign.c ecdsa-sign.c \
......
/* ecc-dup-eh.c
Copyright (C) 2014 Niels Möller
This file is part of GNU Nettle.
GNU Nettle is free software: you can redistribute it and/or
modify it under the terms of either:
* the GNU Lesser General Public License as published by the Free
Software Foundation; either version 3 of the License, or (at your
option) any later version.
or
* the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your
option) any later version.
or both in parallel, as here.
GNU Nettle 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
General Public License for more details.
You should have received copies of the GNU General Public License and
the GNU Lesser General Public License along with this program. If
not, see http://www.gnu.org/licenses/.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include "ecc.h"
#include "ecc-internal.h"
mp_size_t
ecc_dup_eh_itch (const struct ecc_curve *ecc)
{
return ECC_DUP_EH_ITCH (ecc->size);
}
/* Double a point on an Edwards curve, in homogeneous coordinates */
void
ecc_dup_eh (const struct ecc_curve *ecc,
mp_limb_t *r, const mp_limb_t *p,
mp_limb_t *scratch)
{
/* Formulas (from djb,
http://www.hyperelliptic.org/EFD/g1p/auto-edwards-projective.html#doubling-dbl-2007-bl):
Computation Operation Live variables
b = (x+y)^2 sqr b
c = x^2 sqr b, c
d = y^2 sqr b, c, d
e = c+d b, c, d, e
h = z^2 sqr b, c, d, e, h
j = e-2*h b, c, d, e, j
x' = (b-e)*j mul c, d, e, j
y' = e*(c-d) mul e, j
z' = e*j mul
*/
#define b scratch
#define c (scratch + ecc->size)
#define d (scratch + 2*ecc->size)
#define e (scratch + 3*ecc->size)
#define j (scratch + 4*ecc->size)
/* b */
ecc_modp_add (ecc, e, p, p + ecc->size);
ecc_modp_sqr (ecc, b, e);
/* c */
ecc_modp_sqr (ecc, c, p);
/* d */
ecc_modp_sqr (ecc, d, p + ecc->size);
/* h, can use r as scratch, even for in-place operation. */
ecc_modp_sqr (ecc, r, p + 2*ecc->size);
/* e, */
ecc_modp_add (ecc, e, c, d);
/* b - e */
ecc_modp_sub (ecc, b, b, e);
/* j */
ecc_modp_add (ecc, r, r, r);
ecc_modp_sub (ecc, j, e, r);
/* x' */
ecc_modp_mul (ecc, r, b, j);
/* y' */
ecc_modp_sub (ecc, c, c, d);
ecc_modp_mul (ecc, r + ecc->size, e, c);
/* z' */
ecc_modp_mul (ecc, b, e, j);
mpn_copyi (r + 2*ecc->size, b, ecc->size);
}
/* ecc-eh-to-a.c
Copyright (C) 2014 Niels Möller
This file is part of GNU Nettle.
GNU Nettle is free software: you can redistribute it and/or
modify it under the terms of either:
* the GNU Lesser General Public License as published by the Free
Software Foundation; either version 3 of the License, or (at your
option) any later version.
or
* the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your
option) any later version.
or both in parallel, as here.
GNU Nettle 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
General Public License for more details.
You should have received copies of the GNU General Public License and
the GNU Lesser General Public License along with this program. If
not, see http://www.gnu.org/licenses/.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include "ecc.h"
#include "ecc-internal.h"
mp_size_t
ecc_eh_to_a_itch (const struct ecc_curve *ecc)
{
/* Needs 2*ecc->size + scratch for ecc_modq_inv */
return ECC_EH_TO_A_ITCH (ecc->size);
}
/* Convert from homogeneous coordinates on the Edwards curve to affine
coordinates on the corresponding Montgomery curve. */
void
ecc_eh_to_a (const struct ecc_curve *ecc,
int flags,
mp_limb_t *r, const mp_limb_t *p,
mp_limb_t *scratch)
{
#define izp scratch
#define sp (scratch + ecc->size)
#define tp (scratch + 2*ecc->size)
#define xp r
#define yp (r + ecc->size)
#define up p
#define vp (p + ecc->size)
#define wp (p + 2*ecc->size)
/* x = (v+1)/(v-1), y = t x / u (with t = sqrt(b+2))
In homogeneous coordinates,
X = (W + V) U
Y = t (W + V) W
Z = (W - V) U
*/
/* FIXME: Simplify for common case that only x-coordinate is wanted. */
mp_limb_t cy;
ecc_modp_sub (ecc, izp, wp, vp);
/* FIXME: For the infinity point, this subtraction gives zero (mod
p), and the inversion below fails and returns something else. */
ecc_modp_mul (ecc, izp + ecc->size, izp, up);
/* Needs 3*size scratch */
ecc_modp_inv (ecc, izp, izp + ecc->size, izp + 2*ecc->size);
ecc_modp_add (ecc, sp, wp, vp);
ecc_modp_mul (ecc, tp, sp, up);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, izp);
cy = mpn_sub_n (xp, tp, ecc->p, ecc->size);
cnd_copy (cy, xp, tp, ecc->size);
if (flags & 2)
/* Skip y coordinate */
return;
ecc_modp_add (ecc, sp, wp, vp); /* FIXME: Redundant */
ecc_modp_mul (ecc, tp, sp, wp);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, ecc->edwards_root);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, izp);
cy = mpn_sub_n (yp, tp, ecc->p, ecc->size);
cnd_copy (cy, yp, tp, ecc->size);
}
......@@ -237,8 +237,9 @@ sec_modinv (mp_limb_t *vp, mp_limb_t *ap, mp_size_t n,
/* Current scratch needs: */
#define ECC_MODINV_ITCH(size) (3*(size))
#define ECC_J_TO_A_ITCH(size) (5*(size))
#define ECC_DUP_JA_ITCH(size) (5*(size))
#define ECC_EH_TO_A_ITCH(size) (5*(size))
#define ECC_DUP_JJ_ITCH(size) (5*(size))
#define ECC_DUP_EH_ITCH(size) (5*(size))
#define ECC_ADD_JJA_ITCH(size) (6*(size))
#define ECC_ADD_JJJ_ITCH(size) (8*(size))
#define ECC_MUL_G_ITCH(size) (9*(size))
......
......@@ -61,14 +61,16 @@ extern "C" {
#define ecc_a_to_j nettle_ecc_a_to_j
#define ecc_j_to_a_itch nettle_ecc_j_to_a_itch
#define ecc_j_to_a nettle_ecc_j_to_a
#define ecc_dup_ja_itch nettle_ecc_dup_ja_itch
#define ecc_dup_ja nettle_ecc_dup_ja
#define ecc_eh_to_a_itch nettle_ecc_eh_to_a_itch
#define ecc_eh_to_a nettle_ecc_eh_to_a
#define ecc_dup_jj_itch nettle_ecc_dup_jj_itch
#define ecc_dup_jj nettle_ecc_dup_jj
#define ecc_add_jja_itch nettle_ecc_add_jja_itch
#define ecc_add_jja nettle_ecc_add_jja
#define ecc_add_jjj_itch nettle_ecc_add_jjj_itch
#define ecc_add_jjj nettle_ecc_add_jjj
#define ecc_dup_eh_itch nettle_ecc_dup_eh_itch
#define ecc_dup_eh nettle_ecc_dup_eh
#define ecc_mul_g_itch nettle_ecc_mul_g_itch
#define ecc_mul_g nettle_ecc_mul_g
#define ecc_mul_a_itch nettle_ecc_mul_a_itch
......@@ -186,17 +188,18 @@ ecc_j_to_a (const struct ecc_curve *ecc,
mp_limb_t *r, const mp_limb_t *p,
mp_limb_t *scratch);
/* Group operations */
/* Converts a point P on an Edwards curve to affine coordinates on
the corresponding Montgomery curve. */
/* Point doubling, with jacobian output and affine input. Corner
cases: Correctly sets R = 0 (r_Z = 0) if p = 0 or 2p = 0. */
mp_size_t
ecc_dup_ja_itch (const struct ecc_curve *ecc);
ecc_eh_to_a_itch (const struct ecc_curve *ecc);
void
ecc_dup_ja (const struct ecc_curve *ecc,
mp_limb_t *r, const mp_limb_t *p,
mp_limb_t *scratch);
ecc_eh_to_a (const struct ecc_curve *ecc,
int flags,
mp_limb_t *r, const mp_limb_t *p,
mp_limb_t *scratch);
/* Group operations */
/* Point doubling, with jacobian input and output. Corner cases:
Correctly sets R = 0 (r_Z = 0) if p = 0 or 2p = 0. */
......@@ -230,6 +233,15 @@ ecc_add_jjj (const struct ecc_curve *ecc,
mp_limb_t *r, const mp_limb_t *p, const mp_limb_t *q,
mp_limb_t *scratch);
/* FIXME: Use a generic ecc_dup, ecc_add, for any type of curve. */
/* Point doubling on an Edwards curve, with homogeneous
cooordinates. */
mp_size_t
ecc_dup_eh_itch (const struct ecc_curve *ecc);
void
ecc_dup_eh (const struct ecc_curve *ecc,
mp_limb_t *r, const mp_limb_t *p,
mp_limb_t *scratch);
/* Computes N * the group generator. N is an array of ecc_size()
limbs. It must be in the range 0 < N < group order, then R != 0,
......
Markdown is supported
0%
or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment