Commit a79c2ac5 authored by Niels Möller's avatar Niels Möller

Implemented point addition for Edwards curves.

parent 47dffbfb
2014-07-14 Niels Möller <nisse@lysator.liu.se>
* ecc-add-ehh.c (ecc_add_ehh, ecc_add_ehh_itch): New file, new
functions.
* ecc.h (ecc_add_ehh, ecc_add_ehh_itch): Declare them.
* ecc-internal.h (ECC_ADD_EHH_ITCH): New macro.
* Makefile.in (hogweed_SOURCES): Added ecc-add-ehh.c.
* ecc-25519.c (nettle_curve25519): Use ecc_d instead of ecc_b.
* eccdata.c: For curve25519, output the Edwards curve constant,
ecc_d = (121665/121666) mod p.
......
......@@ -167,7 +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-dup-eh.c ecc-add-ehh.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 \
......
......@@ -75,7 +75,7 @@ const struct ecc_curve nettle_curve25519 =
ECC_PIPPENGER_K,
ECC_PIPPENGER_C,
ecc_p,
ecc_b,
ecc_d, /* Use the Edwards curve constant. */
ecc_q,
ecc_g,
ecc_redc_g,
......
/* ecc-add-ehh.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_add_ehh_itch (const struct ecc_curve *ecc)
{
return ECC_ADD_EHH_ITCH (ecc->size);
}
/* Add two points on an Edwards curve, in homogeneous coordinates */
void
ecc_add_ehh (const struct ecc_curve *ecc,
mp_limb_t *r, const mp_limb_t *p, const mp_limb_t *q,
mp_limb_t *scratch)
{
#define x1 p
#define y1 (p + ecc->size)
#define z1 (p + 2*ecc->size)
#define x2 q
#define y2 (q + ecc->size)
#define z2 (q + 2*ecc->size)
#define x3 r
#define y3 (r + ecc->size)
#define z3 (r + 2*ecc->size)
/* Formulas (from djb,
http://www.hyperelliptic.org/EFD/g1p/auto-edwards-projective.html#doubling-dbl-2007-bl):
Computation Operation Live variables
A = z1*z2 mul A
B = A^2 sqr A, B
C = x1*x2 mul A, B, C
D = y1*y2 mul A, B, C, D
E = b*C*D 2 mul A, B, C, D, E
F = B - E A, B, C, D, E, F
G = B + E A, C, D, F, G
x3 = a*f*[(x1+y1)(x2+y2) - c - d] 3 mul A, C, D, G
y3 = a*g*(d-c) 2 mul F, G
z3 = f*g mul
*/
#define A scratch
#define B (scratch + ecc->size)
#define C (scratch + 2*ecc->size)
#define D (scratch + 3*ecc->size)
#define E (scratch + 4*ecc->size)
#define F (scratch + 5*ecc->size)
#define G (scratch + 6*ecc->size)
#define T (scratch + 7*ecc->size)
ecc_modp_mul (ecc, A, z1, z2);
ecc_modp_sqr (ecc, B, A);
ecc_modp_mul (ecc, C, x1, x2);
ecc_modp_mul (ecc, D, y1, y2);
ecc_modp_mul (ecc, T, C, D);
ecc_modp_mul (ecc, E, T, ecc->b);
ecc_modp_sub (ecc, F, B, E);
ecc_modp_add (ecc, G, B, E);
/* x3 */
ecc_modp_add (ecc, B, x1, y1);
ecc_modp_add (ecc, E, x2, y2);
ecc_modp_mul (ecc, T, B, E);
ecc_modp_sub (ecc, T, T, C);
ecc_modp_sub (ecc, x3, T, D);
ecc_modp_mul (ecc, T, x3, A);
ecc_modp_mul (ecc, x3, T, F);
/* y3 */
ecc_modp_sub (ecc, C, D, C);
ecc_modp_mul (ecc, T, A, C);
ecc_modp_mul (ecc, y3, T, G);
/* z3 */
ecc_modp_mul (ecc, T, F, G);
mpn_copyi (z3, T, ecc->size);
}
......@@ -242,6 +242,7 @@ sec_modinv (mp_limb_t *vp, mp_limb_t *ap, mp_size_t n,
#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_ADD_EHH_ITCH(size) (9*(size))
#define ECC_MUL_G_ITCH(size) (9*(size))
#if ECC_MUL_A_WBITS == 0
#define ECC_MUL_A_ITCH(size) (12*(size))
......
......@@ -71,6 +71,8 @@ extern "C" {
#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_add_ehh_itch nettle_ecc_add_ehh_itch
#define ecc_add_ehh nettle_ecc_add_ehh
#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
......@@ -243,6 +245,13 @@ ecc_dup_eh (const struct ecc_curve *ecc,
mp_limb_t *r, const mp_limb_t *p,
mp_limb_t *scratch);
mp_size_t
ecc_add_ehh_itch (const struct ecc_curve *ecc);
void
ecc_add_ehh (const struct ecc_curve *ecc,
mp_limb_t *r, const mp_limb_t *p, const mp_limb_t *q,
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,
and the algorithm can work without any intermediate values getting
......
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