721 lines
18 KiB
C
721 lines
18 KiB
C
/* ec.c - Elliptic Curve functions
|
||
Copyright (C) 2007 Free Software Foundation, Inc.
|
||
|
||
This file is part of Libgcrypt.
|
||
|
||
Libgcrypt is free software; you can redistribute it and/or modify
|
||
it under the terms of the GNU Lesser General Public License as
|
||
published by the Free Software Foundation; either version 2.1 of
|
||
the License, or (at your option) any later version.
|
||
|
||
Libgcrypt 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 Lesser General Public License for more details.
|
||
|
||
You should have received a copy of the GNU Lesser General Public
|
||
License along with this program; if not, write to the Free Software
|
||
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
|
||
USA. */
|
||
|
||
|
||
#include <config.h>
|
||
#include <stdio.h>
|
||
#include <stdlib.h>
|
||
|
||
#include "mpi-internal.h"
|
||
#include "longlong.h"
|
||
#include "g10lib.h"
|
||
|
||
|
||
#define point_init(a) _gcry_mpi_ec_point_init ((a))
|
||
#define point_free(a) _gcry_mpi_ec_point_free ((a))
|
||
|
||
|
||
/* Object to represent a point in projective coordinates. */
|
||
/* Currently defined in mpi.h */
|
||
|
||
/* This context is used with all our EC functions. */
|
||
struct mpi_ec_ctx_s
|
||
{
|
||
/* Domain parameters. */
|
||
gcry_mpi_t p; /* Prime specifying the field GF(p). */
|
||
gcry_mpi_t a; /* First coefficient of the Weierstrass equation. */
|
||
|
||
int a_is_pminus3; /* True if A = P - 3. */
|
||
|
||
/* Some often used constants. */
|
||
gcry_mpi_t one;
|
||
gcry_mpi_t two;
|
||
gcry_mpi_t three;
|
||
gcry_mpi_t four;
|
||
gcry_mpi_t eight;
|
||
gcry_mpi_t two_inv_p;
|
||
|
||
/* Scratch variables. */
|
||
gcry_mpi_t scratch[11];
|
||
|
||
/* Helper for fast reduction. */
|
||
/* int nist_nbits; /\* If this is a NIST curve, the number of bits. *\/ */
|
||
/* gcry_mpi_t s[10]; */
|
||
/* gcry_mpi_t c; */
|
||
|
||
};
|
||
|
||
|
||
|
||
/* Initialized a point object. gcry_mpi_ec_point_free shall be used
|
||
to release this object. */
|
||
void
|
||
_gcry_mpi_ec_point_init (mpi_point_t *p)
|
||
{
|
||
p->x = mpi_new (0);
|
||
p->y = mpi_new (0);
|
||
p->z = mpi_new (0);
|
||
}
|
||
|
||
|
||
/* Release a point object. */
|
||
void
|
||
_gcry_mpi_ec_point_free (mpi_point_t *p)
|
||
{
|
||
mpi_free (p->x); p->x = NULL;
|
||
mpi_free (p->y); p->y = NULL;
|
||
mpi_free (p->z); p->z = NULL;
|
||
}
|
||
|
||
/* Set the value from S into D. */
|
||
static void
|
||
point_set (mpi_point_t *d, mpi_point_t *s)
|
||
{
|
||
mpi_set (d->x, s->x);
|
||
mpi_set (d->y, s->y);
|
||
mpi_set (d->z, s->z);
|
||
}
|
||
|
||
|
||
|
||
static void
|
||
ec_addm (gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, mpi_ec_t ctx)
|
||
{
|
||
mpi_addm (w, u, v, ctx->p);
|
||
}
|
||
|
||
static void
|
||
ec_subm (gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, mpi_ec_t ctx)
|
||
{
|
||
mpi_subm (w, u, v, ctx->p);
|
||
}
|
||
|
||
static void
|
||
ec_mulm (gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, mpi_ec_t ctx)
|
||
{
|
||
#if 0
|
||
/* NOTE: This code works only for limb sizes of 32 bit. */
|
||
mpi_limb_t *wp, *sp;
|
||
|
||
if (ctx->nist_nbits == 192)
|
||
{
|
||
mpi_mul (w, u, v);
|
||
mpi_resize (w, 12);
|
||
wp = w->d;
|
||
|
||
sp = ctx->s[0]->d;
|
||
sp[0*2+0] = wp[0*2+0];
|
||
sp[0*2+1] = wp[0*2+1];
|
||
sp[1*2+0] = wp[1*2+0];
|
||
sp[1*2+1] = wp[1*2+1];
|
||
sp[2*2+0] = wp[2*2+0];
|
||
sp[2*2+1] = wp[2*2+1];
|
||
|
||
sp = ctx->s[1]->d;
|
||
sp[0*2+0] = wp[3*2+0];
|
||
sp[0*2+1] = wp[3*2+1];
|
||
sp[1*2+0] = wp[3*2+0];
|
||
sp[1*2+1] = wp[3*2+1];
|
||
sp[2*2+0] = 0;
|
||
sp[2*2+1] = 0;
|
||
|
||
sp = ctx->s[2]->d;
|
||
sp[0*2+0] = 0;
|
||
sp[0*2+1] = 0;
|
||
sp[1*2+0] = wp[4*2+0];
|
||
sp[1*2+1] = wp[4*2+1];
|
||
sp[2*2+0] = wp[4*2+0];
|
||
sp[2*2+1] = wp[4*2+1];
|
||
|
||
sp = ctx->s[3]->d;
|
||
sp[0*2+0] = wp[5*2+0];
|
||
sp[0*2+1] = wp[5*2+1];
|
||
sp[1*2+0] = wp[5*2+0];
|
||
sp[1*2+1] = wp[5*2+1];
|
||
sp[2*2+0] = wp[5*2+0];
|
||
sp[2*2+1] = wp[5*2+1];
|
||
|
||
ctx->s[0]->nlimbs = 6;
|
||
ctx->s[1]->nlimbs = 6;
|
||
ctx->s[2]->nlimbs = 6;
|
||
ctx->s[3]->nlimbs = 6;
|
||
|
||
mpi_add (ctx->c, ctx->s[0], ctx->s[1]);
|
||
mpi_add (ctx->c, ctx->c, ctx->s[2]);
|
||
mpi_add (ctx->c, ctx->c, ctx->s[3]);
|
||
|
||
while ( mpi_cmp (ctx->c, ctx->p ) >= 0 )
|
||
mpi_sub ( ctx->c, ctx->c, ctx->p );
|
||
mpi_set (w, ctx->c);
|
||
}
|
||
else if (ctx->nist_nbits == 384)
|
||
{
|
||
int i;
|
||
mpi_mul (w, u, v);
|
||
mpi_resize (w, 24);
|
||
wp = w->d;
|
||
|
||
#define NEXT(a) do { ctx->s[(a)]->nlimbs = 12; \
|
||
sp = ctx->s[(a)]->d; \
|
||
i = 0; } while (0)
|
||
#define X(a) do { sp[i++] = wp[(a)];} while (0)
|
||
#define X0(a) do { sp[i++] = 0; } while (0)
|
||
NEXT(0);
|
||
X(0);X(1);X(2);X(3);X(4);X(5);X(6);X(7);X(8);X(9);X(10);X(11);
|
||
NEXT(1);
|
||
X0();X0();X0();X0();X(21);X(22);X(23);X0();X0();X0();X0();X0();
|
||
NEXT(2);
|
||
X(12);X(13);X(14);X(15);X(16);X(17);X(18);X(19);X(20);X(21);X(22);X(23);
|
||
NEXT(3);
|
||
X(21);X(22);X(23);X(12);X(13);X(14);X(15);X(16);X(17);X(18);X(19);X(20);
|
||
NEXT(4);
|
||
X0();X(23);X0();X(20);X(12);X(13);X(14);X(15);X(16);X(17);X(18);X(19);
|
||
NEXT(5);
|
||
X0();X0();X0();X0();X(20);X(21);X(22);X(23);X0();X0();X0();X0();
|
||
NEXT(6);
|
||
X(20);X0();X0();X(21);X(22);X(23);X0();X0();X0();X0();X0();X0();
|
||
NEXT(7);
|
||
X(23);X(12);X(13);X(14);X(15);X(16);X(17);X(18);X(19);X(20);X(21);X(22);
|
||
NEXT(8);
|
||
X0();X(20);X(21);X(22);X(23);X0();X0();X0();X0();X0();X0();X0();
|
||
NEXT(9);
|
||
X0();X0();X0();X(23);X(23);X0();X0();X0();X0();X0();X0();X0();
|
||
#undef X0
|
||
#undef X
|
||
#undef NEXT
|
||
mpi_add (ctx->c, ctx->s[0], ctx->s[1]);
|
||
mpi_add (ctx->c, ctx->c, ctx->s[1]);
|
||
mpi_add (ctx->c, ctx->c, ctx->s[2]);
|
||
mpi_add (ctx->c, ctx->c, ctx->s[3]);
|
||
mpi_add (ctx->c, ctx->c, ctx->s[4]);
|
||
mpi_add (ctx->c, ctx->c, ctx->s[5]);
|
||
mpi_add (ctx->c, ctx->c, ctx->s[6]);
|
||
mpi_sub (ctx->c, ctx->c, ctx->s[7]);
|
||
mpi_sub (ctx->c, ctx->c, ctx->s[8]);
|
||
mpi_sub (ctx->c, ctx->c, ctx->s[9]);
|
||
|
||
while ( mpi_cmp (ctx->c, ctx->p ) >= 0 )
|
||
mpi_sub ( ctx->c, ctx->c, ctx->p );
|
||
while ( ctx->c->sign )
|
||
mpi_add ( ctx->c, ctx->c, ctx->p );
|
||
mpi_set (w, ctx->c);
|
||
}
|
||
else
|
||
#endif /*0*/
|
||
mpi_mulm (w, u, v, ctx->p);
|
||
}
|
||
|
||
static void
|
||
ec_powm (gcry_mpi_t w, const gcry_mpi_t b, const gcry_mpi_t e,
|
||
mpi_ec_t ctx)
|
||
{
|
||
mpi_powm (w, b, e, ctx->p);
|
||
}
|
||
|
||
static void
|
||
ec_invm (gcry_mpi_t x, gcry_mpi_t a, mpi_ec_t ctx)
|
||
{
|
||
mpi_invm (x, a, ctx->p);
|
||
}
|
||
|
||
|
||
|
||
/* This function returns a new context for elliptic curve based on the
|
||
field GF(p). P is the prime specifying thuis field, A is the first
|
||
coefficient.
|
||
|
||
This context needs to be released using _gcry_mpi_ec_free. */
|
||
mpi_ec_t
|
||
_gcry_mpi_ec_init (gcry_mpi_t p, gcry_mpi_t a)
|
||
{
|
||
int i;
|
||
mpi_ec_t ctx;
|
||
gcry_mpi_t tmp;
|
||
|
||
mpi_normalize (p);
|
||
mpi_normalize (a);
|
||
|
||
/* Fixme: Do we want to check some constraints? e.g.
|
||
a < p
|
||
*/
|
||
|
||
ctx = gcry_xcalloc (1, sizeof *ctx);
|
||
|
||
ctx->p = mpi_copy (p);
|
||
ctx->a = mpi_copy (a);
|
||
|
||
tmp = mpi_alloc_like (ctx->p);
|
||
mpi_sub_ui (tmp, ctx->p, 3);
|
||
ctx->a_is_pminus3 = !mpi_cmp (ctx->a, tmp);
|
||
mpi_free (tmp);
|
||
|
||
|
||
/* Allocate constants. */
|
||
ctx->one = mpi_alloc_set_ui (1);
|
||
ctx->two = mpi_alloc_set_ui (2);
|
||
ctx->three = mpi_alloc_set_ui (3);
|
||
ctx->four = mpi_alloc_set_ui (4);
|
||
ctx->eight = mpi_alloc_set_ui (8);
|
||
ctx->two_inv_p = mpi_alloc (0);
|
||
ec_invm (ctx->two_inv_p, ctx->two, ctx);
|
||
|
||
/* Allocate scratch variables. */
|
||
for (i=0; i< DIM(ctx->scratch); i++)
|
||
ctx->scratch[i] = mpi_alloc_like (ctx->p);
|
||
|
||
/* Prepare for fast reduction. */
|
||
/* FIXME: need a test for NIST values. However it does not gain us
|
||
any real advantage, for 384 bits it is actually slower than using
|
||
mpi_mulm. */
|
||
/* ctx->nist_nbits = mpi_get_nbits (ctx->p); */
|
||
/* if (ctx->nist_nbits == 192) */
|
||
/* { */
|
||
/* for (i=0; i < 4; i++) */
|
||
/* ctx->s[i] = mpi_new (192); */
|
||
/* ctx->c = mpi_new (192*2); */
|
||
/* } */
|
||
/* else if (ctx->nist_nbits == 384) */
|
||
/* { */
|
||
/* for (i=0; i < 10; i++) */
|
||
/* ctx->s[i] = mpi_new (384); */
|
||
/* ctx->c = mpi_new (384*2); */
|
||
/* } */
|
||
|
||
return ctx;
|
||
}
|
||
|
||
void
|
||
_gcry_mpi_ec_free (mpi_ec_t ctx)
|
||
{
|
||
int i;
|
||
|
||
if (!ctx)
|
||
return;
|
||
|
||
mpi_free (ctx->p);
|
||
mpi_free (ctx->a);
|
||
|
||
mpi_free (ctx->one);
|
||
mpi_free (ctx->two);
|
||
mpi_free (ctx->three);
|
||
mpi_free (ctx->four);
|
||
mpi_free (ctx->eight);
|
||
|
||
mpi_free (ctx->two_inv_p);
|
||
|
||
for (i=0; i< DIM(ctx->scratch); i++)
|
||
mpi_free (ctx->scratch[i]);
|
||
|
||
/* if (ctx->nist_nbits == 192) */
|
||
/* { */
|
||
/* for (i=0; i < 4; i++) */
|
||
/* mpi_free (ctx->s[i]); */
|
||
/* mpi_free (ctx->c); */
|
||
/* } */
|
||
/* else if (ctx->nist_nbits == 384) */
|
||
/* { */
|
||
/* for (i=0; i < 10; i++) */
|
||
/* mpi_free (ctx->s[i]); */
|
||
/* mpi_free (ctx->c); */
|
||
/* } */
|
||
|
||
gcry_free (ctx);
|
||
}
|
||
|
||
/* Compute the affine coordinates from the projective coordinates in
|
||
POINT. Set them into X and Y. If one coordinate is not required,
|
||
X or Y may be passed as NULL. CTX is the usual context. Returns: 0
|
||
on success or !0 if POINT is at infinity. */
|
||
int
|
||
_gcry_mpi_ec_get_affine (gcry_mpi_t x, gcry_mpi_t y, mpi_point_t *point,
|
||
mpi_ec_t ctx)
|
||
{
|
||
gcry_mpi_t z1, z2, z3;
|
||
|
||
if (!mpi_cmp_ui (point->z, 0))
|
||
return -1;
|
||
|
||
z1 = mpi_new (0);
|
||
z2 = mpi_new (0);
|
||
ec_invm (z1, point->z, ctx); /* z1 = z^(-1) mod p */
|
||
ec_mulm (z2, z1, z1, ctx); /* z2 = z^(-2) mod p */
|
||
|
||
if (x)
|
||
ec_mulm (x, point->x, z2, ctx);
|
||
|
||
if (y)
|
||
{
|
||
z3 = mpi_new (0);
|
||
ec_mulm (z3, z2, z1, ctx); /* z3 = z^(-3) mod p */
|
||
ec_mulm (y, point->y, z3, ctx);
|
||
mpi_free (z3);
|
||
}
|
||
|
||
mpi_free (z2);
|
||
mpi_free (z1);
|
||
return 0;
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
/* RESULT = 2 * POINT */
|
||
void
|
||
_gcry_mpi_ec_dup_point (mpi_point_t *result, mpi_point_t *point, mpi_ec_t ctx)
|
||
{
|
||
#define x3 (result->x)
|
||
#define y3 (result->y)
|
||
#define z3 (result->z)
|
||
#define t1 (ctx->scratch[0])
|
||
#define t2 (ctx->scratch[1])
|
||
#define t3 (ctx->scratch[2])
|
||
#define l1 (ctx->scratch[3])
|
||
#define l2 (ctx->scratch[4])
|
||
#define l3 (ctx->scratch[5])
|
||
|
||
if (!mpi_cmp_ui (point->y, 0) || !mpi_cmp_ui (point->z, 0))
|
||
{
|
||
/* P_y == 0 || P_z == 0 => [1:1:0] */
|
||
mpi_set_ui (x3, 1);
|
||
mpi_set_ui (y3, 1);
|
||
mpi_set_ui (z3, 0);
|
||
}
|
||
else
|
||
{
|
||
if (ctx->a_is_pminus3) /* Use the faster case. */
|
||
{
|
||
/* L1 = 3(X - Z^2)(X + Z^2) */
|
||
/* T1: used for Z^2. */
|
||
/* T2: used for the right term. */
|
||
ec_powm (t1, point->z, ctx->two, ctx);
|
||
ec_subm (l1, point->x, t1, ctx);
|
||
ec_mulm (l1, l1, ctx->three, ctx);
|
||
ec_addm (t2, point->x, t1, ctx);
|
||
ec_mulm (l1, l1, t2, ctx);
|
||
}
|
||
else /* Standard case. */
|
||
{
|
||
/* L1 = 3X^2 + aZ^4 */
|
||
/* T1: used for aZ^4. */
|
||
ec_powm (l1, point->x, ctx->two, ctx);
|
||
ec_mulm (l1, l1, ctx->three, ctx);
|
||
ec_powm (t1, point->z, ctx->four, ctx);
|
||
ec_mulm (t1, t1, ctx->a, ctx);
|
||
ec_addm (l1, l1, t1, ctx);
|
||
}
|
||
/* Z3 = 2YZ */
|
||
ec_mulm (z3, point->y, point->z, ctx);
|
||
ec_mulm (z3, z3, ctx->two, ctx);
|
||
|
||
/* L2 = 4XY^2 */
|
||
/* T2: used for Y2; required later. */
|
||
ec_powm (t2, point->y, ctx->two, ctx);
|
||
ec_mulm (l2, t2, point->x, ctx);
|
||
ec_mulm (l2, l2, ctx->four, ctx);
|
||
|
||
/* X3 = L1^2 - 2L2 */
|
||
/* T1: used for L2^2. */
|
||
ec_powm (x3, l1, ctx->two, ctx);
|
||
ec_mulm (t1, l2, ctx->two, ctx);
|
||
ec_subm (x3, x3, t1, ctx);
|
||
|
||
/* L3 = 8Y^4 */
|
||
/* T2: taken from above. */
|
||
ec_powm (t2, t2, ctx->two, ctx);
|
||
ec_mulm (l3, t2, ctx->eight, ctx);
|
||
|
||
/* Y3 = L1(L2 - X3) - L3 */
|
||
ec_subm (y3, l2, x3, ctx);
|
||
ec_mulm (y3, y3, l1, ctx);
|
||
ec_subm (y3, y3, l3, ctx);
|
||
}
|
||
|
||
#undef x3
|
||
#undef y3
|
||
#undef z3
|
||
#undef t1
|
||
#undef t2
|
||
#undef t3
|
||
#undef l1
|
||
#undef l2
|
||
#undef l3
|
||
}
|
||
|
||
|
||
|
||
/* RESULT = P1 + P2 */
|
||
void
|
||
_gcry_mpi_ec_add_points (mpi_point_t *result,
|
||
mpi_point_t *p1, mpi_point_t *p2,
|
||
mpi_ec_t ctx)
|
||
{
|
||
#define x1 (p1->x )
|
||
#define y1 (p1->y )
|
||
#define z1 (p1->z )
|
||
#define x2 (p2->x )
|
||
#define y2 (p2->y )
|
||
#define z2 (p2->z )
|
||
#define x3 (result->x)
|
||
#define y3 (result->y)
|
||
#define z3 (result->z)
|
||
#define l1 (ctx->scratch[0])
|
||
#define l2 (ctx->scratch[1])
|
||
#define l3 (ctx->scratch[2])
|
||
#define l4 (ctx->scratch[3])
|
||
#define l5 (ctx->scratch[4])
|
||
#define l6 (ctx->scratch[5])
|
||
#define l7 (ctx->scratch[6])
|
||
#define l8 (ctx->scratch[7])
|
||
#define l9 (ctx->scratch[8])
|
||
#define t1 (ctx->scratch[9])
|
||
#define t2 (ctx->scratch[10])
|
||
|
||
if ( (!mpi_cmp (x1, x2)) && (!mpi_cmp (y1, y2)) && (!mpi_cmp (z1, z2)) )
|
||
{
|
||
/* Same point; need to call the duplicate function. */
|
||
_gcry_mpi_ec_dup_point (result, p1, ctx);
|
||
}
|
||
else if (!mpi_cmp_ui (z1, 0))
|
||
{
|
||
/* P1 is at infinity. */
|
||
mpi_set (x3, p2->x);
|
||
mpi_set (y3, p2->y);
|
||
mpi_set (z3, p2->z);
|
||
}
|
||
else if (!mpi_cmp_ui (z2, 0))
|
||
{
|
||
/* P2 is at infinity. */
|
||
mpi_set (x3, p1->x);
|
||
mpi_set (y3, p1->y);
|
||
mpi_set (z3, p1->z);
|
||
}
|
||
else
|
||
{
|
||
int z1_is_one = !mpi_cmp_ui (z1, 1);
|
||
int z2_is_one = !mpi_cmp_ui (z2, 1);
|
||
|
||
/* l1 = x1 z2^2 */
|
||
/* l2 = x2 z1^2 */
|
||
if (z2_is_one)
|
||
mpi_set (l1, x1);
|
||
else
|
||
{
|
||
ec_powm (l1, z2, ctx->two, ctx);
|
||
ec_mulm (l1, l1, x1, ctx);
|
||
}
|
||
if (z1_is_one)
|
||
mpi_set (l2, x2);
|
||
else
|
||
{
|
||
ec_powm (l2, z1, ctx->two, ctx);
|
||
ec_mulm (l2, l2, x2, ctx);
|
||
}
|
||
/* l3 = l1 - l2 */
|
||
ec_subm (l3, l1, l2, ctx);
|
||
/* l4 = y1 z2^3 */
|
||
ec_powm (l4, z2, ctx->three, ctx);
|
||
ec_mulm (l4, l4, y1, ctx);
|
||
/* l5 = y2 z1^3 */
|
||
ec_powm (l5, z1, ctx->three, ctx);
|
||
ec_mulm (l5, l5, y2, ctx);
|
||
/* l6 = l4 - l5 */
|
||
ec_subm (l6, l4, l5, ctx);
|
||
|
||
if (!mpi_cmp_ui (l3, 0))
|
||
{
|
||
if (!mpi_cmp_ui (l6, 0))
|
||
{
|
||
/* P1 and P2 are the same - use duplicate function. */
|
||
_gcry_mpi_ec_dup_point (result, p1, ctx);
|
||
}
|
||
else
|
||
{
|
||
/* P1 is the inverse of P2. */
|
||
mpi_set_ui (x3, 1);
|
||
mpi_set_ui (y3, 1);
|
||
mpi_set_ui (z3, 0);
|
||
}
|
||
}
|
||
else
|
||
{
|
||
/* l7 = l1 + l2 */
|
||
ec_addm (l7, l1, l2, ctx);
|
||
/* l8 = l4 + l5 */
|
||
ec_addm (l8, l4, l5, ctx);
|
||
/* z3 = z1 z2 l3 */
|
||
ec_mulm (z3, z1, z2, ctx);
|
||
ec_mulm (z3, z3, l3, ctx);
|
||
/* x3 = l6^2 - l7 l3^2 */
|
||
ec_powm (t1, l6, ctx->two, ctx);
|
||
ec_powm (t2, l3, ctx->two, ctx);
|
||
ec_mulm (t2, t2, l7, ctx);
|
||
ec_subm (x3, t1, t2, ctx);
|
||
/* l9 = l7 l3^2 - 2 x3 */
|
||
ec_mulm (t1, x3, ctx->two, ctx);
|
||
ec_subm (l9, t2, t1, ctx);
|
||
/* y3 = (l9 l6 - l8 l3^3)/2 */
|
||
ec_mulm (l9, l9, l6, ctx);
|
||
ec_powm (t1, l3, ctx->three, ctx); /* fixme: Use saved value*/
|
||
ec_mulm (t1, t1, l8, ctx);
|
||
ec_subm (y3, l9, t1, ctx);
|
||
ec_mulm (y3, y3, ctx->two_inv_p, ctx);
|
||
}
|
||
}
|
||
|
||
#undef x1
|
||
#undef y1
|
||
#undef z1
|
||
#undef x2
|
||
#undef y2
|
||
#undef z2
|
||
#undef x3
|
||
#undef y3
|
||
#undef z3
|
||
#undef l1
|
||
#undef l2
|
||
#undef l3
|
||
#undef l4
|
||
#undef l5
|
||
#undef l6
|
||
#undef l7
|
||
#undef l8
|
||
#undef l9
|
||
#undef t1
|
||
#undef t2
|
||
}
|
||
|
||
|
||
|
||
/* Scalar point multiplication - the main function for ECC. If takes
|
||
an integer SCALAR and a POINT as well as the usual context CTX.
|
||
RESULT will be set to the resulting point. */
|
||
void
|
||
_gcry_mpi_ec_mul_point (mpi_point_t *result,
|
||
gcry_mpi_t scalar, mpi_point_t *point,
|
||
mpi_ec_t ctx)
|
||
{
|
||
#if 0
|
||
/* Simple left to right binary method. GECC Algorithm 3.27 */
|
||
unsigned int nbits;
|
||
int i;
|
||
|
||
nbits = mpi_get_nbits (scalar);
|
||
mpi_set_ui (result->x, 1);
|
||
mpi_set_ui (result->y, 1);
|
||
mpi_set_ui (result->z, 0);
|
||
|
||
for (i=nbits-1; i >= 0; i--)
|
||
{
|
||
_gcry_mpi_ec_dup_point (result, result, ctx);
|
||
if (mpi_test_bit (scalar, i) == 1)
|
||
_gcry_mpi_ec_add_points (result, result, point, ctx);
|
||
}
|
||
|
||
#else
|
||
gcry_mpi_t x1, y1, z1, k, h, yy;
|
||
unsigned int i, loops;
|
||
mpi_point_t p1, p2, p1inv;
|
||
|
||
x1 = mpi_alloc_like (ctx->p);
|
||
y1 = mpi_alloc_like (ctx->p);
|
||
h = mpi_alloc_like (ctx->p);
|
||
k = mpi_copy (scalar);
|
||
yy = mpi_copy (point->y);
|
||
|
||
if ( mpi_is_neg (k) )
|
||
{
|
||
k->sign = 0;
|
||
ec_invm (yy, yy, ctx);
|
||
}
|
||
|
||
if (!mpi_cmp_ui (point->z, 1))
|
||
{
|
||
mpi_set (x1, point->x);
|
||
mpi_set (y1, yy);
|
||
}
|
||
else
|
||
{
|
||
gcry_mpi_t z2, z3;
|
||
|
||
z2 = mpi_alloc_like (ctx->p);
|
||
z3 = mpi_alloc_like (ctx->p);
|
||
ec_mulm (z2, point->z, point->z, ctx);
|
||
ec_mulm (z3, point->z, z2, ctx);
|
||
ec_invm (z2, z2, ctx);
|
||
ec_mulm (x1, point->x, z2, ctx);
|
||
ec_invm (z3, z3, ctx);
|
||
ec_mulm (y1, yy, z3, ctx);
|
||
mpi_free (z2);
|
||
mpi_free (z3);
|
||
}
|
||
z1 = mpi_copy (ctx->one);
|
||
|
||
mpi_mul (h, k, ctx->three); /* h = 3k */
|
||
loops = mpi_get_nbits (h);
|
||
if (loops < 2)
|
||
{
|
||
/* If SCALAR is zero, the above mpi_mul sets H to zero and thus
|
||
LOOPs will be zero. To avoid an underflow of I in the main
|
||
loop we set LOOP to 2 and the result to (0,0,0). */
|
||
loops = 2;
|
||
mpi_clear (result->x);
|
||
mpi_clear (result->y);
|
||
mpi_clear (result->z);
|
||
}
|
||
else
|
||
{
|
||
mpi_set (result->x, point->x);
|
||
mpi_set (result->y, yy);
|
||
mpi_set (result->z, point->z);
|
||
}
|
||
mpi_free (yy); yy = NULL;
|
||
|
||
p1.x = x1; x1 = NULL;
|
||
p1.y = y1; y1 = NULL;
|
||
p1.z = z1; z1 = NULL;
|
||
point_init (&p2);
|
||
point_init (&p1inv);
|
||
|
||
for (i=loops-2; i > 0; i--)
|
||
{
|
||
_gcry_mpi_ec_dup_point (result, result, ctx);
|
||
if (mpi_test_bit (h, i) == 1 && mpi_test_bit (k, i) == 0)
|
||
{
|
||
point_set (&p2, result);
|
||
_gcry_mpi_ec_add_points (result, &p2, &p1, ctx);
|
||
}
|
||
if (mpi_test_bit (h, i) == 0 && mpi_test_bit (k, i) == 1)
|
||
{
|
||
point_set (&p2, result);
|
||
/* Invert point: y = p - y mod p */
|
||
point_set (&p1inv, &p1);
|
||
ec_subm (p1inv.y, ctx->p, p1inv.y, ctx);
|
||
_gcry_mpi_ec_add_points (result, &p2, &p1inv, ctx);
|
||
}
|
||
}
|
||
|
||
point_free (&p1);
|
||
point_free (&p2);
|
||
point_free (&p1inv);
|
||
mpi_free (h);
|
||
mpi_free (k);
|
||
#endif
|
||
}
|