Page MenuHome GnuPG
Files F21947202

ec.c
No OneTemporary
Actions

ec.c
View Options

/* 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 <assert.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, x1);
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);
mpi_set (result->x, point->x);
mpi_set (result->y, yy); mpi_free (yy); yy = NULL;
mpi_set (result->z, point->z);
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
}

File Metadata

Mime Type
text/x-c
Expires
Sun, Apr 20, 5:56 AM (19 h, 8 m)
Storage Engine
local-disk
Storage Format
Raw Data
Storage Handle
37/66/fdfb334d695d7ade2db75923bd7f

Event Timeline