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crypto: GnuPG based MPI lib - additional sources (part 4)

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Adds the multi-precision-integer maths library which was originally taken
from GnuPG and ported to the kernel by (among others) David Howells.
This version is taken from Fedora kernel 2.6.32-71.14.1.el6.
The difference is that checkpatch reported errors and warnings have been fixed.

This library is used to implemenet RSA digital signature verification
used in IMA/EVM integrity protection subsystem.

Due to patch size limitation, the patch is divided into 4 parts.

This code is unnecessary for RSA digital signature verification,
but for completeness it is included here and can be compiled,
if CONFIG_MPILIB_EXTRA is enabled.

Signed-off-by: Dmitry Kasatkin <dmitry.kasatkin@intel.com>
This commit is contained in:
Dmitry Kasatkin 2011-11-07 15:16:37 +02:00
parent d9c46b184f
commit 7e8dec918e
12 changed files with 1400 additions and 0 deletions
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10
lib/Kconfig
View File

@ -283,4 +283,14 @@ config MPILIB
It is used to implement RSA digital signature verification,
which is used by IMA/EVM digital signature extension.
config MPILIB_EXTRA
bool "Multiprecision maths library - additional sources"
depends on MPILIB
help
Multiprecision maths library from GnuPG.
It is used to implement RSA digital signature verification,
which is used by IMA/EVM digital signature extension.
This code in unnecessary for RSA digital signature verification,
and can be compiled if needed.
endmenu

11
lib/mpi/Makefile
View File

@ -19,3 +19,14 @@ mpi-y = \
mpih-mul.o \
mpi-pow.o \
mpiutil.o
mpi-$(CONFIG_MPILIB_EXTRA) += \
mpi-add.o \
mpi-div.o \
mpi-cmp.o \
mpi-gcd.o \
mpi-inline.o \
mpi-inv.o \
mpi-mpow.o \
mpi-mul.o \
mpi-scan.o

4
lib/mpi/generic_mpi-asm-defs.h Normal file
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@ -0,0 +1,4 @@
/* This file defines some basic constants for the MPI machinery. We
* need to define the types on a per-CPU basis, so it is done with
* this file here. */
#define BYTES_PER_MPI_LIMB (SIZEOF_UNSIGNED_LONG)

234
lib/mpi/mpi-add.c Normal file
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@ -0,0 +1,234 @@
/* mpi-add.c - MPI functions
* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
* Copyright (C) 1994, 1996 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*
* Note: This code is heavily based on the GNU MP Library.
* Actually it's the same code with only minor changes in the
* way the data is stored; this is to support the abstraction
* of an optional secure memory allocation which may be used
* to avoid revealing of sensitive data due to paging etc.
* The GNU MP Library itself is published under the LGPL;
* however I decided to publish this code under the plain GPL.
*/
#include "mpi-internal.h"
/****************
* Add the unsigned integer V to the mpi-integer U and store the
* result in W. U and V may be the same.
*/
int mpi_add_ui(MPI w, const MPI u, unsigned long v)
{
mpi_ptr_t wp, up;
mpi_size_t usize, wsize;
int usign, wsign;
usize = u->nlimbs;
usign = u->sign;
wsign = 0;
/* If not space for W (and possible carry), increase space. */
wsize = usize + 1;
if (w->alloced < wsize)
if (mpi_resize(w, wsize) < 0)
return -ENOMEM;
/* These must be after realloc (U may be the same as W). */
up = u->d;
wp = w->d;
if (!usize) { /* simple */
wp[0] = v;
wsize = v ? 1 : 0;
} else if (!usign) { /* mpi is not negative */
mpi_limb_t cy;
cy = mpihelp_add_1(wp, up, usize, v);
wp[usize] = cy;
wsize = usize + cy;
} else { /* The signs are different. Need exact comparison to determine
* which operand to subtract from which. */
if (usize == 1 && up[0] < v) {
wp[0] = v - up[0];
wsize = 1;
} else {
mpihelp_sub_1(wp, up, usize, v);
/* Size can decrease with at most one limb. */
wsize = usize - (wp[usize - 1] == 0);
wsign = 1;
}
}
w->nlimbs = wsize;
w->sign = wsign;
return 0;
}
int mpi_add(MPI w, MPI u, MPI v)
{
mpi_ptr_t wp, up, vp;
mpi_size_t usize, vsize, wsize;
int usign, vsign, wsign;
if (u->nlimbs < v->nlimbs) { /* Swap U and V. */
usize = v->nlimbs;
usign = v->sign;
vsize = u->nlimbs;
vsign = u->sign;
wsize = usize + 1;
if (RESIZE_IF_NEEDED(w, wsize) < 0)
return -ENOMEM;
/* These must be after realloc (u or v may be the same as w). */
up = v->d;
vp = u->d;
} else {
usize = u->nlimbs;
usign = u->sign;
vsize = v->nlimbs;
vsign = v->sign;
wsize = usize + 1;
if (RESIZE_IF_NEEDED(w, wsize) < 0)
return -ENOMEM;
/* These must be after realloc (u or v may be the same as w). */
up = u->d;
vp = v->d;
}
wp = w->d;
wsign = 0;
if (!vsize) { /* simple */
MPN_COPY(wp, up, usize);
wsize = usize;
wsign = usign;
} else if (usign != vsign) { /* different sign */
/* This test is right since USIZE >= VSIZE */
if (usize != vsize) {
mpihelp_sub(wp, up, usize, vp, vsize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
wsign = usign;
} else if (mpihelp_cmp(up, vp, usize) < 0) {
mpihelp_sub_n(wp, vp, up, usize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
if (!usign)
wsign = 1;
} else {
mpihelp_sub_n(wp, up, vp, usize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
if (usign)
wsign = 1;
}
} else { /* U and V have same sign. Add them. */
mpi_limb_t cy = mpihelp_add(wp, up, usize, vp, vsize);
wp[usize] = cy;
wsize = usize + cy;
if (usign)
wsign = 1;
}
w->nlimbs = wsize;
w->sign = wsign;
return 0;
}
/****************
* Subtract the unsigned integer V from the mpi-integer U and store the
* result in W.
*/
int mpi_sub_ui(MPI w, MPI u, unsigned long v)
{
mpi_ptr_t wp, up;
mpi_size_t usize, wsize;
int usign, wsign;
usize = u->nlimbs;
usign = u->sign;
wsign = 0;
/* If not space for W (and possible carry), increase space. */
wsize = usize + 1;
if (w->alloced < wsize)
if (mpi_resize(w, wsize) < 0)
return -ENOMEM;
/* These must be after realloc (U may be the same as W). */
up = u->d;
wp = w->d;
if (!usize) { /* simple */
wp[0] = v;
wsize = v ? 1 : 0;
wsign = 1;
} else if (usign) { /* mpi and v are negative */
mpi_limb_t cy;
cy = mpihelp_add_1(wp, up, usize, v);
wp[usize] = cy;
wsize = usize + cy;
} else { /* The signs are different. Need exact comparison to determine
* which operand to subtract from which. */
if (usize == 1 && up[0] < v) {
wp[0] = v - up[0];
wsize = 1;
wsign = 1;
} else {
mpihelp_sub_1(wp, up, usize, v);
/* Size can decrease with at most one limb. */
wsize = usize - (wp[usize - 1] == 0);
}
}
w->nlimbs = wsize;
w->sign = wsign;
return 0;
}
int mpi_sub(MPI w, MPI u, MPI v)
{
int rc;
if (w == v) {
MPI vv;
if (mpi_copy(&vv, v) < 0)
return -ENOMEM;
vv->sign = !vv->sign;
rc = mpi_add(w, u, vv);
mpi_free(vv);
} else {
/* fixme: this is not thread-save (we temp. modify v) */
v->sign = !v->sign;
rc = mpi_add(w, u, v);
v->sign = !v->sign;
}
return rc;
}
int mpi_addm(MPI w, MPI u, MPI v, MPI m)
{
if (mpi_add(w, u, v) < 0 || mpi_fdiv_r(w, w, m) < 0)
return -ENOMEM;
return 0;
}
int mpi_subm(MPI w, MPI u, MPI v, MPI m)
{
if (mpi_sub(w, u, v) < 0 || mpi_fdiv_r(w, w, m) < 0)
return -ENOMEM;
return 0;
}

68
lib/mpi/mpi-cmp.c Normal file
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@ -0,0 +1,68 @@
/* mpi-cmp.c - MPI functions
* Copyright (C) 1998, 1999 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
#include "mpi-internal.h"
int mpi_cmp_ui(MPI u, unsigned long v)
{
mpi_limb_t limb = v;
mpi_normalize(u);
if (!u->nlimbs && !limb)
return 0;
if (u->sign)
return -1;
if (u->nlimbs > 1)
return 1;
if (u->d[0] == limb)
return 0;
else if (u->d[0] > limb)
return 1;
else
return -1;
}
int mpi_cmp(MPI u, MPI v)
{
mpi_size_t usize, vsize;
int cmp;
mpi_normalize(u);
mpi_normalize(v);
usize = u->nlimbs;
vsize = v->nlimbs;
if (!u->sign && v->sign)
return 1;
if (u->sign && !v->sign)
return -1;
if (usize != vsize && !u->sign && !v->sign)
return usize - vsize;
if (usize != vsize && u->sign && v->sign)
return vsize + usize;
if (!usize)
return 0;
cmp = mpihelp_cmp(u->d, v->d, usize);
if (!cmp)
return 0;
if ((cmp < 0 ? 1 : 0) == (u->sign ? 1 : 0))
return 1;
return -1;
}

333
lib/mpi/mpi-div.c Normal file
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@ -0,0 +1,333 @@
/* mpi-div.c - MPI functions
* Copyright (C) 1994, 1996 Free Software Foundation, Inc.
* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*
* Note: This code is heavily based on the GNU MP Library.
* Actually it's the same code with only minor changes in the
* way the data is stored; this is to support the abstraction
* of an optional secure memory allocation which may be used
* to avoid revealing of sensitive data due to paging etc.
* The GNU MP Library itself is published under the LGPL;
* however I decided to publish this code under the plain GPL.
*/
#include <linux/string.h>
#include "mpi-internal.h"
#include "longlong.h"
int mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
{
int rc = -ENOMEM;
int divisor_sign = divisor->sign;
MPI temp_divisor = NULL;
/* We need the original value of the divisor after the remainder has been
* preliminary calculated. We have to copy it to temporary space if it's
* the same variable as REM. */
if (rem == divisor) {
if (mpi_copy(&temp_divisor, divisor) < 0)
goto nomem;
divisor = temp_divisor;
}
if (mpi_tdiv_qr(NULL, rem, dividend, divisor) < 0)
goto nomem;
if (((divisor_sign ? 1 : 0) ^ (dividend->sign ? 1 : 0)) && rem->nlimbs)
if (mpi_add(rem, rem, divisor) < 0)
goto nomem;
rc = 0;
nomem:
if (temp_divisor)
mpi_free(temp_divisor);
return rc;
}
/****************
* Division rounding the quotient towards -infinity.
* The remainder gets the same sign as the denominator.
* rem is optional
*/
ulong mpi_fdiv_r_ui(MPI rem, MPI dividend, ulong divisor)
{
mpi_limb_t rlimb;
rlimb = mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
if (rlimb && dividend->sign)
rlimb = divisor - rlimb;
if (rem) {
rem->d[0] = rlimb;
rem->nlimbs = rlimb ? 1 : 0;
}
return rlimb;
}
int mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
{
MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
if (!tmp)
return -ENOMEM;
mpi_fdiv_qr(quot, tmp, dividend, divisor);
mpi_free(tmp);
return 0;
}
int mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
{
int divisor_sign = divisor->sign;
MPI temp_divisor = NULL;
if (quot == divisor || rem == divisor) {
if (mpi_copy(&temp_divisor, divisor) < 0)
return -ENOMEM;
divisor = temp_divisor;
}
if (mpi_tdiv_qr(quot, rem, dividend, divisor) < 0)
goto nomem;
if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
if (mpi_sub_ui(quot, quot, 1) < 0)
goto nomem;
if (mpi_add(rem, rem, divisor) < 0)
goto nomem;
}
if (temp_divisor)
mpi_free(temp_divisor);
return 0;
nomem:
mpi_free(temp_divisor);
return -ENOMEM;
}
/* If den == quot, den needs temporary storage.
* If den == rem, den needs temporary storage.
* If num == quot, num needs temporary storage.
* If den has temporary storage, it can be normalized while being copied,
* i.e no extra storage should be allocated.
*/
int mpi_tdiv_r(MPI rem, MPI num, MPI den)
{
return mpi_tdiv_qr(NULL, rem, num, den);
}
int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
{
int rc = -ENOMEM;
mpi_ptr_t np, dp;
mpi_ptr_t qp, rp;
mpi_size_t nsize = num->nlimbs;
mpi_size_t dsize = den->nlimbs;
mpi_size_t qsize, rsize;
mpi_size_t sign_remainder = num->sign;
mpi_size_t sign_quotient = num->sign ^ den->sign;
unsigned normalization_steps;
mpi_limb_t q_limb;
mpi_ptr_t marker[5];
int markidx = 0;
memset(marker, 0, sizeof(marker));
/* Ensure space is enough for quotient and remainder.
* We need space for an extra limb in the remainder, because it's
* up-shifted (normalized) below. */
rsize = nsize + 1;
if (mpi_resize(rem, rsize) < 0)
goto nomem;
qsize = rsize - dsize; /* qsize cannot be bigger than this. */
if (qsize <= 0) {
if (num != rem) {
rem->nlimbs = num->nlimbs;
rem->sign = num->sign;
MPN_COPY(rem->d, num->d, nsize);
}
if (quot) {
/* This needs to follow the assignment to rem, in case the
* numerator and quotient are the same. */
quot->nlimbs = 0;
quot->sign = 0;
}
return 0;
}
if (quot)
if (mpi_resize(quot, qsize) < 0)
goto nomem;
/* Read pointers here, when reallocation is finished. */
np = num->d;
dp = den->d;
rp = rem->d;
/* Optimize division by a single-limb divisor. */
if (dsize == 1) {
mpi_limb_t rlimb;
if (quot) {
qp = quot->d;
rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
qsize -= qp[qsize - 1] == 0;
quot->nlimbs = qsize;
quot->sign = sign_quotient;
} else
rlimb = mpihelp_mod_1(np, nsize, dp[0]);
rp[0] = rlimb;
rsize = rlimb != 0 ? 1 : 0;
rem->nlimbs = rsize;
rem->sign = sign_remainder;
return 0;
}
if (quot) {
qp = quot->d;
/* Make sure QP and NP point to different objects. Otherwise the
* numerator would be gradually overwritten by the quotient limbs. */
if (qp == np) { /* Copy NP object to temporary space. */
np = marker[markidx++] = mpi_alloc_limb_space(nsize);
MPN_COPY(np, qp, nsize);
}
} else /* Put quotient at top of remainder. */
qp = rp + dsize;
count_leading_zeros(normalization_steps, dp[dsize - 1]);
/* Normalize the denominator, i.e. make its most significant bit set by
* shifting it NORMALIZATION_STEPS bits to the left. Also shift the
* numerator the same number of steps (to keep the quotient the same!).
*/
if (normalization_steps) {
mpi_ptr_t tp;
mpi_limb_t nlimb;
/* Shift up the denominator setting the most significant bit of
* the most significant word. Use temporary storage not to clobber
* the original contents of the denominator. */
tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
if (!tp)
goto nomem;
mpihelp_lshift(tp, dp, dsize, normalization_steps);
dp = tp;
/* Shift up the numerator, possibly introducing a new most
* significant word. Move the shifted numerator in the remainder
* meanwhile. */
nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
if (nlimb) {
rp[nsize] = nlimb;
rsize = nsize + 1;
} else
rsize = nsize;
} else {
/* The denominator is already normalized, as required. Copy it to
* temporary space if it overlaps with the quotient or remainder. */
if (dp == rp || (quot && (dp == qp))) {
mpi_ptr_t tp;
tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
if (!tp)
goto nomem;
MPN_COPY(tp, dp, dsize);
dp = tp;
}
/* Move the numerator to the remainder. */
if (rp != np)
MPN_COPY(rp, np, nsize);
rsize = nsize;
}
q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);
if (quot) {
qsize = rsize - dsize;
if (q_limb) {
qp[qsize] = q_limb;
qsize += 1;
}
quot->nlimbs = qsize;
quot->sign = sign_quotient;
}
rsize = dsize;
MPN_NORMALIZE(rp, rsize);
if (normalization_steps && rsize) {
mpihelp_rshift(rp, rp, rsize, normalization_steps);
rsize -= rp[rsize - 1] == 0 ? 1 : 0;
}
rem->nlimbs = rsize;
rem->sign = sign_remainder;
rc = 0;
nomem:
while (markidx)
mpi_free_limb_space(marker[--markidx]);
return rc;
}
int mpi_tdiv_q_2exp(MPI w, MPI u, unsigned count)
{
mpi_size_t usize, wsize;
mpi_size_t limb_cnt;
usize = u->nlimbs;
limb_cnt = count / BITS_PER_MPI_LIMB;
wsize = usize - limb_cnt;
if (limb_cnt >= usize)
w->nlimbs = 0;
else {
mpi_ptr_t wp;
mpi_ptr_t up;
if (RESIZE_IF_NEEDED(w, wsize) < 0)
return -ENOMEM;
wp = w->d;
up = u->d;
count %= BITS_PER_MPI_LIMB;
if (count) {
mpihelp_rshift(wp, up + limb_cnt, wsize, count);
wsize -= !wp[wsize - 1];
} else {
MPN_COPY_INCR(wp, up + limb_cnt, wsize);
}
w->nlimbs = wsize;
}
return 0;
}
/****************
* Check whether dividend is divisible by divisor
* (note: divisor must fit into a limb)
*/
int mpi_divisible_ui(MPI dividend, ulong divisor)
{
return !mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
}

59
lib/mpi/mpi-gcd.c Normal file
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@ -0,0 +1,59 @@
/* mpi-gcd.c - MPI functions
* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
#include "mpi-internal.h"
/****************
* Find the greatest common divisor G of A and B.
* Return: true if this 1, false in all other cases
*/
int mpi_gcd(MPI g, const MPI xa, const MPI xb)
{
MPI a = NULL, b = NULL;
if (mpi_copy(&a, xa) < 0)
goto nomem;
if (mpi_copy(&b, xb) < 0)
goto nomem;
/* TAOCP Vol II, 4.5.2, Algorithm A */
a->sign = 0;
b->sign = 0;
while (mpi_cmp_ui(b, 0)) {
if (mpi_fdiv_r(g, a, b) < 0) /* g used as temorary variable */
goto nomem;
if (mpi_set(a, b) < 0)
goto nomem;
if (mpi_set(b, g) < 0)
goto nomem;
}
if (mpi_set(g, a) < 0)
goto nomem;
mpi_free(a);
mpi_free(b);
return !mpi_cmp_ui(g, 1);
nomem:
mpi_free(a);
mpi_free(b);
return -ENOMEM;
}

31
lib/mpi/mpi-inline.c Normal file
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@ -0,0 +1,31 @@
/* mpi-inline.c
* Copyright (C) 1999, 2000, 2001 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
/* put the inline functions as real functions into the lib */
#define G10_MPI_INLINE_DECL
#include "mpi-internal.h"
/* always include the header becuase it is only
* included by mpi-internal if __GCC__ is defined but we
* need it here in all cases and the above definition of
* of the macro allows us to do so
*/
#include "mpi-inline.h"

187
lib/mpi/mpi-inv.c Normal file
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@ -0,0 +1,187 @@
/* mpi-inv.c - MPI functions
* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
#include "mpi-internal.h"
/****************
* Calculate the multiplicative inverse X of A mod N
* That is: Find the solution x for
* 1 = (a*x) mod n
*/
int mpi_invm(MPI x, const MPI a, const MPI n)
{
/* Extended Euclid's algorithm (See TAOPC Vol II, 4.5.2, Alg X)
* modified according to Michael Penk's solution for Exercice 35
* with further enhancement */
MPI u = NULL, v = NULL;
MPI u1 = NULL, u2 = NULL, u3 = NULL;
MPI v1 = NULL, v2 = NULL, v3 = NULL;
MPI t1 = NULL, t2 = NULL, t3 = NULL;
unsigned k;
int sign;
int odd = 0;
int rc = -ENOMEM;
if (mpi_copy(&u, a) < 0)
goto cleanup;
if (mpi_copy(&v, n) < 0)
goto cleanup;
for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
if (mpi_rshift(u, u, 1) < 0)
goto cleanup;
if (mpi_rshift(v, v, 1) < 0)
goto cleanup;
}
odd = mpi_test_bit(v, 0);
u1 = mpi_alloc_set_ui(1);
if (!u1)
goto cleanup;
if (!odd) {
u2 = mpi_alloc_set_ui(0);
if (!u2)
goto cleanup;
}
if (mpi_copy(&u3, u) < 0)
goto cleanup;
if (mpi_copy(&v1, v) < 0)
goto cleanup;
if (!odd) {
v2 = mpi_alloc(mpi_get_nlimbs(u));
if (!v2)
goto cleanup;
if (mpi_sub(v2, u1, u) < 0)
goto cleanup; /* U is used as const 1 */
}
if (mpi_copy(&v3, v) < 0)
goto cleanup;
if (mpi_test_bit(u, 0)) { /* u is odd */
t1 = mpi_alloc_set_ui(0);
if (!t1)
goto cleanup;
if (!odd) {
t2 = mpi_alloc_set_ui(1);
if (!t2)
goto cleanup;
t2->sign = 1;
}
if (mpi_copy(&t3, v) < 0)
goto cleanup;
t3->sign = !t3->sign;
goto Y4;
} else {
t1 = mpi_alloc_set_ui(1);
if (!t1)
goto cleanup;
if (!odd) {
t2 = mpi_alloc_set_ui(0);
if (!t2)
goto cleanup;
}
if (mpi_copy(&t3, u) < 0)
goto cleanup;
}
do {
do {
if (!odd) {
if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) { /* one is odd */
if (mpi_add(t1, t1, v) < 0)
goto cleanup;
if (mpi_sub(t2, t2, u) < 0)
goto cleanup;
}
if (mpi_rshift(t1, t1, 1) < 0)
goto cleanup;
if (mpi_rshift(t2, t2, 1) < 0)
goto cleanup;
if (mpi_rshift(t3, t3, 1) < 0)
goto cleanup;
} else {
if (mpi_test_bit(t1, 0))
if (mpi_add(t1, t1, v) < 0)
goto cleanup;
if (mpi_rshift(t1, t1, 1) < 0)
goto cleanup;
if (mpi_rshift(t3, t3, 1) < 0)
goto cleanup;
}
Y4:
;
} while (!mpi_test_bit(t3, 0)); /* while t3 is even */
if (!t3->sign) {
if (mpi_set(u1, t1) < 0)
goto cleanup;
if (!odd)
if (mpi_set(u2, t2) < 0)
goto cleanup;
if (mpi_set(u3, t3) < 0)
goto cleanup;
} else {
if (mpi_sub(v1, v, t1) < 0)
goto cleanup;
sign = u->sign;
u->sign = !u->sign;
if (!odd)
if (mpi_sub(v2, u, t2) < 0)
goto cleanup;
u->sign = sign;
sign = t3->sign;
t3->sign = !t3->sign;
if (mpi_set(v3, t3) < 0)
goto cleanup;
t3->sign = sign;
}
if (mpi_sub(t1, u1, v1) < 0)
goto cleanup;
if (!odd)
if (mpi_sub(t2, u2, v2) < 0)
goto cleanup;
if (mpi_sub(t3, u3, v3) < 0)
goto cleanup;
if (t1->sign) {
if (mpi_add(t1, t1, v) < 0)
goto cleanup;
if (!odd)
if (mpi_sub(t2, t2, u) < 0)
goto cleanup;
}
} while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */
/* mpi_lshift( u3, k ); */
rc = mpi_set(x, u1);
cleanup:
mpi_free(u1);
mpi_free(v1);
mpi_free(t1);
if (!odd) {
mpi_free(u2);
mpi_free(v2);
mpi_free(t2);
}
mpi_free(u3);
mpi_free(v3);
mpi_free(t3);
mpi_free(u);
mpi_free(v);
return rc;
}

133
lib/mpi/mpi-mpow.c Normal file
View File

@ -0,0 +1,133 @@
/* mpi-mpow.c - MPI functions
* Copyright (C) 1998, 1999, 2000 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
#include "mpi-internal.h"
#include "longlong.h"
static int build_index(const MPI *exparray, int k, int i, int t)
{
int j, bitno;
int index = 0;
bitno = t - i;
for (j = k - 1; j >= 0; j--) {
index <<= 1;
if (mpi_test_bit(exparray[j], bitno))
index |= 1;
}
return index;
}
/****************
* RES = (BASE[0] ^ EXP[0]) * (BASE[1] ^ EXP[1]) * ... * mod M
*/
int mpi_mulpowm(MPI res, MPI *basearray, MPI *exparray, MPI m)
{
int rc = -ENOMEM;
int k; /* number of elements */
int t; /* bit size of largest exponent */
int i, j, idx;
MPI *G = NULL; /* table with precomputed values of size 2^k */
MPI tmp = NULL;
for (k = 0; basearray[k]; k++)
;
if (!k) {
pr_emerg("mpi_mulpowm: assert(k) failed\n");
BUG();
}
for (t = 0, i = 0; (tmp = exparray[i]); i++) {
j = mpi_get_nbits(tmp);
if (j > t)
t = j;
}
if (i != k) {
pr_emerg("mpi_mulpowm: assert(i==k) failed\n");
BUG();
}
if (!t) {
pr_emerg("mpi_mulpowm: assert(t) failed\n");
BUG();
}
if (k >= 10) {
pr_emerg("mpi_mulpowm: assert(k<10) failed\n");
BUG();
}
G = kzalloc((1 << k) * sizeof *G, GFP_KERNEL);
if (!G)
goto nomem;
/* and calculate */
tmp = mpi_alloc(mpi_get_nlimbs(m) + 1);
if (!tmp)
goto nomem;
if (mpi_set_ui(res, 1) < 0)
goto nomem;
for (i = 1; i <= t; i++) {
if (mpi_mulm(tmp, res, res, m) < 0)
goto nomem;
idx = build_index(exparray, k, i, t);
if (!(idx >= 0 && idx < (1 << k))) {
pr_emerg("mpi_mulpowm: assert(idx >= 0 && idx < (1<<k)) failed\n");
BUG();
}
if (!G[idx]) {
if (!idx) {
G[0] = mpi_alloc_set_ui(1);
if (!G[0])
goto nomem;
} else {
for (j = 0; j < k; j++) {
if ((idx & (1 << j))) {
if (!G[idx]) {
if (mpi_copy
(&G[idx],
basearray[j]) < 0)
goto nomem;
} else {
if (mpi_mulm
(G[idx], G[idx],
basearray[j],
m) < 0)
goto nomem;
}
}
}
if (!G[idx]) {
G[idx] = mpi_alloc(0);
if (!G[idx])
goto nomem;
}
}
}
if (mpi_mulm(res, tmp, G[idx], m) < 0)
goto nomem;
}
rc = 0;
nomem:
/* cleanup */
mpi_free(tmp);
for (i = 0; i < (1 << k); i++)
mpi_free(G[i]);
kfree(G);
return rc;
}

194
lib/mpi/mpi-mul.c Normal file
View File

@ -0,0 +1,194 @@
/* mpi-mul.c - MPI functions
* Copyright (C) 1994, 1996 Free Software Foundation, Inc.
* Copyright (C) 1998, 2001 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*
* Note: This code is heavily based on the GNU MP Library.
* Actually it's the same code with only minor changes in the
* way the data is stored; this is to support the abstraction
* of an optional secure memory allocation which may be used
* to avoid revealing of sensitive data due to paging etc.
* The GNU MP Library itself is published under the LGPL;
* however I decided to publish this code under the plain GPL.
*/
#include "mpi-internal.h"
int mpi_mul_ui(MPI prod, MPI mult, unsigned long small_mult)
{
mpi_size_t size, prod_size;
mpi_ptr_t prod_ptr;
mpi_limb_t cy;
int sign;
size = mult->nlimbs;
sign = mult->sign;
if (!size || !small_mult) {
prod->nlimbs = 0;
prod->sign = 0;
return 0;
}
prod_size = size + 1;
if (prod->alloced < prod_size)
if (mpi_resize(prod, prod_size) < 0)
return -ENOMEM;
prod_ptr = prod->d;
cy = mpihelp_mul_1(prod_ptr, mult->d, size, (mpi_limb_t) small_mult);
if (cy)
prod_ptr[size++] = cy;
prod->nlimbs = size;
prod->sign = sign;
return 0;
}
int mpi_mul_2exp(MPI w, MPI u, unsigned long cnt)
{
mpi_size_t usize, wsize, limb_cnt;
mpi_ptr_t wp;
mpi_limb_t wlimb;
int usign, wsign;
usize = u->nlimbs;
usign = u->sign;
if (!usize) {
w->nlimbs = 0;
w->sign = 0;
return 0;
}
limb_cnt = cnt / BITS_PER_MPI_LIMB;
wsize = usize + limb_cnt + 1;
if (w->alloced < wsize)
if (mpi_resize(w, wsize) < 0)
return -ENOMEM;
wp = w->d;
wsize = usize + limb_cnt;
wsign = usign;
cnt %= BITS_PER_MPI_LIMB;
if (cnt) {
wlimb = mpihelp_lshift(wp + limb_cnt, u->d, usize, cnt);
if (wlimb) {
wp[wsize] = wlimb;
wsize++;
}
} else {
MPN_COPY_DECR(wp + limb_cnt, u->d, usize);
}
/* Zero all whole limbs at low end. Do it here and not before calling
* mpn_lshift, not to lose for U == W. */
MPN_ZERO(wp, limb_cnt);
w->nlimbs = wsize;
w->sign = wsign;
return 0;
}
int mpi_mul(MPI w, MPI u, MPI v)
{
int rc = -ENOMEM;
mpi_size_t usize, vsize, wsize;
mpi_ptr_t up, vp, wp;
mpi_limb_t cy;
int usign, vsign, sign_product;
int assign_wp = 0;
mpi_ptr_t tmp_limb = NULL;
if (u->nlimbs < v->nlimbs) { /* Swap U and V. */
usize = v->nlimbs;
usign = v->sign;
up = v->d;
vsize = u->nlimbs;
vsign = u->sign;
vp = u->d;
} else {
usize = u->nlimbs;
usign = u->sign;
up = u->d;
vsize = v->nlimbs;
vsign = v->sign;
vp = v->d;
}
sign_product = usign ^ vsign;
wp = w->d;
/* Ensure W has space enough to store the result. */
wsize = usize + vsize;
if (w->alloced < (size_t) wsize) {
if (wp == up || wp == vp) {
wp = mpi_alloc_limb_space(wsize);
if (!wp)
goto nomem;
assign_wp = 1;
} else {
if (mpi_resize(w, wsize) < 0)
goto nomem;
wp = w->d;
}
} else { /* Make U and V not overlap with W. */
if (wp == up) {
/* W and U are identical. Allocate temporary space for U. */
up = tmp_limb = mpi_alloc_limb_space(usize);
if (!up)
goto nomem;
/* Is V identical too? Keep it identical with U. */
if (wp == vp)
vp = up;
/* Copy to the temporary space. */
MPN_COPY(up, wp, usize);
} else if (wp == vp) {
/* W and V are identical. Allocate temporary space for V. */
vp = tmp_limb = mpi_alloc_limb_space(vsize);
if (!vp)
goto nomem;
/* Copy to the temporary space. */
MPN_COPY(vp, wp, vsize);
}
}
if (!vsize)
wsize = 0;
else {
if (mpihelp_mul(wp, up, usize, vp, vsize, &cy) < 0)
goto nomem;
wsize -= cy ? 0 : 1;
}
if (assign_wp)
mpi_assign_limb_space(w, wp, wsize);
w->nlimbs = wsize;
w->sign = sign_product;
rc = 0;
nomem:
if (tmp_limb)
mpi_free_limb_space(tmp_limb);
return rc;
}
int mpi_mulm(MPI w, MPI u, MPI v, MPI m)
{
if (mpi_mul(w, u, v) < 0)
return -ENOMEM;
return mpi_fdiv_r(w, w, m);
}

136
lib/mpi/mpi-scan.c Normal file
View File

@ -0,0 +1,136 @@
/* mpi-scan.c - MPI functions
* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
*
* This file is part of GnuPG.
*
* GnuPG is free software; you can redistribute it and/or modify
* it under the terms of 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.
*
* GnuPG 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 a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
#include "mpi-internal.h"
#include "longlong.h"
/****************
* Scan through an mpi and return byte for byte. a -1 is returned to indicate
* the end of the mpi. Scanning is done from the lsb to the msb, returned
* values are in the range of 0 .. 255.
*
* FIXME: This code is VERY ugly!
*/
int mpi_getbyte(const MPI a, unsigned idx)
{
int i, j;
unsigned n;
mpi_ptr_t ap;
mpi_limb_t limb;
ap = a->d;
for (n = 0, i = 0; i < a->nlimbs; i++) {
limb = ap[i];
for (j = 0; j < BYTES_PER_MPI_LIMB; j++, n++)
if (n == idx)
return (limb >> j * 8) & 0xff;
}
return -1;
}
/****************
* Put a value at position IDX into A. idx counts from lsb to msb
*/
void mpi_putbyte(MPI a, unsigned idx, int xc)
{
int i, j;
unsigned n;
mpi_ptr_t ap;
mpi_limb_t limb, c;
c = xc & 0xff;
ap = a->d;
for (n = 0, i = 0; i < a->alloced; i++) {
limb = ap[i];
for (j = 0; j < BYTES_PER_MPI_LIMB; j++, n++)
if (n == idx) {
#if BYTES_PER_MPI_LIMB == 4
if (j == 0)
limb = (limb & 0xffffff00) | c;
else if (j == 1)
limb = (limb & 0xffff00ff) | (c << 8);
else if (j == 2)
limb = (limb & 0xff00ffff) | (c << 16);
else
limb = (limb & 0x00ffffff) | (c << 24);
#elif BYTES_PER_MPI_LIMB == 8
if (j == 0)
limb = (limb & 0xffffffffffffff00) | c;
else if (j == 1)
limb =
(limb & 0xffffffffffff00ff) | (c <<
8);
else if (j == 2)
limb =
(limb & 0xffffffffff00ffff) | (c <<
16);
else if (j == 3)
limb =
(limb & 0xffffffff00ffffff) | (c <<
24);
else if (j == 4)
limb =
(limb & 0xffffff00ffffffff) | (c <<
32);
else if (j == 5)
limb =
(limb & 0xffff00ffffffffff) | (c <<
40);
else if (j == 6)
limb =
(limb & 0xff00ffffffffffff) | (c <<
48);
else
limb =
(limb & 0x00ffffffffffffff) | (c <<
56);
#else
#error please enhance this function, its ugly - i know.
#endif
if (a->nlimbs <= i)
a->nlimbs = i + 1;
ap[i] = limb;
return;
}
}
log_bug("index out of range\n");
}
/****************
* Count the number of zerobits at the low end of A
*/
unsigned mpi_trailing_zeros(const MPI a)
{
unsigned n, count = 0;
for (n = 0; n < a->nlimbs; n++) {
if (a->d[n]) {
unsigned nn;
mpi_limb_t alimb = a->d[n];
count_trailing_zeros(nn, alimb);
count += nn;
break;
}
count += BITS_PER_MPI_LIMB;
}
return count;
}