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authorDmitry Kasatkin <dmitry.kasatkin@intel.com>2011-11-07 15:16:37 +0200
committerDmitry Kasatkin <dmitry.kasatkin@intel.com>2011-11-09 11:47:26 +0200
commit7e8dec918ef8e0f68b4937c3c50fa57002077a4d (patch)
treea17d33fa54fcb18c335b36c4550b889b206015f4 /lib/mpi
parentd9c46b184fcfd33c85a7dc48a653435a08e21f56 (diff)
downloadlinux-linaro-stable-7e8dec918ef8e0f68b4937c3c50fa57002077a4d.tar.gz
crypto: GnuPG based MPI lib - additional sources (part 4)
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>
Diffstat (limited to 'lib/mpi')
-rw-r--r--lib/mpi/Makefile11
-rw-r--r--lib/mpi/generic_mpi-asm-defs.h4
-rw-r--r--lib/mpi/mpi-add.c234
-rw-r--r--lib/mpi/mpi-cmp.c68
-rw-r--r--lib/mpi/mpi-div.c333
-rw-r--r--lib/mpi/mpi-gcd.c59
-rw-r--r--lib/mpi/mpi-inline.c31
-rw-r--r--lib/mpi/mpi-inv.c187
-rw-r--r--lib/mpi/mpi-mpow.c133
-rw-r--r--lib/mpi/mpi-mul.c194
-rw-r--r--lib/mpi/mpi-scan.c136
11 files changed, 1390 insertions, 0 deletions
diff --git a/lib/mpi/Makefile b/lib/mpi/Makefile
index 45ca90a8639c..567d52e74d77 100644
--- a/lib/mpi/Makefile
+++ b/lib/mpi/Makefile
@@ -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
diff --git a/lib/mpi/generic_mpi-asm-defs.h b/lib/mpi/generic_mpi-asm-defs.h
new file mode 100644
index 000000000000..047d1f5a7249
--- /dev/null
+++ b/lib/mpi/generic_mpi-asm-defs.h
@@ -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)
diff --git a/lib/mpi/mpi-add.c b/lib/mpi/mpi-add.c
new file mode 100644
index 000000000000..f56b9ba295e6
--- /dev/null
+++ b/lib/mpi/mpi-add.c
@@ -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;
+}
diff --git a/lib/mpi/mpi-cmp.c b/lib/mpi/mpi-cmp.c
new file mode 100644
index 000000000000..914bc42a8a80
--- /dev/null
+++ b/lib/mpi/mpi-cmp.c
@@ -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;
+}
diff --git a/lib/mpi/mpi-div.c b/lib/mpi/mpi-div.c
new file mode 100644
index 000000000000..c3087d1390ce
--- /dev/null
+++ b/lib/mpi/mpi-div.c
@@ -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);
+}
diff --git a/lib/mpi/mpi-gcd.c b/lib/mpi/mpi-gcd.c
new file mode 100644
index 000000000000..13c48aef9c4e
--- /dev/null
+++ b/lib/mpi/mpi-gcd.c
@@ -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;
+}
diff --git a/lib/mpi/mpi-inline.c b/lib/mpi/mpi-inline.c
new file mode 100644
index 000000000000..654f68aeed8b
--- /dev/null
+++ b/lib/mpi/mpi-inline.c
@@ -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"
diff --git a/lib/mpi/mpi-inv.c b/lib/mpi/mpi-inv.c
new file mode 100644
index 000000000000..0951f9847745
--- /dev/null
+++ b/lib/mpi/mpi-inv.c
@@ -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;
+}
diff --git a/lib/mpi/mpi-mpow.c b/lib/mpi/mpi-mpow.c
new file mode 100644
index 000000000000..4cc75933c5a7
--- /dev/null
+++ b/lib/mpi/mpi-mpow.c
@@ -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;
+}
diff --git a/lib/mpi/mpi-mul.c b/lib/mpi/mpi-mul.c
new file mode 100644
index 000000000000..1f3219e27292
--- /dev/null
+++ b/lib/mpi/mpi-mul.c
@@ -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);
+}
diff --git a/lib/mpi/mpi-scan.c b/lib/mpi/mpi-scan.c
new file mode 100644
index 000000000000..b2da5ad96199
--- /dev/null
+++ b/lib/mpi/mpi-scan.c
@@ -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;
+
+}