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>

12 files changed, 1400 insertions, 0 deletions

diff --git a/lib/Kconfig b/lib/Kconfig
index 4af07ec7f2de..d411de53be4f 100644
--- a/lib/Kconfig
+++ b/lib/Kconfig
@@ -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
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;
+
+}