14 files changed, 2076 insertions, 10 deletions

diff --git a/include/linux/mpi.h b/include/linux/mpi.h
index 5d906dfbf3ed..3c9e41603cf6 100644
--- a/include/linux/mpi.h
+++ b/include/linux/mpi.h
@@ -40,21 +40,79 @@ struct gcry_mpi {
 typedef struct gcry_mpi *MPI;
 
 #define mpi_get_nlimbs(a)     ((a)->nlimbs)
+#define mpi_has_sign(a)       ((a)->sign)
 
 /*-- mpiutil.c --*/
 MPI mpi_alloc(unsigned nlimbs);
+void mpi_clear(MPI a);
 void mpi_free(MPI a);
 int mpi_resize(MPI a, unsigned nlimbs);
 
+static inline MPI mpi_new(unsigned int nbits)
+{
+	return mpi_alloc((nbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB);
+}
+
+MPI mpi_copy(MPI a);
+MPI mpi_alloc_like(MPI a);
+void mpi_snatch(MPI w, MPI u);
+MPI mpi_set(MPI w, MPI u);
+MPI mpi_set_ui(MPI w, unsigned long u);
+MPI mpi_alloc_set_ui(unsigned long u);
+void mpi_swap_cond(MPI a, MPI b, unsigned long swap);
+
+/* Constants used to return constant MPIs.  See mpi_init if you
+ * want to add more constants.
+ */
+#define MPI_NUMBER_OF_CONSTANTS 6
+enum gcry_mpi_constants {
+	MPI_C_ZERO,
+	MPI_C_ONE,
+	MPI_C_TWO,
+	MPI_C_THREE,
+	MPI_C_FOUR,
+	MPI_C_EIGHT
+};
+
+MPI mpi_const(enum gcry_mpi_constants no);
+
 /*-- mpicoder.c --*/
+
+/* Different formats of external big integer representation. */
+enum gcry_mpi_format {
+	GCRYMPI_FMT_NONE = 0,
+	GCRYMPI_FMT_STD = 1,    /* Twos complement stored without length. */
+	GCRYMPI_FMT_PGP = 2,    /* As used by OpenPGP (unsigned only). */
+	GCRYMPI_FMT_SSH = 3,    /* As used by SSH (like STD but with length). */
+	GCRYMPI_FMT_HEX = 4,    /* Hex format. */
+	GCRYMPI_FMT_USG = 5,    /* Like STD but unsigned. */
+	GCRYMPI_FMT_OPAQUE = 8  /* Opaque format (some functions only). */
+};
+
 MPI mpi_read_raw_data(const void *xbuffer, size_t nbytes);
 MPI mpi_read_from_buffer(const void *buffer, unsigned *ret_nread);
+int mpi_fromstr(MPI val, const char *str);
+MPI mpi_scanval(const char *string);
 MPI mpi_read_raw_from_sgl(struct scatterlist *sgl, unsigned int len);
 void *mpi_get_buffer(MPI a, unsigned *nbytes, int *sign);
 int mpi_read_buffer(MPI a, uint8_t *buf, unsigned buf_len, unsigned *nbytes,
 		    int *sign);
 int mpi_write_to_sgl(MPI a, struct scatterlist *sg, unsigned nbytes,
 		     int *sign);
+int mpi_print(enum gcry_mpi_format format, unsigned char *buffer,
+			size_t buflen, size_t *nwritten, MPI a);
+
+/*-- mpi-mod.c --*/
+void mpi_mod(MPI rem, MPI dividend, MPI divisor);
+
+/* Context used with Barrett reduction.  */
+struct barrett_ctx_s;
+typedef struct barrett_ctx_s *mpi_barrett_t;
+
+mpi_barrett_t mpi_barrett_init(MPI m, int copy);
+void mpi_barrett_free(mpi_barrett_t ctx);
+void mpi_mod_barrett(MPI r, MPI x, mpi_barrett_t ctx);
+void mpi_mul_barrett(MPI w, MPI u, MPI v, mpi_barrett_t ctx);
 
 /*-- mpi-pow.c --*/
 int mpi_powm(MPI res, MPI base, MPI exp, MPI mod);
@@ -62,6 +120,7 @@ int mpi_powm(MPI res, MPI base, MPI exp, MPI mod);
 /*-- mpi-cmp.c --*/
 int mpi_cmp_ui(MPI u, ulong v);
 int mpi_cmp(MPI u, MPI v);
+int mpi_cmpabs(MPI u, MPI v);
 
 /*-- mpi-sub-ui.c --*/
 int mpi_sub_ui(MPI w, MPI u, unsigned long vval);
@@ -69,6 +128,34 @@ int mpi_sub_ui(MPI w, MPI u, unsigned long vval);
 /*-- mpi-bit.c --*/
 void mpi_normalize(MPI a);
 unsigned mpi_get_nbits(MPI a);
+int mpi_test_bit(MPI a, unsigned int n);
+void mpi_set_bit(MPI a, unsigned int n);
+void mpi_set_highbit(MPI a, unsigned int n);
+void mpi_clear_highbit(MPI a, unsigned int n);
+void mpi_clear_bit(MPI a, unsigned int n);
+void mpi_rshift_limbs(MPI a, unsigned int count);
+void mpi_rshift(MPI x, MPI a, unsigned int n);
+void mpi_lshift_limbs(MPI a, unsigned int count);
+void mpi_lshift(MPI x, MPI a, unsigned int n);
+
+/*-- mpi-add.c --*/
+void mpi_add_ui(MPI w, MPI u, unsigned long v);
+void mpi_add(MPI w, MPI u, MPI v);
+void mpi_sub(MPI w, MPI u, MPI v);
+void mpi_addm(MPI w, MPI u, MPI v, MPI m);
+void mpi_subm(MPI w, MPI u, MPI v, MPI m);
+
+/*-- mpi-mul.c --*/
+void mpi_mul(MPI w, MPI u, MPI v);
+void mpi_mulm(MPI w, MPI u, MPI v, MPI m);
+
+/*-- mpi-div.c --*/
+void mpi_tdiv_r(MPI rem, MPI num, MPI den);
+void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor);
+void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor);
+
+/*-- mpi-inv.c --*/
+int mpi_invm(MPI x, MPI a, MPI n);
 
 /* inline functions */
 
diff --git a/lib/mpi/Makefile b/lib/mpi/Makefile
index 43b8fce14079..477debd7ed50 100644
--- a/lib/mpi/Makefile
+++ b/lib/mpi/Makefile
@@ -14,9 +14,14 @@ mpi-y = \
 	generic_mpih-sub1.o		\
 	generic_mpih-add1.o		\
 	mpicoder.o			\
+	mpi-add.o			\
 	mpi-bit.o			\
 	mpi-cmp.o			\
 	mpi-sub-ui.o			\
+	mpi-div.o			\
+	mpi-inv.o			\
+	mpi-mod.o			\
+	mpi-mul.o			\
 	mpih-cmp.o			\
 	mpih-div.o			\
 	mpih-mul.o			\
diff --git a/lib/mpi/mpi-add.c b/lib/mpi/mpi-add.c
new file mode 100644
index 000000000000..2cdae54c1bd0
--- /dev/null
+++ b/lib/mpi/mpi-add.c
@@ -0,0 +1,155 @@
+/* mpi-add.c  -  MPI functions
+ * Copyright (C) 1994, 1996, 1998, 2001, 2002,
+ *               2003 Free Software Foundation, Inc.
+ *
+ * This file is part of Libgcrypt.
+ *
+ * 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.
+ */
+
+#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.
+ */
+void mpi_add_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)
+		mpi_resize(w, wsize);
+
+	/* 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;
+}
+
+
+void 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;
+		RESIZE_IF_NEEDED(w, wsize);
+		/* 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;
+		RESIZE_IF_NEEDED(w, wsize);
+		/* 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;
+}
+EXPORT_SYMBOL_GPL(mpi_add);
+
+void mpi_sub(MPI w, MPI u, MPI v)
+{
+	MPI vv = mpi_copy(v);
+	vv->sign = !vv->sign;
+	mpi_add(w, u, vv);
+	mpi_free(vv);
+}
+
+
+void mpi_addm(MPI w, MPI u, MPI v, MPI m)
+{
+	mpi_add(w, u, v);
+	mpi_mod(w, w, m);
+}
+EXPORT_SYMBOL_GPL(mpi_addm);
+
+void mpi_subm(MPI w, MPI u, MPI v, MPI m)
+{
+	mpi_sub(w, u, v);
+	mpi_mod(w, w, m);
+}
+EXPORT_SYMBOL_GPL(mpi_subm);
diff --git a/lib/mpi/mpi-bit.c b/lib/mpi/mpi-bit.c
index 503537e08436..a5119a2bcdd4 100644
--- a/lib/mpi/mpi-bit.c
+++ b/lib/mpi/mpi-bit.c
@@ -32,6 +32,7 @@ void mpi_normalize(MPI a)
 	for (; a->nlimbs && !a->d[a->nlimbs - 1]; a->nlimbs--)
 		;
 }
+EXPORT_SYMBOL_GPL(mpi_normalize);
 
 /****************
  * Return the number of bits in A.
@@ -54,3 +55,253 @@ unsigned mpi_get_nbits(MPI a)
 	return n;
 }
 EXPORT_SYMBOL_GPL(mpi_get_nbits);
+
+/****************
+ * Test whether bit N is set.
+ */
+int mpi_test_bit(MPI a, unsigned int n)
+{
+	unsigned int limbno, bitno;
+	mpi_limb_t limb;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno  = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs)
+		return 0; /* too far left: this is a 0 */
+	limb = a->d[limbno];
+	return (limb & (A_LIMB_1 << bitno)) ? 1 : 0;
+}
+EXPORT_SYMBOL_GPL(mpi_test_bit);
+
+/****************
+ * Set bit N of A.
+ */
+void mpi_set_bit(MPI a, unsigned int n)
+{
+	unsigned int i, limbno, bitno;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno  = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs) {
+		for (i = a->nlimbs; i < a->alloced; i++)
+			a->d[i] = 0;
+		mpi_resize(a, limbno+1);
+		a->nlimbs = limbno+1;
+	}
+	a->d[limbno] |= (A_LIMB_1<<bitno);
+}
+
+/****************
+ * Set bit N of A. and clear all bits above
+ */
+void mpi_set_highbit(MPI a, unsigned int n)
+{
+	unsigned int i, limbno, bitno;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno  = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs) {
+		for (i = a->nlimbs; i < a->alloced; i++)
+			a->d[i] = 0;
+		mpi_resize(a, limbno+1);
+		a->nlimbs = limbno+1;
+	}
+	a->d[limbno] |= (A_LIMB_1<<bitno);
+	for (bitno++; bitno < BITS_PER_MPI_LIMB; bitno++)
+		a->d[limbno] &= ~(A_LIMB_1 << bitno);
+	a->nlimbs = limbno+1;
+}
+EXPORT_SYMBOL_GPL(mpi_set_highbit);
+
+/****************
+ * clear bit N of A and all bits above
+ */
+void mpi_clear_highbit(MPI a, unsigned int n)
+{
+	unsigned int limbno, bitno;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno  = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs)
+		return; /* not allocated, therefore no need to clear bits :-) */
+
+	for ( ; bitno < BITS_PER_MPI_LIMB; bitno++)
+		a->d[limbno] &= ~(A_LIMB_1 << bitno);
+	a->nlimbs = limbno+1;
+}
+
+/****************
+ * Clear bit N of A.
+ */
+void mpi_clear_bit(MPI a, unsigned int n)
+{
+	unsigned int limbno, bitno;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno  = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs)
+		return; /* Don't need to clear this bit, it's far too left.  */
+	a->d[limbno] &= ~(A_LIMB_1 << bitno);
+}
+EXPORT_SYMBOL_GPL(mpi_clear_bit);
+
+
+/****************
+ * Shift A by COUNT limbs to the right
+ * This is used only within the MPI library
+ */
+void mpi_rshift_limbs(MPI a, unsigned int count)
+{
+	mpi_ptr_t ap = a->d;
+	mpi_size_t n = a->nlimbs;
+	unsigned int i;
+
+	if (count >= n) {
+		a->nlimbs = 0;
+		return;
+	}
+
+	for (i = 0; i < n - count; i++)
+		ap[i] = ap[i+count];
+	ap[i] = 0;
+	a->nlimbs -= count;
+}
+
+/*
+ * Shift A by N bits to the right.
+ */
+void mpi_rshift(MPI x, MPI a, unsigned int n)
+{
+	mpi_size_t xsize;
+	unsigned int i;
+	unsigned int nlimbs = (n/BITS_PER_MPI_LIMB);
+	unsigned int nbits = (n%BITS_PER_MPI_LIMB);
+
+	if (x == a) {
+		/* In-place operation.  */
+		if (nlimbs >= x->nlimbs) {
+			x->nlimbs = 0;
+			return;
+		}
+
+		if (nlimbs) {
+			for (i = 0; i < x->nlimbs - nlimbs; i++)
+				x->d[i] = x->d[i+nlimbs];
+			x->d[i] = 0;
+			x->nlimbs -= nlimbs;
+		}
+		if (x->nlimbs && nbits)
+			mpihelp_rshift(x->d, x->d, x->nlimbs, nbits);
+	} else if (nlimbs) {
+		/* Copy and shift by more or equal bits than in a limb. */
+		xsize = a->nlimbs;
+		x->sign = a->sign;
+		RESIZE_IF_NEEDED(x, xsize);
+		x->nlimbs = xsize;
+		for (i = 0; i < a->nlimbs; i++)
+			x->d[i] = a->d[i];
+		x->nlimbs = i;
+
+		if (nlimbs >= x->nlimbs) {
+			x->nlimbs = 0;
+			return;
+		}
+
+		if (nlimbs) {
+			for (i = 0; i < x->nlimbs - nlimbs; i++)
+				x->d[i] = x->d[i+nlimbs];
+			x->d[i] = 0;
+			x->nlimbs -= nlimbs;
+		}
+
+		if (x->nlimbs && nbits)
+			mpihelp_rshift(x->d, x->d, x->nlimbs, nbits);
+	} else {
+		/* Copy and shift by less than bits in a limb.  */
+		xsize = a->nlimbs;
+		x->sign = a->sign;
+		RESIZE_IF_NEEDED(x, xsize);
+		x->nlimbs = xsize;
+
+		if (xsize) {
+			if (nbits)
+				mpihelp_rshift(x->d, a->d, x->nlimbs, nbits);
+			else {
+				/* The rshift helper function is not specified for
+				 * NBITS==0, thus we do a plain copy here.
+				 */
+				for (i = 0; i < x->nlimbs; i++)
+					x->d[i] = a->d[i];
+			}
+		}
+	}
+	MPN_NORMALIZE(x->d, x->nlimbs);
+}
+
+/****************
+ * Shift A by COUNT limbs to the left
+ * This is used only within the MPI library
+ */
+void mpi_lshift_limbs(MPI a, unsigned int count)
+{
+	mpi_ptr_t ap;
+	int n = a->nlimbs;
+	int i;
+
+	if (!count || !n)
+		return;
+
+	RESIZE_IF_NEEDED(a, n+count);
+
+	ap = a->d;
+	for (i = n-1; i >= 0; i--)
+		ap[i+count] = ap[i];
+	for (i = 0; i < count; i++)
+		ap[i] = 0;
+	a->nlimbs += count;
+}
+
+/*
+ * Shift A by N bits to the left.
+ */
+void mpi_lshift(MPI x, MPI a, unsigned int n)
+{
+	unsigned int nlimbs = (n/BITS_PER_MPI_LIMB);
+	unsigned int nbits = (n%BITS_PER_MPI_LIMB);
+
+	if (x == a && !n)
+		return;  /* In-place shift with an amount of zero.  */
+
+	if (x != a) {
+		/* Copy A to X.  */
+		unsigned int alimbs = a->nlimbs;
+		int asign = a->sign;
+		mpi_ptr_t xp, ap;
+
+		RESIZE_IF_NEEDED(x, alimbs+nlimbs+1);
+		xp = x->d;
+		ap = a->d;
+		MPN_COPY(xp, ap, alimbs);
+		x->nlimbs = alimbs;
+		x->flags = a->flags;
+		x->sign = asign;
+	}
+
+	if (nlimbs && !nbits) {
+		/* Shift a full number of limbs.  */
+		mpi_lshift_limbs(x, nlimbs);
+	} else if (n) {
+		/* We use a very dump approach: Shift left by the number of
+		 * limbs plus one and than fix it up by an rshift.
+		 */
+		mpi_lshift_limbs(x, nlimbs+1);
+		mpi_rshift(x, x, BITS_PER_MPI_LIMB - nbits);
+	}
+
+	MPN_NORMALIZE(x->d, x->nlimbs);
+}
diff --git a/lib/mpi/mpi-cmp.c b/lib/mpi/mpi-cmp.c
index d25e9e96c310..c4cfa3ff0581 100644
--- a/lib/mpi/mpi-cmp.c
+++ b/lib/mpi/mpi-cmp.c
@@ -41,28 +41,54 @@ int mpi_cmp_ui(MPI u, unsigned long v)
 }
 EXPORT_SYMBOL_GPL(mpi_cmp_ui);
 
-int mpi_cmp(MPI u, MPI v)
+static int do_mpi_cmp(MPI u, MPI v, int absmode)
 {
-	mpi_size_t usize, vsize;
+	mpi_size_t usize;
+	mpi_size_t vsize;
+	int usign;
+	int vsign;
 	int cmp;
 
 	mpi_normalize(u);
 	mpi_normalize(v);
+
 	usize = u->nlimbs;
 	vsize = v->nlimbs;
-	if (!u->sign && v->sign)
+	usign = absmode ? 0 : u->sign;
+	vsign = absmode ? 0 : v->sign;
+
+	/* Compare sign bits.  */
+
+	if (!usign && vsign)
 		return 1;
-	if (u->sign && !v->sign)
+	if (usign && !vsign)
 		return -1;
-	if (usize != vsize && !u->sign && !v->sign)
+
+	/* U and V are either both positive or both negative.  */
+
+	if (usize != vsize && !usign && !vsign)
 		return usize - vsize;
-	if (usize != vsize && u->sign && v->sign)
-		return vsize - usize;
+	if (usize != vsize && usign && vsign)
+		return vsize + usize;
 	if (!usize)
 		return 0;
 	cmp = mpihelp_cmp(u->d, v->d, usize);
-	if (u->sign)
-		return -cmp;
-	return cmp;
+	if (!cmp)
+		return 0;
+	if ((cmp < 0?1:0) == (usign?1:0))
+		return 1;
+
+	return -1;
+}
+
+int mpi_cmp(MPI u, MPI v)
+{
+	return do_mpi_cmp(u, v, 0);
 }
 EXPORT_SYMBOL_GPL(mpi_cmp);
+
+int mpi_cmpabs(MPI u, MPI v)
+{
+	return do_mpi_cmp(u, v, 1);
+}
+EXPORT_SYMBOL_GPL(mpi_cmpabs);
diff --git a/lib/mpi/mpi-div.c b/lib/mpi/mpi-div.c
new file mode 100644
index 000000000000..21332dab97d4
--- /dev/null
+++ b/lib/mpi/mpi-div.c
@@ -0,0 +1,238 @@
+/* mpi-div.c  -  MPI functions
+ * Copyright (C) 1994, 1996, 1998, 2001, 2002,
+ *               2003 Free Software Foundation, Inc.
+ *
+ * This file is part of Libgcrypt.
+ *
+ * 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.
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
+void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);
+
+void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
+{
+	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) {
+		temp_divisor = mpi_copy(divisor);
+		divisor = temp_divisor;
+	}
+
+	mpi_tdiv_r(rem, dividend, divisor);
+
+	if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs)
+		mpi_add(rem, rem, divisor);
+
+	if (temp_divisor)
+		mpi_free(temp_divisor);
+}
+
+void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
+{
+	MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
+	mpi_fdiv_qr(quot, tmp, dividend, divisor);
+	mpi_free(tmp);
+}
+
+void 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) {
+		temp_divisor = mpi_copy(divisor);
+		divisor = temp_divisor;
+	}
+
+	mpi_tdiv_qr(quot, rem, dividend, divisor);
+
+	if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
+		mpi_sub_ui(quot, quot, 1);
+		mpi_add(rem, rem, divisor);
+	}
+
+	if (temp_divisor)
+		mpi_free(temp_divisor);
+}
+
+/* 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.
+ */
+
+void mpi_tdiv_r(MPI rem, MPI num, MPI den)
+{
+	mpi_tdiv_qr(NULL, rem, num, den);
+}
+
+void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
+{
+	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 int normalization_steps;
+	mpi_limb_t q_limb;
+	mpi_ptr_t marker[5];
+	unsigned int marker_nlimbs[5];
+	int markidx = 0;
+
+	/* 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;
+	mpi_resize(rem, rsize);
+
+	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;
+	}
+
+	if (quot)
+		mpi_resize(quot, qsize);
+
+	/* 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;
+	}
+
+
+	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.  */
+			marker_nlimbs[markidx] = nsize;
+			np = marker[markidx++] = mpi_alloc_limb_space(nsize);
+			MPN_COPY(np, qp, nsize);
+		}
+	} else /* Put quotient at top of remainder. */
+		qp = rp + dsize;
+
+	normalization_steps = count_leading_zeros(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.
+		 */
+		marker_nlimbs[markidx] = dsize;
+		tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
+		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;
+
+			marker_nlimbs[markidx] = dsize;
+			tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
+			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;
+	while (markidx) {
+		markidx--;
+		mpi_free_limb_space(marker[markidx]);
+	}
+}
diff --git a/lib/mpi/mpi-internal.h b/lib/mpi/mpi-internal.h
index 91df5f0b70f2..d29c4537c3a3 100644
--- a/lib/mpi/mpi-internal.h
+++ b/lib/mpi/mpi-internal.h
@@ -52,6 +52,12 @@
 typedef mpi_limb_t *mpi_ptr_t;	/* pointer to a limb */
 typedef int mpi_size_t;		/* (must be a signed type) */
 
+#define RESIZE_IF_NEEDED(a, b)			\
+	do {					\
+		if ((a)->alloced < (b))		\
+			mpi_resize((a), (b));	\
+	} while (0)
+
 /* Copy N limbs from S to D.  */
 #define MPN_COPY(d, s, n) \
 	do {					\
@@ -60,6 +66,14 @@ typedef int mpi_size_t;		/* (must be a signed type) */
 			(d)[_i] = (s)[_i];	\
 	} while (0)
 
+#define MPN_COPY_INCR(d, s, n)		\
+	do {					\
+		mpi_size_t _i;			\
+		for (_i = 0; _i < (n); _i++)	\
+			(d)[_i] = (s)[_i];	\
+	} while (0)
+
+
 #define MPN_COPY_DECR(d, s, n) \
 	do {					\
 		mpi_size_t _i;			\
@@ -92,6 +106,38 @@ typedef int mpi_size_t;		/* (must be a signed type) */
 			mul_n(prodp, up, vp, size, tspace);	\
 	} while (0);
 
+/* Divide the two-limb number in (NH,,NL) by D, with DI being the largest
+ * limb not larger than (2**(2*BITS_PER_MP_LIMB))/D - (2**BITS_PER_MP_LIMB).
+ * If this would yield overflow, DI should be the largest possible number
+ * (i.e., only ones).  For correct operation, the most significant bit of D
+ * has to be set.  Put the quotient in Q and the remainder in R.
+ */
+#define UDIV_QRNND_PREINV(q, r, nh, nl, d, di)				\
+	do {								\
+		mpi_limb_t _ql;						\
+		mpi_limb_t _q, _r;					\
+		mpi_limb_t _xh, _xl;					\
+		umul_ppmm(_q, _ql, (nh), (di));				\
+		_q += (nh);	/* DI is 2**BITS_PER_MPI_LIMB too small */ \
+		umul_ppmm(_xh, _xl, _q, (d));				\
+		sub_ddmmss(_xh, _r, (nh), (nl), _xh, _xl);		\
+		if (_xh) {						\
+			sub_ddmmss(_xh, _r, _xh, _r, 0, (d));		\
+			_q++;						\
+			if (_xh) {					\
+				sub_ddmmss(_xh, _r, _xh, _r, 0, (d));	\
+				_q++;					\
+			}						\
+		}							\
+		if (_r >= (d)) {					\
+			_r -= (d);					\
+			_q++;						\
+		}							\
+		(r) = _r;						\
+		(q) = _q;						\
+	} while (0)
+
+
 /*-- mpiutil.c --*/
 mpi_ptr_t mpi_alloc_limb_space(unsigned nlimbs);
 void mpi_free_limb_space(mpi_ptr_t a);
@@ -135,6 +181,8 @@ int mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
 void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size);
 void mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size,
 		mpi_ptr_t tspace);
+void mpihelp_mul_n(mpi_ptr_t prodp,
+		mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size);
 
 int mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
 			       mpi_ptr_t up, mpi_size_t usize,
@@ -146,9 +194,14 @@ mpi_limb_t mpihelp_mul_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
 			 mpi_size_t s1_size, mpi_limb_t s2_limb);
 
 /*-- mpih-div.c --*/
+mpi_limb_t mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
+			 mpi_limb_t divisor_limb);
 mpi_limb_t mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
 			  mpi_ptr_t np, mpi_size_t nsize,
 			  mpi_ptr_t dp, mpi_size_t dsize);
+mpi_limb_t mpihelp_divmod_1(mpi_ptr_t quot_ptr,
+			    mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
+			    mpi_limb_t divisor_limb);
 
 /*-- generic_mpih-[lr]shift.c --*/
 mpi_limb_t mpihelp_lshift(mpi_ptr_t wp, mpi_ptr_t up, mpi_size_t usize,
diff --git a/lib/mpi/mpi-inv.c b/lib/mpi/mpi-inv.c
new file mode 100644
index 000000000000..61e37d18f793
--- /dev/null
+++ b/lib/mpi/mpi-inv.c
@@ -0,0 +1,143 @@
+/* mpi-inv.c  -  MPI functions
+ *	Copyright (C) 1998, 2001, 2002, 2003 Free Software Foundation, Inc.
+ *
+ * This file is part of Libgcrypt.
+ *
+ * Libgcrypt is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser General Public License as
+ * published by the Free Software Foundation; either version 2.1 of
+ * the License, or (at your option) any later version.
+ *
+ * Libgcrypt is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this program; if not, see <http://www.gnu.org/licenses/>.
+ */
+
+#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, MPI a, MPI n)
+{
+	/* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X)
+	 * modified according to Michael Penk's solution for Exercise 35
+	 * with further enhancement
+	 */
+	MPI u, v, u1, u2 = NULL, u3, v1, v2 = NULL, v3, t1, t2 = NULL, t3;
+	unsigned int k;
+	int sign;
+	int odd;
+
+	if (!mpi_cmp_ui(a, 0))
+		return 0; /* Inverse does not exists.  */
+	if (!mpi_cmp_ui(n, 1))
+		return 0; /* Inverse does not exists.  */
+
+	u = mpi_copy(a);
+	v = mpi_copy(n);
+
+	for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
+		mpi_rshift(u, u, 1);
+		mpi_rshift(v, v, 1);
+	}
+	odd = mpi_test_bit(v, 0);
+
+	u1 = mpi_alloc_set_ui(1);
+	if (!odd)
+		u2 = mpi_alloc_set_ui(0);
+	u3 = mpi_copy(u);
+	v1 = mpi_copy(v);
+	if (!odd) {
+		v2 = mpi_alloc(mpi_get_nlimbs(u));
+		mpi_sub(v2, u1, u); /* U is used as const 1 */
+	}
+	v3 = mpi_copy(v);
+	if (mpi_test_bit(u, 0)) { /* u is odd */
+		t1 = mpi_alloc_set_ui(0);
+		if (!odd) {
+			t2 = mpi_alloc_set_ui(1);
+			t2->sign = 1;
+		}
+		t3 = mpi_copy(v);
+		t3->sign = !t3->sign;
+		goto Y4;
+	} else {
+		t1 = mpi_alloc_set_ui(1);
+		if (!odd)
+			t2 = mpi_alloc_set_ui(0);
+		t3 = mpi_copy(u);
+	}
+
+	do {
+		do {
+			if (!odd) {
+				if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) {
+					/* one is odd */
+					mpi_add(t1, t1, v);
+					mpi_sub(t2, t2, u);
+				}
+				mpi_rshift(t1, t1, 1);
+				mpi_rshift(t2, t2, 1);
+				mpi_rshift(t3, t3, 1);
+			} else {
+				if (mpi_test_bit(t1, 0))
+					mpi_add(t1, t1, v);
+				mpi_rshift(t1, t1, 1);
+				mpi_rshift(t3, t3, 1);
+			}
+Y4:
+			;