[PATCH v5 2/8] lib/mpi: Extend the MPI library
Marcelo Henrique Cerri
marcelo.cerri at canonical.com
Fri Jul 10 09:12:03 EDT 2020
Hi, Tianjia.
On Thu, Jul 09, 2020 at 04:40:09PM +0800, Tianjia Zhang wrote:
> Expand the mpi library based on libgcrypt, and the ECC algorithm of
> mpi based on libgcrypt requires these functions.
> Some other algorithms will be developed based on mpi ecc, such as SM2.
>
> Signed-off-by: Tianjia Zhang <tianjia.zhang at linux.alibaba.com>
> ---
> include/linux/mpi.h | 88 +++++++++++
> lib/mpi/Makefile | 5 +
> lib/mpi/mpi-add.c | 207 +++++++++++++++++++++++++
> lib/mpi/mpi-bit.c | 251 ++++++++++++++++++++++++++++++
> lib/mpi/mpi-cmp.c | 46 ++++--
> lib/mpi/mpi-div.c | 238 +++++++++++++++++++++++++++++
> lib/mpi/mpi-internal.h | 53 +++++++
> lib/mpi/mpi-inv.c | 143 ++++++++++++++++++
> lib/mpi/mpi-mod.c | 155 +++++++++++++++++++
> lib/mpi/mpi-mul.c | 94 ++++++++++++
> lib/mpi/mpicoder.c | 336 +++++++++++++++++++++++++++++++++++++++++
> lib/mpi/mpih-div.c | 294 ++++++++++++++++++++++++++++++++++++
> lib/mpi/mpih-mul.c | 25 +++
> lib/mpi/mpiutil.c | 204 +++++++++++++++++++++++++
> 14 files changed, 2129 insertions(+), 10 deletions(-)
> create mode 100644 lib/mpi/mpi-add.c
> create mode 100644 lib/mpi/mpi-div.c
> create mode 100644 lib/mpi/mpi-inv.c
> create mode 100644 lib/mpi/mpi-mod.c
> create mode 100644 lib/mpi/mpi-mul.c
>
> diff --git a/include/linux/mpi.h b/include/linux/mpi.h
> index 7bd6d8af0004..2dddf4c6e011 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);
> @@ -62,10 +120,40 @@ 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-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_ui(MPI w, MPI u, unsigned long 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 d5874a7f5ff9..5f40f93ff3d9 100644
> --- a/lib/mpi/Makefile
> +++ b/lib/mpi/Makefile
> @@ -14,8 +14,13 @@ mpi-y = \
> generic_mpih-sub1.o \
> generic_mpih-add1.o \
> mpicoder.o \
> + mpi-add.o \
> mpi-bit.o \
> mpi-cmp.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..9afad7832737
> --- /dev/null
> +++ b/lib/mpi/mpi-add.c
> @@ -0,0 +1,207 @@
> +/* 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);
You are ignoring the mpi_resize() return. I believe these new functions
need to return an int to indicate errors as mpi_powm() does.
> +
> + /* 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);
> +
> +
> +/****************
> + * Subtract the unsigned integer V from the mpi-integer U and store the
> + * result in W.
> + */
> +void 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)
> + 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;
> + 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;
> +}
> +
> +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:
> + ;
> + } while (!mpi_test_bit(t3, 0)); /* while t3 is even */
> +
> + if (!t3->sign) {
> + mpi_set(u1, t1);
> + if (!odd)
> + mpi_set(u2, t2);
> + mpi_set(u3, t3);
> + } else {
> + mpi_sub(v1, v, t1);
> + sign = u->sign; u->sign = !u->sign;
> + if (!odd)
> + mpi_sub(v2, u, t2);
> + u->sign = sign;
> + sign = t3->sign; t3->sign = !t3->sign;
> + mpi_set(v3, t3);
> + t3->sign = sign;
> + }
> + mpi_sub(t1, u1, v1);
> + if (!odd)
> + mpi_sub(t2, u2, v2);
> + mpi_sub(t3, u3, v3);
> + if (t1->sign) {
> + mpi_add(t1, t1, v);
> + if (!odd)
> + mpi_sub(t2, t2, u);
> + }
> + } while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */
> + /* mpi_lshift( u3, k ); */
> + mpi_set(x, u1);
> +
> + 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 1;
> +}
> +EXPORT_SYMBOL_GPL(mpi_invm);
> diff --git a/lib/mpi/mpi-mod.c b/lib/mpi/mpi-mod.c
> new file mode 100644
> index 000000000000..47bc59edd4ff
> --- /dev/null
> +++ b/lib/mpi/mpi-mod.c
> @@ -0,0 +1,155 @@
> +/* mpi-mod.c - Modular reduction
> + * Copyright (C) 1998, 1999, 2001, 2002, 2003,
> + * 2007 Free Software Foundation, Inc.
> + *
> + * This file is part of Libgcrypt.
> + */
> +
> +
> +#include "mpi-internal.h"
> +#include "longlong.h"
> +
> +/* Context used with Barrett reduction. */
> +struct barrett_ctx_s {
> + MPI m; /* The modulus - may not be modified. */
> + int m_copied; /* If true, M needs to be released. */
> + int k;
> + MPI y;
> + MPI r1; /* Helper MPI. */
> + MPI r2; /* Helper MPI. */
> + MPI r3; /* Helper MPI allocated on demand. */
> +};
> +
> +
> +
> +void mpi_mod(MPI rem, MPI dividend, MPI divisor)
> +{
> + mpi_fdiv_r(rem, dividend, divisor);
> +}
> +
> +/* This function returns a new context for Barrett based operations on
> + * the modulus M. This context needs to be released using
> + * _gcry_mpi_barrett_free. If COPY is true M will be transferred to
> + * the context and the user may change M. If COPY is false, M may not
> + * be changed until gcry_mpi_barrett_free has been called.
> + */
> +mpi_barrett_t mpi_barrett_init(MPI m, int copy)
> +{
> + mpi_barrett_t ctx;
> + MPI tmp;
> +
> + mpi_normalize(m);
> + ctx = kcalloc(1, sizeof(*ctx), GFP_KERNEL);
> +
> + if (copy) {
> + ctx->m = mpi_copy(m);
> + ctx->m_copied = 1;
> + } else
> + ctx->m = m;
> +
> + ctx->k = mpi_get_nlimbs(m);
> + tmp = mpi_alloc(ctx->k + 1);
> +
> + /* Barrett precalculation: y = floor(b^(2k) / m). */
> + mpi_set_ui(tmp, 1);
> + mpi_lshift_limbs(tmp, 2 * ctx->k);
> + mpi_fdiv_q(tmp, tmp, m);
> +
> + ctx->y = tmp;
> + ctx->r1 = mpi_alloc(2 * ctx->k + 1);
> + ctx->r2 = mpi_alloc(2 * ctx->k + 1);
> +
> + return ctx;
> +}
> +
> +void mpi_barrett_free(mpi_barrett_t ctx)
> +{
> + if (ctx) {
> + mpi_free(ctx->y);
> + mpi_free(ctx->r1);
> + mpi_free(ctx->r2);
> + if (ctx->r3)
> + mpi_free(ctx->r3);
> + if (ctx->m_copied)
> + mpi_free(ctx->m);
> + kfree(ctx);
> + }
> +}
> +
> +
> +/* R = X mod M
> + *
> + * Using Barrett reduction. Before using this function
> + * _gcry_mpi_barrett_init must have been called to do the
> + * precalculations. CTX is the context created by this precalculation
> + * and also conveys M. If the Barret reduction could no be done a
> + * straightforward reduction method is used.
> + *
> + * We assume that these conditions are met:
> + * Input: x =(x_2k-1 ...x_0)_b
> + * m =(m_k-1 ....m_0)_b with m_k-1 != 0
> + * Output: r = x mod m
> + */
> +void mpi_mod_barrett(MPI r, MPI x, mpi_barrett_t ctx)
> +{
> + MPI m = ctx->m;
> + int k = ctx->k;
> + MPI y = ctx->y;
> + MPI r1 = ctx->r1;
> + MPI r2 = ctx->r2;
> + int sign;
> +
> + mpi_normalize(x);
> + if (mpi_get_nlimbs(x) > 2*k) {
> + mpi_mod(r, x, m);
> + return;
> + }
> +
> + sign = x->sign;
> + x->sign = 0;
> +
> + /* 1. q1 = floor( x / b^k-1)
> + * q2 = q1 * y
> + * q3 = floor( q2 / b^k+1 )
> + * Actually, we don't need qx, we can work direct on r2
> + */
> + mpi_set(r2, x);
> + mpi_rshift_limbs(r2, k-1);
> + mpi_mul(r2, r2, y);
> + mpi_rshift_limbs(r2, k+1);
> +
> + /* 2. r1 = x mod b^k+1
> + * r2 = q3 * m mod b^k+1
> + * r = r1 - r2
> + * 3. if r < 0 then r = r + b^k+1
> + */
> + mpi_set(r1, x);
> + if (r1->nlimbs > k+1) /* Quick modulo operation. */
> + r1->nlimbs = k+1;
> + mpi_mul(r2, r2, m);
> + if (r2->nlimbs > k+1) /* Quick modulo operation. */
> + r2->nlimbs = k+1;
> + mpi_sub(r, r1, r2);
> +
> + if (mpi_has_sign(r)) {
> + if (!ctx->r3) {
> + ctx->r3 = mpi_alloc(k + 2);
> + mpi_set_ui(ctx->r3, 1);
> + mpi_lshift_limbs(ctx->r3, k + 1);
> + }
> + mpi_add(r, r, ctx->r3);
> + }
> +
> + /* 4. while r >= m do r = r - m */
> + while (mpi_cmp(r, m) >= 0)
> + mpi_sub(r, r, m);
> +
> + x->sign = sign;
> +}
> +
> +
> +void mpi_mul_barrett(MPI w, MPI u, MPI v, mpi_barrett_t ctx)
> +{
> + mpi_mul(w, u, v);
> + mpi_mod_barrett(w, w, ctx);
> +}
> diff --git a/lib/mpi/mpi-mul.c b/lib/mpi/mpi-mul.c
> new file mode 100644
> index 000000000000..587e6335cc12
> --- /dev/null
> +++ b/lib/mpi/mpi-mul.c
> @@ -0,0 +1,94 @@
> +/* mpi-mul.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"
> +
> +void mpi_mul(MPI w, MPI u, MPI v)
> +{
> + 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;
> + unsigned int tmp_limb_nlimbs = 0;
> +
> + 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 < wsize) {
> + if (wp == up || wp == vp) {
> + wp = mpi_alloc_limb_space(wsize);
> + assign_wp = 1;
> + } else {
> + mpi_resize(w, wsize);
> + 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. */
> + tmp_limb_nlimbs = usize;
> + up = tmp_limb = mpi_alloc_limb_space(usize);
> + /* 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. */
> + tmp_limb_nlimbs = vsize;
> + vp = tmp_limb = mpi_alloc_limb_space(vsize);
> + /* Copy to the temporary space. */
> + MPN_COPY(vp, wp, vsize);
> + }
> + }
> +
> + if (!vsize)
> + wsize = 0;
> + else {
> + mpihelp_mul(wp, up, usize, vp, vsize, &cy);
> + wsize -= cy ? 0:1;
> + }
> +
> + if (assign_wp)
> + mpi_assign_limb_space(w, wp, wsize);
> + w->nlimbs = wsize;
> + w->sign = sign_product;
> + if (tmp_limb)
> + mpi_free_limb_space(tmp_limb);
> +}
> +
> +void mpi_mulm(MPI w, MPI u, MPI v, MPI m)
> +{
> + mpi_mul(w, u, v);
> + mpi_tdiv_r(w, w, m);
> +}
> +EXPORT_SYMBOL_GPL(mpi_mulm);
> diff --git a/lib/mpi/mpicoder.c b/lib/mpi/mpicoder.c
> index eead4b339466..7ea225b2204f 100644
> --- a/lib/mpi/mpicoder.c
> +++ b/lib/mpi/mpicoder.c
> @@ -25,6 +25,7 @@
> #include <linux/string.h>
> #include "mpi-internal.h"
>
> +#define MAX_EXTERN_SCAN_BYTES (16*1024*1024)
> #define MAX_EXTERN_MPI_BITS 16384
>
> /**
> @@ -109,6 +110,112 @@ MPI mpi_read_from_buffer(const void *xbuffer, unsigned *ret_nread)
> }
> EXPORT_SYMBOL_GPL(mpi_read_from_buffer);
>
> +/****************
> + * Fill the mpi VAL from the hex string in STR.
> + */
> +int mpi_fromstr(MPI val, const char *str)
> +{
> + int sign = 0;
> + int prepend_zero = 0;
> + int i, j, c, c1, c2;
> + unsigned int nbits, nbytes, nlimbs;
> + mpi_limb_t a;
> +
> + if (*str == '-') {
> + sign = 1;
> + str++;
> + }
> +
> + /* Skip optional hex prefix. */
> + if (*str == '0' && str[1] == 'x')
> + str += 2;
> +
> + nbits = strlen(str);
> + if (nbits > MAX_EXTERN_SCAN_BYTES) {
> + mpi_clear(val);
> + return -EINVAL;
> + }
> + nbits *= 4;
> + if ((nbits % 8))
> + prepend_zero = 1;
> +
> + nbytes = (nbits+7) / 8;
> + nlimbs = (nbytes+BYTES_PER_MPI_LIMB-1) / BYTES_PER_MPI_LIMB;
> +
> + if (val->alloced < nlimbs)
> + mpi_resize(val, nlimbs);
> +
> + i = BYTES_PER_MPI_LIMB - (nbytes % BYTES_PER_MPI_LIMB);
> + i %= BYTES_PER_MPI_LIMB;
> + j = val->nlimbs = nlimbs;
> + val->sign = sign;
> + for (; j > 0; j--) {
> + a = 0;
> + for (; i < BYTES_PER_MPI_LIMB; i++) {
> + if (prepend_zero) {
> + c1 = '0';
> + prepend_zero = 0;
> + } else
> + c1 = *str++;
> +
> + if (!c1) {
> + mpi_clear(val);
> + return -EINVAL;
> + }
> + c2 = *str++;
> + if (!c2) {
> + mpi_clear(val);
> + return -EINVAL;
> + }
> + if (c1 >= '0' && c1 <= '9')
> + c = c1 - '0';
> + else if (c1 >= 'a' && c1 <= 'f')
> + c = c1 - 'a' + 10;
> + else if (c1 >= 'A' && c1 <= 'F')
> + c = c1 - 'A' + 10;
> + else {
> + mpi_clear(val);
> + return -EINVAL;
> + }
> + c <<= 4;
> + if (c2 >= '0' && c2 <= '9')
> + c |= c2 - '0';
> + else if (c2 >= 'a' && c2 <= 'f')
> + c |= c2 - 'a' + 10;
> + else if (c2 >= 'A' && c2 <= 'F')
> + c |= c2 - 'A' + 10;
> + else {
> + mpi_clear(val);
> + return -EINVAL;
> + }
> + a <<= 8;
> + a |= c;
> + }
> + i = 0;
> + val->d[j-1] = a;
> + }
> +
> + return 0;
> +}
> +EXPORT_SYMBOL_GPL(mpi_fromstr);
> +
> +MPI mpi_scanval(const char *string)
> +{
> + MPI a;
> +
> + a = mpi_alloc(0);
> + if (!a)
> + return NULL;
> +
> + if (mpi_fromstr(a, string)) {
> + mpi_free(a);
> + return NULL;
> + }
> + mpi_normalize(a);
> + return a;
> +}
> +EXPORT_SYMBOL_GPL(mpi_scanval);
> +
> static int count_lzeros(MPI a)
> {
> mpi_limb_t alimb;
> @@ -413,3 +520,232 @@ MPI mpi_read_raw_from_sgl(struct scatterlist *sgl, unsigned int nbytes)
> return val;
> }
> EXPORT_SYMBOL_GPL(mpi_read_raw_from_sgl);
> +
> +/* Perform a two's complement operation on buffer P of size N bytes. */
> +static void twocompl(unsigned char *p, unsigned int n)
> +{
> + int i;
> +
> + for (i = n-1; i >= 0 && !p[i]; i--)
> + ;
> + if (i >= 0) {
> + if ((p[i] & 0x01))
> + p[i] = (((p[i] ^ 0xfe) | 0x01) & 0xff);
> + else if ((p[i] & 0x02))
> + p[i] = (((p[i] ^ 0xfc) | 0x02) & 0xfe);
> + else if ((p[i] & 0x04))
> + p[i] = (((p[i] ^ 0xf8) | 0x04) & 0xfc);
> + else if ((p[i] & 0x08))
> + p[i] = (((p[i] ^ 0xf0) | 0x08) & 0xf8);
> + else if ((p[i] & 0x10))
> + p[i] = (((p[i] ^ 0xe0) | 0x10) & 0xf0);
> + else if ((p[i] & 0x20))
> + p[i] = (((p[i] ^ 0xc0) | 0x20) & 0xe0);
> + else if ((p[i] & 0x40))
> + p[i] = (((p[i] ^ 0x80) | 0x40) & 0xc0);
> + else
> + p[i] = 0x80;
> +
> + for (i--; i >= 0; i--)
> + p[i] ^= 0xff;
> + }
> +}
> +
> +int mpi_print(enum gcry_mpi_format format, unsigned char *buffer,
> + size_t buflen, size_t *nwritten, MPI a)
> +{
> + unsigned int nbits = mpi_get_nbits(a);
> + size_t len;
> + size_t dummy_nwritten;
> + int negative;
> +
> + if (!nwritten)
> + nwritten = &dummy_nwritten;
> +
> + /* Libgcrypt does no always care to set clear the sign if the value
> + * is 0. For printing this is a bit of a surprise, in particular
> + * because if some of the formats don't support negative numbers but
> + * should be able to print a zero. Thus we need this extra test
> + * for a negative number.
> + */
> + if (a->sign && mpi_cmp_ui(a, 0))
> + negative = 1;
> + else
> + negative = 0;
> +
> + len = buflen;
> + *nwritten = 0;
> + if (format == GCRYMPI_FMT_STD) {
> + unsigned char *tmp;
> + int extra = 0;
> + unsigned int n;
> +
> + tmp = mpi_get_buffer(a, &n, NULL);
> + if (!tmp)
> + return -EINVAL;
> +
> + if (negative) {
> + twocompl(tmp, n);
> + if (!(*tmp & 0x80)) {
> + /* Need to extend the sign. */
> + n++;
> + extra = 2;
> + }
> + } else if (n && (*tmp & 0x80)) {
> + /* Positive but the high bit of the returned buffer is set.
> + * Thus we need to print an extra leading 0x00 so that the
> + * output is interpreted as a positive number.
> + */
> + n++;
> + extra = 1;
> + }
> +
> + if (buffer && n > len) {
> + /* The provided buffer is too short. */
> + kfree(tmp);
> + return -E2BIG;
> + }
> + if (buffer) {
> + unsigned char *s = buffer;
> +
> + if (extra == 1)
> + *s++ = 0;
> + else if (extra)
> + *s++ = 0xff;
> + memcpy(s, tmp, n-!!extra);
> + }
> + kfree(tmp);
> + *nwritten = n;
> + return 0;
> + } else if (format == GCRYMPI_FMT_USG) {
> + unsigned int n = (nbits + 7)/8;
> +
> + /* Note: We ignore the sign for this format. */
> + /* FIXME: for performance reasons we should put this into
> + * mpi_aprint because we can then use the buffer directly.
> + */
> +
> + if (buffer && n > len)
> + return -E2BIG;
> + if (buffer) {
> + unsigned char *tmp;
> +
> + tmp = mpi_get_buffer(a, &n, NULL);
> + if (!tmp)
> + return -EINVAL;
> + memcpy(buffer, tmp, n);
> + kfree(tmp);
> + }
> + *nwritten = n;
> + return 0;
> + } else if (format == GCRYMPI_FMT_PGP) {
> + unsigned int n = (nbits + 7)/8;
> +
> + /* The PGP format can only handle unsigned integers. */
> + if (negative)
> + return -EINVAL;
> +
> + if (buffer && n+2 > len)
> + return -E2BIG;
> +
> + if (buffer) {
> + unsigned char *tmp;
> + unsigned char *s = buffer;
> +
> + s[0] = nbits >> 8;
> + s[1] = nbits;
> +
> + tmp = mpi_get_buffer(a, &n, NULL);
> + if (!tmp)
> + return -EINVAL;
> + memcpy(s+2, tmp, n);
> + kfree(tmp);
> + }
> + *nwritten = n+2;
> + return 0;
> + } else if (format == GCRYMPI_FMT_SSH) {
> + unsigned char *tmp;
> + int extra = 0;
> + unsigned int n;
> +
> + tmp = mpi_get_buffer(a, &n, NULL);
> + if (!tmp)
> + return -EINVAL;
> +
> + if (negative) {
> + twocompl(tmp, n);
> + if (!(*tmp & 0x80)) {
> + /* Need to extend the sign. */
> + n++;
> + extra = 2;
> + }
> + } else if (n && (*tmp & 0x80)) {
> + n++;
> + extra = 1;
> + }
> +
> + if (buffer && n+4 > len) {
> + kfree(tmp);
> + return -E2BIG;
> + }
> +
> + if (buffer) {
> + unsigned char *s = buffer;
> +
> + *s++ = n >> 24;
> + *s++ = n >> 16;
> + *s++ = n >> 8;
> + *s++ = n;
> + if (extra == 1)
> + *s++ = 0;
> + else if (extra)
> + *s++ = 0xff;
> + memcpy(s, tmp, n-!!extra);
> + }
> + kfree(tmp);
> + *nwritten = 4+n;
> + return 0;
> + } else if (format == GCRYMPI_FMT_HEX) {
> + unsigned char *tmp;
> + int i;
> + int extra = 0;
> + unsigned int n = 0;
> +
> + tmp = mpi_get_buffer(a, &n, NULL);
> + if (!tmp)
> + return -EINVAL;
> + if (!n || (*tmp & 0x80))
> + extra = 2;
> +
> + if (buffer && 2*n + extra + negative + 1 > len) {
> + kfree(tmp);
> + return -E2BIG;
> + }
> + if (buffer) {
> + unsigned char *s = buffer;
> +
> + if (negative)
> + *s++ = '-';
> + if (extra) {
> + *s++ = '0';
> + *s++ = '0';
> + }
> +
> + for (i = 0; i < n; i++) {
> + unsigned int c = tmp[i];
> +
> + *s++ = (c >> 4) < 10 ? '0'+(c>>4) : 'A'+(c>>4)-10;
> + c &= 15;
> + *s++ = c < 10 ? '0'+c : 'A'+c-10;
> + }
> + *s++ = 0;
> + *nwritten = s - buffer;
> + } else {
> + *nwritten = 2*n + extra + negative + 1;
> + }
> + kfree(tmp);
> + return 0;
> + } else
> + return -EINVAL;
> +}
> +EXPORT_SYMBOL_GPL(mpi_print);
> diff --git a/lib/mpi/mpih-div.c b/lib/mpi/mpih-div.c
> index 913a519eb005..182a656a1ba0 100644
> --- a/lib/mpi/mpih-div.c
> +++ b/lib/mpi/mpih-div.c
> @@ -24,6 +24,150 @@
> #define UDIV_TIME UMUL_TIME
> #endif
>
> +
> +mpi_limb_t
> +mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
> + mpi_limb_t divisor_limb)
> +{
> + mpi_size_t i;
> + mpi_limb_t n1, n0, r;
> + mpi_limb_t dummy;
> +
> + /* Botch: Should this be handled at all? Rely on callers? */
> + if (!dividend_size)
> + return 0;
> +
> + /* If multiplication is much faster than division, and the
> + * dividend is large, pre-invert the divisor, and use
> + * only multiplications in the inner loop.
> + *
> + * This test should be read:
> + * Does it ever help to use udiv_qrnnd_preinv?
> + * && Does what we save compensate for the inversion overhead?
> + */
> + if (UDIV_TIME > (2 * UMUL_TIME + 6)
> + && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
> + int normalization_steps;
> +
> + normalization_steps = count_leading_zeros(divisor_limb);
> + if (normalization_steps) {
> + mpi_limb_t divisor_limb_inverted;
> +
> + divisor_limb <<= normalization_steps;
> +
> + /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
> + * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
> + * most significant bit (with weight 2**N) implicit.
> + *
> + * Special case for DIVISOR_LIMB == 100...000.
> + */
> + if (!(divisor_limb << 1))
> + divisor_limb_inverted = ~(mpi_limb_t)0;
> + else
> + udiv_qrnnd(divisor_limb_inverted, dummy,
> + -divisor_limb, 0, divisor_limb);
> +
> + n1 = dividend_ptr[dividend_size - 1];
> + r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
> +
> + /* Possible optimization:
> + * if (r == 0
> + * && divisor_limb > ((n1 << normalization_steps)
> + * | (dividend_ptr[dividend_size - 2] >> ...)))
> + * ...one division less...
> + */
> + for (i = dividend_size - 2; i >= 0; i--) {
> + n0 = dividend_ptr[i];
> + UDIV_QRNND_PREINV(dummy, r, r,
> + ((n1 << normalization_steps)
> + | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
> + divisor_limb, divisor_limb_inverted);
> + n1 = n0;
> + }
> + UDIV_QRNND_PREINV(dummy, r, r,
> + n1 << normalization_steps,
> + divisor_limb, divisor_limb_inverted);
> + return r >> normalization_steps;
> + } else {
> + mpi_limb_t divisor_limb_inverted;
> +
> + /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
> + * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
> + * most significant bit (with weight 2**N) implicit.
> + *
> + * Special case for DIVISOR_LIMB == 100...000.
> + */
> + if (!(divisor_limb << 1))
> + divisor_limb_inverted = ~(mpi_limb_t)0;
> + else
> + udiv_qrnnd(divisor_limb_inverted, dummy,
> + -divisor_limb, 0, divisor_limb);
> +
> + i = dividend_size - 1;
> + r = dividend_ptr[i];
> +
> + if (r >= divisor_limb)
> + r = 0;
> + else
> + i--;
> +
> + for ( ; i >= 0; i--) {
> + n0 = dividend_ptr[i];
> + UDIV_QRNND_PREINV(dummy, r, r,
> + n0, divisor_limb, divisor_limb_inverted);
> + }
> + return r;
> + }
> + } else {
> + if (UDIV_NEEDS_NORMALIZATION) {
> + int normalization_steps;
> +
> + normalization_steps = count_leading_zeros(divisor_limb);
> + if (normalization_steps) {
> + divisor_limb <<= normalization_steps;
> +
> + n1 = dividend_ptr[dividend_size - 1];
> + r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
> +
> + /* Possible optimization:
> + * if (r == 0
> + * && divisor_limb > ((n1 << normalization_steps)
> + * | (dividend_ptr[dividend_size - 2] >> ...)))
> + * ...one division less...
> + */
> + for (i = dividend_size - 2; i >= 0; i--) {
> + n0 = dividend_ptr[i];
> + udiv_qrnnd(dummy, r, r,
> + ((n1 << normalization_steps)
> + | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
> + divisor_limb);
> + n1 = n0;
> + }
> + udiv_qrnnd(dummy, r, r,
> + n1 << normalization_steps,
> + divisor_limb);
> + return r >> normalization_steps;
> + }
> + }
> + /* No normalization needed, either because udiv_qrnnd doesn't require
> + * it, or because DIVISOR_LIMB is already normalized.
> + */
> + i = dividend_size - 1;
> + r = dividend_ptr[i];
> +
> + if (r >= divisor_limb)
> + r = 0;
> + else
> + i--;
> +
> + for (; i >= 0; i--) {
> + n0 = dividend_ptr[i];
> + udiv_qrnnd(dummy, r, r, n0, divisor_limb);
> + }
> + return r;
> + }
> +}
> +
> /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
> * the NSIZE-DSIZE least significant quotient limbs at QP
> * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
> @@ -221,3 +365,153 @@ mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
>
> return most_significant_q_limb;
> }
> +
> +/****************
> + * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
> + * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
> + * Return the single-limb remainder.
> + * There are no constraints on the value of the divisor.
> + *
> + * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
> + */
> +
> +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)
> +{
> + mpi_size_t i;
> + mpi_limb_t n1, n0, r;
> + mpi_limb_t dummy;
> +
> + if (!dividend_size)
> + return 0;
> +
> + /* If multiplication is much faster than division, and the
> + * dividend is large, pre-invert the divisor, and use
> + * only multiplications in the inner loop.
> + *
> + * This test should be read:
> + * Does it ever help to use udiv_qrnnd_preinv?
> + * && Does what we save compensate for the inversion overhead?
> + */
> + if (UDIV_TIME > (2 * UMUL_TIME + 6)
> + && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
> + int normalization_steps;
> +
> + normalization_steps = count_leading_zeros(divisor_limb);
> + if (normalization_steps) {
> + mpi_limb_t divisor_limb_inverted;
> +
> + divisor_limb <<= normalization_steps;
> +
> + /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
> + * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
> + * most significant bit (with weight 2**N) implicit.
> + */
> + /* Special case for DIVISOR_LIMB == 100...000. */
> + if (!(divisor_limb << 1))
> + divisor_limb_inverted = ~(mpi_limb_t)0;
> + else
> + udiv_qrnnd(divisor_limb_inverted, dummy,
> + -divisor_limb, 0, divisor_limb);
> +
> + n1 = dividend_ptr[dividend_size - 1];
> + r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
> +
> + /* Possible optimization:
> + * if (r == 0
> + * && divisor_limb > ((n1 << normalization_steps)
> + * | (dividend_ptr[dividend_size - 2] >> ...)))
> + * ...one division less...
> + */
> + for (i = dividend_size - 2; i >= 0; i--) {
> + n0 = dividend_ptr[i];
> + UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r,
> + ((n1 << normalization_steps)
> + | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
> + divisor_limb, divisor_limb_inverted);
> + n1 = n0;
> + }
> + UDIV_QRNND_PREINV(quot_ptr[0], r, r,
> + n1 << normalization_steps,
> + divisor_limb, divisor_limb_inverted);
> + return r >> normalization_steps;
> + } else {
> + mpi_limb_t divisor_limb_inverted;
> +
> + /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
> + * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
> + * most significant bit (with weight 2**N) implicit.
> + */
> + /* Special case for DIVISOR_LIMB == 100...000. */
> + if (!(divisor_limb << 1))
> + divisor_limb_inverted = ~(mpi_limb_t) 0;
> + else
> + udiv_qrnnd(divisor_limb_inverted, dummy,
> + -divisor_limb, 0, divisor_limb);
> +
> + i = dividend_size - 1;
> + r = dividend_ptr[i];
> +
> + if (r >= divisor_limb)
> + r = 0;
> + else
> + quot_ptr[i--] = 0;
> +
> + for ( ; i >= 0; i--) {
> + n0 = dividend_ptr[i];
> + UDIV_QRNND_PREINV(quot_ptr[i], r, r,
> + n0, divisor_limb, divisor_limb_inverted);
> + }
> + return r;
> + }
> + } else {
> + if (UDIV_NEEDS_NORMALIZATION) {
> + int normalization_steps;
> +
> + normalization_steps = count_leading_zeros(divisor_limb);
> + if (normalization_steps) {
> + divisor_limb <<= normalization_steps;
> +
> + n1 = dividend_ptr[dividend_size - 1];
> + r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
> +
> + /* Possible optimization:
> + * if (r == 0
> + * && divisor_limb > ((n1 << normalization_steps)
> + * | (dividend_ptr[dividend_size - 2] >> ...)))
> + * ...one division less...
> + */
> + for (i = dividend_size - 2; i >= 0; i--) {
> + n0 = dividend_ptr[i];
> + udiv_qrnnd(quot_ptr[i + 1], r, r,
> + ((n1 << normalization_steps)
> + | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
> + divisor_limb);
> + n1 = n0;
> + }
> + udiv_qrnnd(quot_ptr[0], r, r,
> + n1 << normalization_steps,
> + divisor_limb);
> + return r >> normalization_steps;
> + }
> + }
> + /* No normalization needed, either because udiv_qrnnd doesn't require
> + * it, or because DIVISOR_LIMB is already normalized.
> + */
> + i = dividend_size - 1;
> + r = dividend_ptr[i];
> +
> + if (r >= divisor_limb)
> + r = 0;
> + else
> + quot_ptr[i--] = 0;
> +
> + for (; i >= 0; i--) {
> + n0 = dividend_ptr[i];
> + udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb);
> + }
> + return r;
> + }
> +}
> diff --git a/lib/mpi/mpih-mul.c b/lib/mpi/mpih-mul.c
> index a93647564054..e5f1c84e3c48 100644
> --- a/lib/mpi/mpih-mul.c
> +++ b/lib/mpi/mpih-mul.c
> @@ -317,6 +317,31 @@ 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)
> +{
> + if (up == vp) {
> + if (size < KARATSUBA_THRESHOLD)
> + mpih_sqr_n_basecase(prodp, up, size);
> + else {
> + mpi_ptr_t tspace;
> + tspace = mpi_alloc_limb_space(2 * size);
> + mpih_sqr_n(prodp, up, size, tspace);
> + mpi_free_limb_space(tspace);
> + }
> + } else {
> + if (size < KARATSUBA_THRESHOLD)
> + mul_n_basecase(prodp, up, vp, size);
> + else {
> + mpi_ptr_t tspace;
> + tspace = mpi_alloc_limb_space(2 * size);
> + mul_n(prodp, up, vp, size, tspace);
> + mpi_free_limb_space(tspace);
> + }
> + }
> +}
> +
> int
> mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
> mpi_ptr_t up, mpi_size_t usize,
> diff --git a/lib/mpi/mpiutil.c b/lib/mpi/mpiutil.c
> index 20ed0f766787..e4046f74f336 100644
> --- a/lib/mpi/mpiutil.c
> +++ b/lib/mpi/mpiutil.c
> @@ -20,6 +20,63 @@
>
> #include "mpi-internal.h"
>
> +/* Constants allocated right away at startup. */
> +static MPI constants[MPI_NUMBER_OF_CONSTANTS];
> +
> +/* Initialize the MPI subsystem. This is called early and allows to
> + * do some initialization without taking care of threading issues.
> + */
> +static int __init mpi_init(void)
> +{
> + int idx;
> + unsigned long value;
> +
> + for (idx = 0; idx < MPI_NUMBER_OF_CONSTANTS; idx++) {
> + switch (idx) {
> + case MPI_C_ZERO:
> + value = 0;
> + break;
> + case MPI_C_ONE:
> + value = 1;
> + break;
> + case MPI_C_TWO:
> + value = 2;
> + break;
> + case MPI_C_THREE:
> + value = 3;
> + break;
> + case MPI_C_FOUR:
> + value = 4;
> + break;
> + case MPI_C_EIGHT:
> + value = 8;
> + break;
> + default:
> + pr_err("MPI: invalid mpi_const selector %d\n", idx);
> + return -EFAULT;
> + }
> + constants[idx] = mpi_alloc_set_ui(value);
> + constants[idx]->flags = (16|32);
> + }
> +
> + return 0;
> +}
> +postcore_initcall(mpi_init);
> +
> +/* Return a constant MPI descripbed by NO which is one of the
> + * MPI_C_xxx macros. There is no need to copy this returned value; it
> + * may be used directly.
> + */
> +MPI mpi_const(enum gcry_mpi_constants no)
> +{
> + if ((int)no < 0 || no > MPI_NUMBER_OF_CONSTANTS)
> + pr_err("MPI: invalid mpi_const selector %d\n", no);
> + if (!constants[no])
> + pr_err("MPI: MPI subsystem not initialized\n");
> + return constants[no];
> +}
> +EXPORT_SYMBOL_GPL(mpi_const);
> +
> /****************
> * Note: It was a bad idea to use the number of limbs to allocate
> * because on a alpha the limbs are large but we normally need
> @@ -106,6 +163,15 @@ int mpi_resize(MPI a, unsigned nlimbs)
> return 0;
> }
>
> +void mpi_clear(MPI a)
> +{
> + if (!a)
> + return;
> + a->nlimbs = 0;
> + a->flags = 0;
> +}
> +EXPORT_SYMBOL_GPL(mpi_clear);
> +
> void mpi_free(MPI a)
> {
> if (!a)
> @@ -122,5 +188,143 @@ void mpi_free(MPI a)
> }
> EXPORT_SYMBOL_GPL(mpi_free);
>
> +/****************
> + * Note: This copy function should not interpret the MPI
> + * but copy it transparently.
> + */
> +MPI mpi_copy(MPI a)
> +{
> + int i;
> + MPI b;
> +
> + if (a) {
> + b = mpi_alloc(a->nlimbs);
> + b->nlimbs = a->nlimbs;
> + b->sign = a->sign;
> + b->flags = a->flags;
> + b->flags &= ~(16|32); /* Reset the immutable and constant flags. */
> + for (i = 0; i < b->nlimbs; i++)
> + b->d[i] = a->d[i];
> + } else
> + b = NULL;
> + return b;
> +}
> +
> +/****************
> + * This function allocates an MPI which is optimized to hold
> + * a value as large as the one given in the argument and allocates it
> + * with the same flags as A.
> + */
> +MPI mpi_alloc_like(MPI a)
> +{
> + MPI b;
> +
> + if (a) {
> + b = mpi_alloc(a->nlimbs);
> + b->nlimbs = 0;
> + b->sign = 0;
> + b->flags = a->flags;
> + } else
> + b = NULL;
> +
> + return b;
> +}
> +
> +
> +/* Set U into W and release U. If W is NULL only U will be released. */
> +void mpi_snatch(MPI w, MPI u)
> +{
> + if (w) {
> + mpi_assign_limb_space(w, u->d, u->alloced);
> + w->nlimbs = u->nlimbs;
> + w->sign = u->sign;
> + w->flags = u->flags;
> + u->alloced = 0;
> + u->nlimbs = 0;
> + u->d = NULL;
> + }
> + mpi_free(u);
> +}
> +
> +
> +MPI mpi_set(MPI w, MPI u)
> +{
> + mpi_ptr_t wp, up;
> + mpi_size_t usize = u->nlimbs;
> + int usign = u->sign;
> +
> + if (!w)
> + w = mpi_alloc(mpi_get_nlimbs(u));
> + RESIZE_IF_NEEDED(w, usize);
> + wp = w->d;
> + up = u->d;
> + MPN_COPY(wp, up, usize);
> + w->nlimbs = usize;
> + w->flags = u->flags;
> + w->flags &= ~(16|32); /* Reset the immutable and constant flags. */
> + w->sign = usign;
> + return w;
> +}
> +EXPORT_SYMBOL_GPL(mpi_set);
> +
> +MPI mpi_set_ui(MPI w, unsigned long u)
> +{
> + if (!w)
> + w = mpi_alloc(1);
> + /* FIXME: If U is 0 we have no need to resize and thus possible
> + * allocating the the limbs.
> + */
> + RESIZE_IF_NEEDED(w, 1);
> + w->d[0] = u;
> + w->nlimbs = u ? 1 : 0;
> + w->sign = 0;
> + w->flags = 0;
> + return w;
> +}
> +EXPORT_SYMBOL_GPL(mpi_set_ui);
> +
> +MPI mpi_alloc_set_ui(unsigned long u)
> +{
> + MPI w = mpi_alloc(1);
> + w->d[0] = u;
> + w->nlimbs = u ? 1 : 0;
> + w->sign = 0;
> + return w;
> +}
> +
> +/****************
> + * Swap the value of A and B, when SWAP is 1.
> + * Leave the value when SWAP is 0.
> + * This implementation should be constant-time regardless of SWAP.
> + */
> +void mpi_swap_cond(MPI a, MPI b, unsigned long swap)
> +{
> + mpi_size_t i;
> + mpi_size_t nlimbs;
> + mpi_limb_t mask = ((mpi_limb_t)0) - swap;
> + mpi_limb_t x;
> +
> + if (a->alloced > b->alloced)
> + nlimbs = b->alloced;
> + else
> + nlimbs = a->alloced;
> + if (a->nlimbs > nlimbs || b->nlimbs > nlimbs)
> + return;
> +
> + for (i = 0; i < nlimbs; i++) {
> + x = mask & (a->d[i] ^ b->d[i]);
> + a->d[i] = a->d[i] ^ x;
> + b->d[i] = b->d[i] ^ x;
> + }
> +
> + x = mask & (a->nlimbs ^ b->nlimbs);
> + a->nlimbs = a->nlimbs ^ x;
> + b->nlimbs = b->nlimbs ^ x;
> +
> + x = mask & (a->sign ^ b->sign);
> + a->sign = a->sign ^ x;
> + b->sign = b->sign ^ x;
> +}
> +
> MODULE_DESCRIPTION("Multiprecision maths library");
> MODULE_LICENSE("GPL");
> --
> 2.17.1
>
--
Regards,
Marcelo
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