| Index: net/third_party/nss/ssl/mpi/mpi.c
|
| diff --git a/net/third_party/nss/ssl/mpi/mpi.c b/net/third_party/nss/ssl/mpi/mpi.c
|
| new file mode 100644
|
| index 0000000000000000000000000000000000000000..8cd6ca6ad592b6ef35f9595a0be2e326e52243b0
|
| --- /dev/null
|
| +++ b/net/third_party/nss/ssl/mpi/mpi.c
|
| @@ -0,0 +1,4852 @@
|
| +/*
|
| + * mpi.c
|
| + *
|
| + * Arbitrary precision integer arithmetic library
|
| + *
|
| + * ***** BEGIN LICENSE BLOCK *****
|
| + * Version: MPL 1.1/GPL 2.0/LGPL 2.1
|
| + *
|
| + * The contents of this file are subject to the Mozilla Public License Version
|
| + * 1.1 (the "License"); you may not use this file except in compliance with
|
| + * the License. You may obtain a copy of the License at
|
| + * http://www.mozilla.org/MPL/
|
| + *
|
| + * Software distributed under the License is distributed on an "AS IS" basis,
|
| + * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
|
| + * for the specific language governing rights and limitations under the
|
| + * License.
|
| + *
|
| + * The Original Code is the MPI Arbitrary Precision Integer Arithmetic library.
|
| + *
|
| + * The Initial Developer of the Original Code is
|
| + * Michael J. Fromberger.
|
| + * Portions created by the Initial Developer are Copyright (C) 1998
|
| + * the Initial Developer. All Rights Reserved.
|
| + *
|
| + * Contributor(s):
|
| + * Netscape Communications Corporation
|
| + * Douglas Stebila <douglas@stebila.ca> of Sun Laboratories.
|
| + *
|
| + * Alternatively, the contents of this file may be used under the terms of
|
| + * either the GNU General Public License Version 2 or later (the "GPL"), or
|
| + * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
|
| + * in which case the provisions of the GPL or the LGPL are applicable instead
|
| + * of those above. If you wish to allow use of your version of this file only
|
| + * under the terms of either the GPL or the LGPL, and not to allow others to
|
| + * use your version of this file under the terms of the MPL, indicate your
|
| + * decision by deleting the provisions above and replace them with the notice
|
| + * and other provisions required by the GPL or the LGPL. If you do not delete
|
| + * the provisions above, a recipient may use your version of this file under
|
| + * the terms of any one of the MPL, the GPL or the LGPL.
|
| + *
|
| + * ***** END LICENSE BLOCK ***** */
|
| +/* $Id: mpi.c,v 1.47 2010/05/02 22:36:41 nelson%bolyard.com Exp $ */
|
| +
|
| +#define MP_API_COMPATIBLE 1
|
| +#include "mpi-priv.h"
|
| +#if defined(OSF1)
|
| +#include <c_asm.h>
|
| +#endif
|
| +
|
| +#if MP_LOGTAB
|
| +/*
|
| + A table of the logs of 2 for various bases (the 0 and 1 entries of
|
| + this table are meaningless and should not be referenced).
|
| +
|
| + This table is used to compute output lengths for the mp_toradix()
|
| + function. Since a number n in radix r takes up about log_r(n)
|
| + digits, we estimate the output size by taking the least integer
|
| + greater than log_r(n), where:
|
| +
|
| + log_r(n) = log_2(n) * log_r(2)
|
| +
|
| + This table, therefore, is a table of log_r(2) for 2 <= r <= 36,
|
| + which are the output bases supported.
|
| + */
|
| +#include "logtab.h"
|
| +#endif
|
| +
|
| +/* {{{ Constant strings */
|
| +
|
| +/* Constant strings returned by mp_strerror() */
|
| +static const char *mp_err_string[] = {
|
| + "unknown result code", /* say what? */
|
| + "boolean true", /* MP_OKAY, MP_YES */
|
| + "boolean false", /* MP_NO */
|
| + "out of memory", /* MP_MEM */
|
| + "argument out of range", /* MP_RANGE */
|
| + "invalid input parameter", /* MP_BADARG */
|
| + "result is undefined" /* MP_UNDEF */
|
| +};
|
| +
|
| +/* Value to digit maps for radix conversion */
|
| +
|
| +/* s_dmap_1 - standard digits and letters */
|
| +static const char *s_dmap_1 =
|
| + "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
|
| +
|
| +/* }}} */
|
| +
|
| +unsigned long mp_allocs;
|
| +unsigned long mp_frees;
|
| +unsigned long mp_copies;
|
| +
|
| +/* {{{ Default precision manipulation */
|
| +
|
| +/* Default precision for newly created mp_int's */
|
| +static mp_size s_mp_defprec = MP_DEFPREC;
|
| +
|
| +mp_size mp_get_prec(void)
|
| +{
|
| + return s_mp_defprec;
|
| +
|
| +} /* end mp_get_prec() */
|
| +
|
| +void mp_set_prec(mp_size prec)
|
| +{
|
| + if(prec == 0)
|
| + s_mp_defprec = MP_DEFPREC;
|
| + else
|
| + s_mp_defprec = prec;
|
| +
|
| +} /* end mp_set_prec() */
|
| +
|
| +/* }}} */
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* {{{ mp_init(mp) */
|
| +
|
| +/*
|
| + mp_init(mp)
|
| +
|
| + Initialize a new zero-valued mp_int. Returns MP_OKAY if successful,
|
| + MP_MEM if memory could not be allocated for the structure.
|
| + */
|
| +
|
| +mp_err mp_init(mp_int *mp)
|
| +{
|
| + return mp_init_size(mp, s_mp_defprec);
|
| +
|
| +} /* end mp_init() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_init_size(mp, prec) */
|
| +
|
| +/*
|
| + mp_init_size(mp, prec)
|
| +
|
| + Initialize a new zero-valued mp_int with at least the given
|
| + precision; returns MP_OKAY if successful, or MP_MEM if memory could
|
| + not be allocated for the structure.
|
| + */
|
| +
|
| +mp_err mp_init_size(mp_int *mp, mp_size prec)
|
| +{
|
| + ARGCHK(mp != NULL && prec > 0, MP_BADARG);
|
| +
|
| + prec = MP_ROUNDUP(prec, s_mp_defprec);
|
| + if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL)
|
| + return MP_MEM;
|
| +
|
| + SIGN(mp) = ZPOS;
|
| + USED(mp) = 1;
|
| + ALLOC(mp) = prec;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_init_size() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_init_copy(mp, from) */
|
| +
|
| +/*
|
| + mp_init_copy(mp, from)
|
| +
|
| + Initialize mp as an exact copy of from. Returns MP_OKAY if
|
| + successful, MP_MEM if memory could not be allocated for the new
|
| + structure.
|
| + */
|
| +
|
| +mp_err mp_init_copy(mp_int *mp, const mp_int *from)
|
| +{
|
| + ARGCHK(mp != NULL && from != NULL, MP_BADARG);
|
| +
|
| + if(mp == from)
|
| + return MP_OKAY;
|
| +
|
| + if((DIGITS(mp) = s_mp_alloc(ALLOC(from), sizeof(mp_digit))) == NULL)
|
| + return MP_MEM;
|
| +
|
| + s_mp_copy(DIGITS(from), DIGITS(mp), USED(from));
|
| + USED(mp) = USED(from);
|
| + ALLOC(mp) = ALLOC(from);
|
| + SIGN(mp) = SIGN(from);
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_init_copy() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_copy(from, to) */
|
| +
|
| +/*
|
| + mp_copy(from, to)
|
| +
|
| + Copies the mp_int 'from' to the mp_int 'to'. It is presumed that
|
| + 'to' has already been initialized (if not, use mp_init_copy()
|
| + instead). If 'from' and 'to' are identical, nothing happens.
|
| + */
|
| +
|
| +mp_err mp_copy(const mp_int *from, mp_int *to)
|
| +{
|
| + ARGCHK(from != NULL && to != NULL, MP_BADARG);
|
| +
|
| + if(from == to)
|
| + return MP_OKAY;
|
| +
|
| + ++mp_copies;
|
| + { /* copy */
|
| + mp_digit *tmp;
|
| +
|
| + /*
|
| + If the allocated buffer in 'to' already has enough space to hold
|
| + all the used digits of 'from', we'll re-use it to avoid hitting
|
| + the memory allocater more than necessary; otherwise, we'd have
|
| + to grow anyway, so we just allocate a hunk and make the copy as
|
| + usual
|
| + */
|
| + if(ALLOC(to) >= USED(from)) {
|
| + s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from));
|
| + s_mp_copy(DIGITS(from), DIGITS(to), USED(from));
|
| +
|
| + } else {
|
| + if((tmp = s_mp_alloc(ALLOC(from), sizeof(mp_digit))) == NULL)
|
| + return MP_MEM;
|
| +
|
| + s_mp_copy(DIGITS(from), tmp, USED(from));
|
| +
|
| + if(DIGITS(to) != NULL) {
|
| +#if MP_CRYPTO
|
| + s_mp_setz(DIGITS(to), ALLOC(to));
|
| +#endif
|
| + s_mp_free(DIGITS(to));
|
| + }
|
| +
|
| + DIGITS(to) = tmp;
|
| + ALLOC(to) = ALLOC(from);
|
| + }
|
| +
|
| + /* Copy the precision and sign from the original */
|
| + USED(to) = USED(from);
|
| + SIGN(to) = SIGN(from);
|
| + } /* end copy */
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_copy() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_exch(mp1, mp2) */
|
| +
|
| +/*
|
| + mp_exch(mp1, mp2)
|
| +
|
| + Exchange mp1 and mp2 without allocating any intermediate memory
|
| + (well, unless you count the stack space needed for this call and the
|
| + locals it creates...). This cannot fail.
|
| + */
|
| +
|
| +void mp_exch(mp_int *mp1, mp_int *mp2)
|
| +{
|
| +#if MP_ARGCHK == 2
|
| + assert(mp1 != NULL && mp2 != NULL);
|
| +#else
|
| + if(mp1 == NULL || mp2 == NULL)
|
| + return;
|
| +#endif
|
| +
|
| + s_mp_exch(mp1, mp2);
|
| +
|
| +} /* end mp_exch() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_clear(mp) */
|
| +
|
| +/*
|
| + mp_clear(mp)
|
| +
|
| + Release the storage used by an mp_int, and void its fields so that
|
| + if someone calls mp_clear() again for the same int later, we won't
|
| + get tollchocked.
|
| + */
|
| +
|
| +void mp_clear(mp_int *mp)
|
| +{
|
| + if(mp == NULL)
|
| + return;
|
| +
|
| + if(DIGITS(mp) != NULL) {
|
| +#if MP_CRYPTO
|
| + s_mp_setz(DIGITS(mp), ALLOC(mp));
|
| +#endif
|
| + s_mp_free(DIGITS(mp));
|
| + DIGITS(mp) = NULL;
|
| + }
|
| +
|
| + USED(mp) = 0;
|
| + ALLOC(mp) = 0;
|
| +
|
| +} /* end mp_clear() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_zero(mp) */
|
| +
|
| +/*
|
| + mp_zero(mp)
|
| +
|
| + Set mp to zero. Does not change the allocated size of the structure,
|
| + and therefore cannot fail (except on a bad argument, which we ignore)
|
| + */
|
| +void mp_zero(mp_int *mp)
|
| +{
|
| + if(mp == NULL)
|
| + return;
|
| +
|
| + s_mp_setz(DIGITS(mp), ALLOC(mp));
|
| + USED(mp) = 1;
|
| + SIGN(mp) = ZPOS;
|
| +
|
| +} /* end mp_zero() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_set(mp, d) */
|
| +
|
| +void mp_set(mp_int *mp, mp_digit d)
|
| +{
|
| + if(mp == NULL)
|
| + return;
|
| +
|
| + mp_zero(mp);
|
| + DIGIT(mp, 0) = d;
|
| +
|
| +} /* end mp_set() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_set_int(mp, z) */
|
| +
|
| +mp_err mp_set_int(mp_int *mp, long z)
|
| +{
|
| + int ix;
|
| + unsigned long v = labs(z);
|
| + mp_err res;
|
| +
|
| + ARGCHK(mp != NULL, MP_BADARG);
|
| +
|
| + mp_zero(mp);
|
| + if(z == 0)
|
| + return MP_OKAY; /* shortcut for zero */
|
| +
|
| + if (sizeof v <= sizeof(mp_digit)) {
|
| + DIGIT(mp,0) = v;
|
| + } else {
|
| + for (ix = sizeof(long) - 1; ix >= 0; ix--) {
|
| + if ((res = s_mp_mul_d(mp, (UCHAR_MAX + 1))) != MP_OKAY)
|
| + return res;
|
| +
|
| + res = s_mp_add_d(mp, (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX));
|
| + if (res != MP_OKAY)
|
| + return res;
|
| + }
|
| + }
|
| + if(z < 0)
|
| + SIGN(mp) = NEG;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_set_int() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_set_ulong(mp, z) */
|
| +
|
| +mp_err mp_set_ulong(mp_int *mp, unsigned long z)
|
| +{
|
| + int ix;
|
| + mp_err res;
|
| +
|
| + ARGCHK(mp != NULL, MP_BADARG);
|
| +
|
| + mp_zero(mp);
|
| + if(z == 0)
|
| + return MP_OKAY; /* shortcut for zero */
|
| +
|
| + if (sizeof z <= sizeof(mp_digit)) {
|
| + DIGIT(mp,0) = z;
|
| + } else {
|
| + for (ix = sizeof(long) - 1; ix >= 0; ix--) {
|
| + if ((res = s_mp_mul_d(mp, (UCHAR_MAX + 1))) != MP_OKAY)
|
| + return res;
|
| +
|
| + res = s_mp_add_d(mp, (mp_digit)((z >> (ix * CHAR_BIT)) & UCHAR_MAX));
|
| + if (res != MP_OKAY)
|
| + return res;
|
| + }
|
| + }
|
| + return MP_OKAY;
|
| +} /* end mp_set_ulong() */
|
| +
|
| +/* }}} */
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* {{{ Digit arithmetic */
|
| +
|
| +/* {{{ mp_add_d(a, d, b) */
|
| +
|
| +/*
|
| + mp_add_d(a, d, b)
|
| +
|
| + Compute the sum b = a + d, for a single digit d. Respects the sign of
|
| + its primary addend (single digits are unsigned anyway).
|
| + */
|
| +
|
| +mp_err mp_add_d(const mp_int *a, mp_digit d, mp_int *b)
|
| +{
|
| + mp_int tmp;
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
|
| + return res;
|
| +
|
| + if(SIGN(&tmp) == ZPOS) {
|
| + if((res = s_mp_add_d(&tmp, d)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + } else if(s_mp_cmp_d(&tmp, d) >= 0) {
|
| + if((res = s_mp_sub_d(&tmp, d)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + } else {
|
| + mp_neg(&tmp, &tmp);
|
| +
|
| + DIGIT(&tmp, 0) = d - DIGIT(&tmp, 0);
|
| + }
|
| +
|
| + if(s_mp_cmp_d(&tmp, 0) == 0)
|
| + SIGN(&tmp) = ZPOS;
|
| +
|
| + s_mp_exch(&tmp, b);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&tmp);
|
| + return res;
|
| +
|
| +} /* end mp_add_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_sub_d(a, d, b) */
|
| +
|
| +/*
|
| + mp_sub_d(a, d, b)
|
| +
|
| + Compute the difference b = a - d, for a single digit d. Respects the
|
| + sign of its subtrahend (single digits are unsigned anyway).
|
| + */
|
| +
|
| +mp_err mp_sub_d(const mp_int *a, mp_digit d, mp_int *b)
|
| +{
|
| + mp_int tmp;
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
|
| + return res;
|
| +
|
| + if(SIGN(&tmp) == NEG) {
|
| + if((res = s_mp_add_d(&tmp, d)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + } else if(s_mp_cmp_d(&tmp, d) >= 0) {
|
| + if((res = s_mp_sub_d(&tmp, d)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + } else {
|
| + mp_neg(&tmp, &tmp);
|
| +
|
| + DIGIT(&tmp, 0) = d - DIGIT(&tmp, 0);
|
| + SIGN(&tmp) = NEG;
|
| + }
|
| +
|
| + if(s_mp_cmp_d(&tmp, 0) == 0)
|
| + SIGN(&tmp) = ZPOS;
|
| +
|
| + s_mp_exch(&tmp, b);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&tmp);
|
| + return res;
|
| +
|
| +} /* end mp_sub_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_mul_d(a, d, b) */
|
| +
|
| +/*
|
| + mp_mul_d(a, d, b)
|
| +
|
| + Compute the product b = a * d, for a single digit d. Respects the sign
|
| + of its multiplicand (single digits are unsigned anyway)
|
| + */
|
| +
|
| +mp_err mp_mul_d(const mp_int *a, mp_digit d, mp_int *b)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL, MP_BADARG);
|
| +
|
| + if(d == 0) {
|
| + mp_zero(b);
|
| + return MP_OKAY;
|
| + }
|
| +
|
| + if((res = mp_copy(a, b)) != MP_OKAY)
|
| + return res;
|
| +
|
| + res = s_mp_mul_d(b, d);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_mul_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_mul_2(a, c) */
|
| +
|
| +mp_err mp_mul_2(const mp_int *a, mp_int *c)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_copy(a, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + return s_mp_mul_2(c);
|
| +
|
| +} /* end mp_mul_2() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_div_d(a, d, q, r) */
|
| +
|
| +/*
|
| + mp_div_d(a, d, q, r)
|
| +
|
| + Compute the quotient q = a / d and remainder r = a mod d, for a
|
| + single digit d. Respects the sign of its divisor (single digits are
|
| + unsigned anyway).
|
| + */
|
| +
|
| +mp_err mp_div_d(const mp_int *a, mp_digit d, mp_int *q, mp_digit *r)
|
| +{
|
| + mp_err res;
|
| + mp_int qp;
|
| + mp_digit rem;
|
| + int pow;
|
| +
|
| + ARGCHK(a != NULL, MP_BADARG);
|
| +
|
| + if(d == 0)
|
| + return MP_RANGE;
|
| +
|
| + /* Shortcut for powers of two ... */
|
| + if((pow = s_mp_ispow2d(d)) >= 0) {
|
| + mp_digit mask;
|
| +
|
| + mask = ((mp_digit)1 << pow) - 1;
|
| + rem = DIGIT(a, 0) & mask;
|
| +
|
| + if(q) {
|
| + mp_copy(a, q);
|
| + s_mp_div_2d(q, pow);
|
| + }
|
| +
|
| + if(r)
|
| + *r = rem;
|
| +
|
| + return MP_OKAY;
|
| + }
|
| +
|
| + if((res = mp_init_copy(&qp, a)) != MP_OKAY)
|
| + return res;
|
| +
|
| + res = s_mp_div_d(&qp, d, &rem);
|
| +
|
| + if(s_mp_cmp_d(&qp, 0) == 0)
|
| + SIGN(q) = ZPOS;
|
| +
|
| + if(r)
|
| + *r = rem;
|
| +
|
| + if(q)
|
| + s_mp_exch(&qp, q);
|
| +
|
| + mp_clear(&qp);
|
| + return res;
|
| +
|
| +} /* end mp_div_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_div_2(a, c) */
|
| +
|
| +/*
|
| + mp_div_2(a, c)
|
| +
|
| + Compute c = a / 2, disregarding the remainder.
|
| + */
|
| +
|
| +mp_err mp_div_2(const mp_int *a, mp_int *c)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_copy(a, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + s_mp_div_2(c);
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_div_2() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_expt_d(a, d, b) */
|
| +
|
| +mp_err mp_expt_d(const mp_int *a, mp_digit d, mp_int *c)
|
| +{
|
| + mp_int s, x;
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_init(&s)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_init_copy(&x, a)) != MP_OKAY)
|
| + goto X;
|
| +
|
| + DIGIT(&s, 0) = 1;
|
| +
|
| + while(d != 0) {
|
| + if(d & 1) {
|
| + if((res = s_mp_mul(&s, &x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + d /= 2;
|
| +
|
| + if((res = s_mp_sqr(&x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + s_mp_exch(&s, c);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&x);
|
| +X:
|
| + mp_clear(&s);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_expt_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* {{{ Full arithmetic */
|
| +
|
| +/* {{{ mp_abs(a, b) */
|
| +
|
| +/*
|
| + mp_abs(a, b)
|
| +
|
| + Compute b = |a|. 'a' and 'b' may be identical.
|
| + */
|
| +
|
| +mp_err mp_abs(const mp_int *a, mp_int *b)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_copy(a, b)) != MP_OKAY)
|
| + return res;
|
| +
|
| + SIGN(b) = ZPOS;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_abs() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_neg(a, b) */
|
| +
|
| +/*
|
| + mp_neg(a, b)
|
| +
|
| + Compute b = -a. 'a' and 'b' may be identical.
|
| + */
|
| +
|
| +mp_err mp_neg(const mp_int *a, mp_int *b)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_copy(a, b)) != MP_OKAY)
|
| + return res;
|
| +
|
| + if(s_mp_cmp_d(b, 0) == MP_EQ)
|
| + SIGN(b) = ZPOS;
|
| + else
|
| + SIGN(b) = (SIGN(b) == NEG) ? ZPOS : NEG;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_neg() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_add(a, b, c) */
|
| +
|
| +/*
|
| + mp_add(a, b, c)
|
| +
|
| + Compute c = a + b. All parameters may be identical.
|
| + */
|
| +
|
| +mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if(SIGN(a) == SIGN(b)) { /* same sign: add values, keep sign */
|
| + MP_CHECKOK( s_mp_add_3arg(a, b, c) );
|
| + } else if(s_mp_cmp(a, b) >= 0) { /* different sign: |a| >= |b| */
|
| + MP_CHECKOK( s_mp_sub_3arg(a, b, c) );
|
| + } else { /* different sign: |a| < |b| */
|
| + MP_CHECKOK( s_mp_sub_3arg(b, a, c) );
|
| + }
|
| +
|
| + if (s_mp_cmp_d(c, 0) == MP_EQ)
|
| + SIGN(c) = ZPOS;
|
| +
|
| +CLEANUP:
|
| + return res;
|
| +
|
| +} /* end mp_add() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_sub(a, b, c) */
|
| +
|
| +/*
|
| + mp_sub(a, b, c)
|
| +
|
| + Compute c = a - b. All parameters may be identical.
|
| + */
|
| +
|
| +mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
|
| +{
|
| + mp_err res;
|
| + int magDiff;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if (a == b) {
|
| + mp_zero(c);
|
| + return MP_OKAY;
|
| + }
|
| +
|
| + if (MP_SIGN(a) != MP_SIGN(b)) {
|
| + MP_CHECKOK( s_mp_add_3arg(a, b, c) );
|
| + } else if (!(magDiff = s_mp_cmp(a, b))) {
|
| + mp_zero(c);
|
| + res = MP_OKAY;
|
| + } else if (magDiff > 0) {
|
| + MP_CHECKOK( s_mp_sub_3arg(a, b, c) );
|
| + } else {
|
| + MP_CHECKOK( s_mp_sub_3arg(b, a, c) );
|
| + MP_SIGN(c) = !MP_SIGN(a);
|
| + }
|
| +
|
| + if (s_mp_cmp_d(c, 0) == MP_EQ)
|
| + MP_SIGN(c) = MP_ZPOS;
|
| +
|
| +CLEANUP:
|
| + return res;
|
| +
|
| +} /* end mp_sub() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_mul(a, b, c) */
|
| +
|
| +/*
|
| + mp_mul(a, b, c)
|
| +
|
| + Compute c = a * b. All parameters may be identical.
|
| + */
|
| +mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int * c)
|
| +{
|
| + mp_digit *pb;
|
| + mp_int tmp;
|
| + mp_err res;
|
| + mp_size ib;
|
| + mp_size useda, usedb;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if (a == c) {
|
| + if ((res = mp_init_copy(&tmp, a)) != MP_OKAY)
|
| + return res;
|
| + if (a == b)
|
| + b = &tmp;
|
| + a = &tmp;
|
| + } else if (b == c) {
|
| + if ((res = mp_init_copy(&tmp, b)) != MP_OKAY)
|
| + return res;
|
| + b = &tmp;
|
| + } else {
|
| + MP_DIGITS(&tmp) = 0;
|
| + }
|
| +
|
| + if (MP_USED(a) < MP_USED(b)) {
|
| + const mp_int *xch = b; /* switch a and b, to do fewer outer loops */
|
| + b = a;
|
| + a = xch;
|
| + }
|
| +
|
| + MP_USED(c) = 1; MP_DIGIT(c, 0) = 0;
|
| + if((res = s_mp_pad(c, USED(a) + USED(b))) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| +#ifdef NSS_USE_COMBA
|
| + if ((MP_USED(a) == MP_USED(b)) && IS_POWER_OF_2(MP_USED(b))) {
|
| + if (MP_USED(a) == 4) {
|
| + s_mp_mul_comba_4(a, b, c);
|
| + goto CLEANUP;
|
| + }
|
| + if (MP_USED(a) == 8) {
|
| + s_mp_mul_comba_8(a, b, c);
|
| + goto CLEANUP;
|
| + }
|
| + if (MP_USED(a) == 16) {
|
| + s_mp_mul_comba_16(a, b, c);
|
| + goto CLEANUP;
|
| + }
|
| + if (MP_USED(a) == 32) {
|
| + s_mp_mul_comba_32(a, b, c);
|
| + goto CLEANUP;
|
| + }
|
| + }
|
| +#endif
|
| +
|
| + pb = MP_DIGITS(b);
|
| + s_mpv_mul_d(MP_DIGITS(a), MP_USED(a), *pb++, MP_DIGITS(c));
|
| +
|
| + /* Outer loop: Digits of b */
|
| + useda = MP_USED(a);
|
| + usedb = MP_USED(b);
|
| + for (ib = 1; ib < usedb; ib++) {
|
| + mp_digit b_i = *pb++;
|
| +
|
| + /* Inner product: Digits of a */
|
| + if (b_i)
|
| + s_mpv_mul_d_add(MP_DIGITS(a), useda, b_i, MP_DIGITS(c) + ib);
|
| + else
|
| + MP_DIGIT(c, ib + useda) = b_i;
|
| + }
|
| +
|
| + s_mp_clamp(c);
|
| +
|
| + if(SIGN(a) == SIGN(b) || s_mp_cmp_d(c, 0) == MP_EQ)
|
| + SIGN(c) = ZPOS;
|
| + else
|
| + SIGN(c) = NEG;
|
| +
|
| +CLEANUP:
|
| + mp_clear(&tmp);
|
| + return res;
|
| +} /* end mp_mul() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_sqr(a, sqr) */
|
| +
|
| +#if MP_SQUARE
|
| +/*
|
| + Computes the square of a. This can be done more
|
| + efficiently than a general multiplication, because many of the
|
| + computation steps are redundant when squaring. The inner product
|
| + step is a bit more complicated, but we save a fair number of
|
| + iterations of the multiplication loop.
|
| + */
|
| +
|
| +/* sqr = a^2; Caller provides both a and tmp; */
|
| +mp_err mp_sqr(const mp_int *a, mp_int *sqr)
|
| +{
|
| + mp_digit *pa;
|
| + mp_digit d;
|
| + mp_err res;
|
| + mp_size ix;
|
| + mp_int tmp;
|
| + int count;
|
| +
|
| + ARGCHK(a != NULL && sqr != NULL, MP_BADARG);
|
| +
|
| + if (a == sqr) {
|
| + if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
|
| + return res;
|
| + a = &tmp;
|
| + } else {
|
| + DIGITS(&tmp) = 0;
|
| + res = MP_OKAY;
|
| + }
|
| +
|
| + ix = 2 * MP_USED(a);
|
| + if (ix > MP_ALLOC(sqr)) {
|
| + MP_USED(sqr) = 1;
|
| + MP_CHECKOK( s_mp_grow(sqr, ix) );
|
| + }
|
| + MP_USED(sqr) = ix;
|
| + MP_DIGIT(sqr, 0) = 0;
|
| +
|
| +#ifdef NSS_USE_COMBA
|
| + if (IS_POWER_OF_2(MP_USED(a))) {
|
| + if (MP_USED(a) == 4) {
|
| + s_mp_sqr_comba_4(a, sqr);
|
| + goto CLEANUP;
|
| + }
|
| + if (MP_USED(a) == 8) {
|
| + s_mp_sqr_comba_8(a, sqr);
|
| + goto CLEANUP;
|
| + }
|
| + if (MP_USED(a) == 16) {
|
| + s_mp_sqr_comba_16(a, sqr);
|
| + goto CLEANUP;
|
| + }
|
| + if (MP_USED(a) == 32) {
|
| + s_mp_sqr_comba_32(a, sqr);
|
| + goto CLEANUP;
|
| + }
|
| + }
|
| +#endif
|
| +
|
| + pa = MP_DIGITS(a);
|
| + count = MP_USED(a) - 1;
|
| + if (count > 0) {
|
| + d = *pa++;
|
| + s_mpv_mul_d(pa, count, d, MP_DIGITS(sqr) + 1);
|
| + for (ix = 3; --count > 0; ix += 2) {
|
| + d = *pa++;
|
| + s_mpv_mul_d_add(pa, count, d, MP_DIGITS(sqr) + ix);
|
| + } /* for(ix ...) */
|
| + MP_DIGIT(sqr, MP_USED(sqr)-1) = 0; /* above loop stopped short of this. */
|
| +
|
| + /* now sqr *= 2 */
|
| + s_mp_mul_2(sqr);
|
| + } else {
|
| + MP_DIGIT(sqr, 1) = 0;
|
| + }
|
| +
|
| + /* now add the squares of the digits of a to sqr. */
|
| + s_mpv_sqr_add_prop(MP_DIGITS(a), MP_USED(a), MP_DIGITS(sqr));
|
| +
|
| + SIGN(sqr) = ZPOS;
|
| + s_mp_clamp(sqr);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&tmp);
|
| + return res;
|
| +
|
| +} /* end mp_sqr() */
|
| +#endif
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_div(a, b, q, r) */
|
| +
|
| +/*
|
| + mp_div(a, b, q, r)
|
| +
|
| + Compute q = a / b and r = a mod b. Input parameters may be re-used
|
| + as output parameters. If q or r is NULL, that portion of the
|
| + computation will be discarded (although it will still be computed)
|
| + */
|
| +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r)
|
| +{
|
| + mp_err res;
|
| + mp_int *pQ, *pR;
|
| + mp_int qtmp, rtmp, btmp;
|
| + int cmp;
|
| + mp_sign signA;
|
| + mp_sign signB;
|
| +
|
| + ARGCHK(a != NULL && b != NULL, MP_BADARG);
|
| +
|
| + signA = MP_SIGN(a);
|
| + signB = MP_SIGN(b);
|
| +
|
| + if(mp_cmp_z(b) == MP_EQ)
|
| + return MP_RANGE;
|
| +
|
| + DIGITS(&qtmp) = 0;
|
| + DIGITS(&rtmp) = 0;
|
| + DIGITS(&btmp) = 0;
|
| +
|
| + /* Set up some temporaries... */
|
| + if (!r || r == a || r == b) {
|
| + MP_CHECKOK( mp_init_copy(&rtmp, a) );
|
| + pR = &rtmp;
|
| + } else {
|
| + MP_CHECKOK( mp_copy(a, r) );
|
| + pR = r;
|
| + }
|
| +
|
| + if (!q || q == a || q == b) {
|
| + MP_CHECKOK( mp_init_size(&qtmp, MP_USED(a)) );
|
| + pQ = &qtmp;
|
| + } else {
|
| + MP_CHECKOK( s_mp_pad(q, MP_USED(a)) );
|
| + pQ = q;
|
| + mp_zero(pQ);
|
| + }
|
| +
|
| + /*
|
| + If |a| <= |b|, we can compute the solution without division;
|
| + otherwise, we actually do the work required.
|
| + */
|
| + if ((cmp = s_mp_cmp(a, b)) <= 0) {
|
| + if (cmp) {
|
| + /* r was set to a above. */
|
| + mp_zero(pQ);
|
| + } else {
|
| + mp_set(pQ, 1);
|
| + mp_zero(pR);
|
| + }
|
| + } else {
|
| + MP_CHECKOK( mp_init_copy(&btmp, b) );
|
| + MP_CHECKOK( s_mp_div(pR, &btmp, pQ) );
|
| + }
|
| +
|
| + /* Compute the signs for the output */
|
| + MP_SIGN(pR) = signA; /* Sr = Sa */
|
| + /* Sq = ZPOS if Sa == Sb */ /* Sq = NEG if Sa != Sb */
|
| + MP_SIGN(pQ) = (signA == signB) ? ZPOS : NEG;
|
| +
|
| + if(s_mp_cmp_d(pQ, 0) == MP_EQ)
|
| + SIGN(pQ) = ZPOS;
|
| + if(s_mp_cmp_d(pR, 0) == MP_EQ)
|
| + SIGN(pR) = ZPOS;
|
| +
|
| + /* Copy output, if it is needed */
|
| + if(q && q != pQ)
|
| + s_mp_exch(pQ, q);
|
| +
|
| + if(r && r != pR)
|
| + s_mp_exch(pR, r);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&btmp);
|
| + mp_clear(&rtmp);
|
| + mp_clear(&qtmp);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_div() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_div_2d(a, d, q, r) */
|
| +
|
| +mp_err mp_div_2d(const mp_int *a, mp_digit d, mp_int *q, mp_int *r)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL, MP_BADARG);
|
| +
|
| + if(q) {
|
| + if((res = mp_copy(a, q)) != MP_OKAY)
|
| + return res;
|
| + }
|
| + if(r) {
|
| + if((res = mp_copy(a, r)) != MP_OKAY)
|
| + return res;
|
| + }
|
| + if(q) {
|
| + s_mp_div_2d(q, d);
|
| + }
|
| + if(r) {
|
| + s_mp_mod_2d(r, d);
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_div_2d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_expt(a, b, c) */
|
| +
|
| +/*
|
| + mp_expt(a, b, c)
|
| +
|
| + Compute c = a ** b, that is, raise a to the b power. Uses a
|
| + standard iterative square-and-multiply technique.
|
| + */
|
| +
|
| +mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c)
|
| +{
|
| + mp_int s, x;
|
| + mp_err res;
|
| + mp_digit d;
|
| + int dig, bit;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if(mp_cmp_z(b) < 0)
|
| + return MP_RANGE;
|
| +
|
| + if((res = mp_init(&s)) != MP_OKAY)
|
| + return res;
|
| +
|
| + mp_set(&s, 1);
|
| +
|
| + if((res = mp_init_copy(&x, a)) != MP_OKAY)
|
| + goto X;
|
| +
|
| + /* Loop over low-order digits in ascending order */
|
| + for(dig = 0; dig < (USED(b) - 1); dig++) {
|
| + d = DIGIT(b, dig);
|
| +
|
| + /* Loop over bits of each non-maximal digit */
|
| + for(bit = 0; bit < DIGIT_BIT; bit++) {
|
| + if(d & 1) {
|
| + if((res = s_mp_mul(&s, &x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + d >>= 1;
|
| +
|
| + if((res = s_mp_sqr(&x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| + }
|
| +
|
| + /* Consider now the last digit... */
|
| + d = DIGIT(b, dig);
|
| +
|
| + while(d) {
|
| + if(d & 1) {
|
| + if((res = s_mp_mul(&s, &x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + d >>= 1;
|
| +
|
| + if((res = s_mp_sqr(&x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + if(mp_iseven(b))
|
| + SIGN(&s) = SIGN(a);
|
| +
|
| + res = mp_copy(&s, c);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&x);
|
| +X:
|
| + mp_clear(&s);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_expt() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_2expt(a, k) */
|
| +
|
| +/* Compute a = 2^k */
|
| +
|
| +mp_err mp_2expt(mp_int *a, mp_digit k)
|
| +{
|
| + ARGCHK(a != NULL, MP_BADARG);
|
| +
|
| + return s_mp_2expt(a, k);
|
| +
|
| +} /* end mp_2expt() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_mod(a, m, c) */
|
| +
|
| +/*
|
| + mp_mod(a, m, c)
|
| +
|
| + Compute c = a (mod m). Result will always be 0 <= c < m.
|
| + */
|
| +
|
| +mp_err mp_mod(const mp_int *a, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_err res;
|
| + int mag;
|
| +
|
| + ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if(SIGN(m) == NEG)
|
| + return MP_RANGE;
|
| +
|
| + /*
|
| + If |a| > m, we need to divide to get the remainder and take the
|
| + absolute value.
|
| +
|
| + If |a| < m, we don't need to do any division, just copy and adjust
|
| + the sign (if a is negative).
|
| +
|
| + If |a| == m, we can simply set the result to zero.
|
| +
|
| + This order is intended to minimize the average path length of the
|
| + comparison chain on common workloads -- the most frequent cases are
|
| + that |a| != m, so we do those first.
|
| + */
|
| + if((mag = s_mp_cmp(a, m)) > 0) {
|
| + if((res = mp_div(a, m, NULL, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + if(SIGN(c) == NEG) {
|
| + if((res = mp_add(c, m, c)) != MP_OKAY)
|
| + return res;
|
| + }
|
| +
|
| + } else if(mag < 0) {
|
| + if((res = mp_copy(a, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + if(mp_cmp_z(a) < 0) {
|
| + if((res = mp_add(c, m, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + }
|
| +
|
| + } else {
|
| + mp_zero(c);
|
| +
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_mod() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_mod_d(a, d, c) */
|
| +
|
| +/*
|
| + mp_mod_d(a, d, c)
|
| +
|
| + Compute c = a (mod d). Result will always be 0 <= c < d
|
| + */
|
| +mp_err mp_mod_d(const mp_int *a, mp_digit d, mp_digit *c)
|
| +{
|
| + mp_err res;
|
| + mp_digit rem;
|
| +
|
| + ARGCHK(a != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if(s_mp_cmp_d(a, d) > 0) {
|
| + if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY)
|
| + return res;
|
| +
|
| + } else {
|
| + if(SIGN(a) == NEG)
|
| + rem = d - DIGIT(a, 0);
|
| + else
|
| + rem = DIGIT(a, 0);
|
| + }
|
| +
|
| + if(c)
|
| + *c = rem;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_mod_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_sqrt(a, b) */
|
| +
|
| +/*
|
| + mp_sqrt(a, b)
|
| +
|
| + Compute the integer square root of a, and store the result in b.
|
| + Uses an integer-arithmetic version of Newton's iterative linear
|
| + approximation technique to determine this value; the result has the
|
| + following two properties:
|
| +
|
| + b^2 <= a
|
| + (b+1)^2 >= a
|
| +
|
| + It is a range error to pass a negative value.
|
| + */
|
| +mp_err mp_sqrt(const mp_int *a, mp_int *b)
|
| +{
|
| + mp_int x, t;
|
| + mp_err res;
|
| + mp_size used;
|
| +
|
| + ARGCHK(a != NULL && b != NULL, MP_BADARG);
|
| +
|
| + /* Cannot take square root of a negative value */
|
| + if(SIGN(a) == NEG)
|
| + return MP_RANGE;
|
| +
|
| + /* Special cases for zero and one, trivial */
|
| + if(mp_cmp_d(a, 1) <= 0)
|
| + return mp_copy(a, b);
|
| +
|
| + /* Initialize the temporaries we'll use below */
|
| + if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
|
| + return res;
|
| +
|
| + /* Compute an initial guess for the iteration as a itself */
|
| + if((res = mp_init_copy(&x, a)) != MP_OKAY)
|
| + goto X;
|
| +
|
| + used = MP_USED(&x);
|
| + if (used > 1) {
|
| + s_mp_rshd(&x, used / 2);
|
| + }
|
| +
|
| + for(;;) {
|
| + /* t = (x * x) - a */
|
| + mp_copy(&x, &t); /* can't fail, t is big enough for original x */
|
| + if((res = mp_sqr(&t, &t)) != MP_OKAY ||
|
| + (res = mp_sub(&t, a, &t)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + /* t = t / 2x */
|
| + s_mp_mul_2(&x);
|
| + if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + s_mp_div_2(&x);
|
| +
|
| + /* Terminate the loop, if the quotient is zero */
|
| + if(mp_cmp_z(&t) == MP_EQ)
|
| + break;
|
| +
|
| + /* x = x - t */
|
| + if((res = mp_sub(&x, &t, &x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + }
|
| +
|
| + /* Copy result to output parameter */
|
| + mp_sub_d(&x, 1, &x);
|
| + s_mp_exch(&x, b);
|
| +
|
| + CLEANUP:
|
| + mp_clear(&x);
|
| + X:
|
| + mp_clear(&t);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_sqrt() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* {{{ Modular arithmetic */
|
| +
|
| +#if MP_MODARITH
|
| +/* {{{ mp_addmod(a, b, m, c) */
|
| +
|
| +/*
|
| + mp_addmod(a, b, m, c)
|
| +
|
| + Compute c = (a + b) mod m
|
| + */
|
| +
|
| +mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_add(a, b, c)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_mod(c, m, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +}
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_submod(a, b, m, c) */
|
| +
|
| +/*
|
| + mp_submod(a, b, m, c)
|
| +
|
| + Compute c = (a - b) mod m
|
| + */
|
| +
|
| +mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_sub(a, b, c)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_mod(c, m, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +}
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_mulmod(a, b, m, c) */
|
| +
|
| +/*
|
| + mp_mulmod(a, b, m, c)
|
| +
|
| + Compute c = (a * b) mod m
|
| + */
|
| +
|
| +mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_mul(a, b, c)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_mod(c, m, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +}
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_sqrmod(a, m, c) */
|
| +
|
| +#if MP_SQUARE
|
| +mp_err mp_sqrmod(const mp_int *a, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_sqr(a, c)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_mod(c, m, c)) != MP_OKAY)
|
| + return res;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_sqrmod() */
|
| +#endif
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_exptmod(a, b, m, c) */
|
| +
|
| +/*
|
| + s_mp_exptmod(a, b, m, c)
|
| +
|
| + Compute c = (a ** b) mod m. Uses a standard square-and-multiply
|
| + method with modular reductions at each step. (This is basically the
|
| + same code as mp_expt(), except for the addition of the reductions)
|
| +
|
| + The modular reductions are done using Barrett's algorithm (see
|
| + s_mp_reduce() below for details)
|
| + */
|
| +
|
| +mp_err s_mp_exptmod(const mp_int *a, const mp_int *b, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_int s, x, mu;
|
| + mp_err res;
|
| + mp_digit d;
|
| + int dig, bit;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0)
|
| + return MP_RANGE;
|
| +
|
| + if((res = mp_init(&s)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_init_copy(&x, a)) != MP_OKAY ||
|
| + (res = mp_mod(&x, m, &x)) != MP_OKAY)
|
| + goto X;
|
| + if((res = mp_init(&mu)) != MP_OKAY)
|
| + goto MU;
|
| +
|
| + mp_set(&s, 1);
|
| +
|
| + /* mu = b^2k / m */
|
| + s_mp_add_d(&mu, 1);
|
| + s_mp_lshd(&mu, 2 * USED(m));
|
| + if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + /* Loop over digits of b in ascending order, except highest order */
|
| + for(dig = 0; dig < (USED(b) - 1); dig++) {
|
| + d = DIGIT(b, dig);
|
| +
|
| + /* Loop over the bits of the lower-order digits */
|
| + for(bit = 0; bit < DIGIT_BIT; bit++) {
|
| + if(d & 1) {
|
| + if((res = s_mp_mul(&s, &x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + d >>= 1;
|
| +
|
| + if((res = s_mp_sqr(&x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| + }
|
| +
|
| + /* Now do the last digit... */
|
| + d = DIGIT(b, dig);
|
| +
|
| + while(d) {
|
| + if(d & 1) {
|
| + if((res = s_mp_mul(&s, &x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + d >>= 1;
|
| +
|
| + if((res = s_mp_sqr(&x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + s_mp_exch(&s, c);
|
| +
|
| + CLEANUP:
|
| + mp_clear(&mu);
|
| + MU:
|
| + mp_clear(&x);
|
| + X:
|
| + mp_clear(&s);
|
| +
|
| + return res;
|
| +
|
| +} /* end s_mp_exptmod() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_exptmod_d(a, d, m, c) */
|
| +
|
| +mp_err mp_exptmod_d(const mp_int *a, mp_digit d, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_int s, x;
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if((res = mp_init(&s)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_init_copy(&x, a)) != MP_OKAY)
|
| + goto X;
|
| +
|
| + mp_set(&s, 1);
|
| +
|
| + while(d != 0) {
|
| + if(d & 1) {
|
| + if((res = s_mp_mul(&s, &x)) != MP_OKAY ||
|
| + (res = mp_mod(&s, m, &s)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + d /= 2;
|
| +
|
| + if((res = s_mp_sqr(&x)) != MP_OKAY ||
|
| + (res = mp_mod(&x, m, &x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + s_mp_exch(&s, c);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&x);
|
| +X:
|
| + mp_clear(&s);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_exptmod_d() */
|
| +
|
| +/* }}} */
|
| +#endif /* if MP_MODARITH */
|
| +
|
| +/* }}} */
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* {{{ Comparison functions */
|
| +
|
| +/* {{{ mp_cmp_z(a) */
|
| +
|
| +/*
|
| + mp_cmp_z(a)
|
| +
|
| + Compare a <=> 0. Returns <0 if a<0, 0 if a=0, >0 if a>0.
|
| + */
|
| +
|
| +int mp_cmp_z(const mp_int *a)
|
| +{
|
| + if(SIGN(a) == NEG)
|
| + return MP_LT;
|
| + else if(USED(a) == 1 && DIGIT(a, 0) == 0)
|
| + return MP_EQ;
|
| + else
|
| + return MP_GT;
|
| +
|
| +} /* end mp_cmp_z() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_cmp_d(a, d) */
|
| +
|
| +/*
|
| + mp_cmp_d(a, d)
|
| +
|
| + Compare a <=> d. Returns <0 if a<d, 0 if a=d, >0 if a>d
|
| + */
|
| +
|
| +int mp_cmp_d(const mp_int *a, mp_digit d)
|
| +{
|
| + ARGCHK(a != NULL, MP_EQ);
|
| +
|
| + if(SIGN(a) == NEG)
|
| + return MP_LT;
|
| +
|
| + return s_mp_cmp_d(a, d);
|
| +
|
| +} /* end mp_cmp_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_cmp(a, b) */
|
| +
|
| +int mp_cmp(const mp_int *a, const mp_int *b)
|
| +{
|
| + ARGCHK(a != NULL && b != NULL, MP_EQ);
|
| +
|
| + if(SIGN(a) == SIGN(b)) {
|
| + int mag;
|
| +
|
| + if((mag = s_mp_cmp(a, b)) == MP_EQ)
|
| + return MP_EQ;
|
| +
|
| + if(SIGN(a) == ZPOS)
|
| + return mag;
|
| + else
|
| + return -mag;
|
| +
|
| + } else if(SIGN(a) == ZPOS) {
|
| + return MP_GT;
|
| + } else {
|
| + return MP_LT;
|
| + }
|
| +
|
| +} /* end mp_cmp() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_cmp_mag(a, b) */
|
| +
|
| +/*
|
| + mp_cmp_mag(a, b)
|
| +
|
| + Compares |a| <=> |b|, and returns an appropriate comparison result
|
| + */
|
| +
|
| +int mp_cmp_mag(mp_int *a, mp_int *b)
|
| +{
|
| + ARGCHK(a != NULL && b != NULL, MP_EQ);
|
| +
|
| + return s_mp_cmp(a, b);
|
| +
|
| +} /* end mp_cmp_mag() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_cmp_int(a, z) */
|
| +
|
| +/*
|
| + This just converts z to an mp_int, and uses the existing comparison
|
| + routines. This is sort of inefficient, but it's not clear to me how
|
| + frequently this wil get used anyway. For small positive constants,
|
| + you can always use mp_cmp_d(), and for zero, there is mp_cmp_z().
|
| + */
|
| +int mp_cmp_int(const mp_int *a, long z)
|
| +{
|
| + mp_int tmp;
|
| + int out;
|
| +
|
| + ARGCHK(a != NULL, MP_EQ);
|
| +
|
| + mp_init(&tmp); mp_set_int(&tmp, z);
|
| + out = mp_cmp(a, &tmp);
|
| + mp_clear(&tmp);
|
| +
|
| + return out;
|
| +
|
| +} /* end mp_cmp_int() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_isodd(a) */
|
| +
|
| +/*
|
| + mp_isodd(a)
|
| +
|
| + Returns a true (non-zero) value if a is odd, false (zero) otherwise.
|
| + */
|
| +int mp_isodd(const mp_int *a)
|
| +{
|
| + ARGCHK(a != NULL, 0);
|
| +
|
| + return (int)(DIGIT(a, 0) & 1);
|
| +
|
| +} /* end mp_isodd() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_iseven(a) */
|
| +
|
| +int mp_iseven(const mp_int *a)
|
| +{
|
| + return !mp_isodd(a);
|
| +
|
| +} /* end mp_iseven() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* {{{ Number theoretic functions */
|
| +
|
| +#if MP_NUMTH
|
| +/* {{{ mp_gcd(a, b, c) */
|
| +
|
| +/*
|
| + Like the old mp_gcd() function, except computes the GCD using the
|
| + binary algorithm due to Josef Stein in 1961 (via Knuth).
|
| + */
|
| +mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c)
|
| +{
|
| + mp_err res;
|
| + mp_int u, v, t;
|
| + mp_size k = 0;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
|
| +
|
| + if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ)
|
| + return MP_RANGE;
|
| + if(mp_cmp_z(a) == MP_EQ) {
|
| + return mp_copy(b, c);
|
| + } else if(mp_cmp_z(b) == MP_EQ) {
|
| + return mp_copy(a, c);
|
| + }
|
| +
|
| + if((res = mp_init(&t)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_init_copy(&u, a)) != MP_OKAY)
|
| + goto U;
|
| + if((res = mp_init_copy(&v, b)) != MP_OKAY)
|
| + goto V;
|
| +
|
| + SIGN(&u) = ZPOS;
|
| + SIGN(&v) = ZPOS;
|
| +
|
| + /* Divide out common factors of 2 until at least 1 of a, b is even */
|
| + while(mp_iseven(&u) && mp_iseven(&v)) {
|
| + s_mp_div_2(&u);
|
| + s_mp_div_2(&v);
|
| + ++k;
|
| + }
|
| +
|
| + /* Initialize t */
|
| + if(mp_isodd(&u)) {
|
| + if((res = mp_copy(&v, &t)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + /* t = -v */
|
| + if(SIGN(&v) == ZPOS)
|
| + SIGN(&t) = NEG;
|
| + else
|
| + SIGN(&t) = ZPOS;
|
| +
|
| + } else {
|
| + if((res = mp_copy(&u, &t)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + }
|
| +
|
| + for(;;) {
|
| + while(mp_iseven(&t)) {
|
| + s_mp_div_2(&t);
|
| + }
|
| +
|
| + if(mp_cmp_z(&t) == MP_GT) {
|
| + if((res = mp_copy(&t, &u)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + } else {
|
| + if((res = mp_copy(&t, &v)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + /* v = -t */
|
| + if(SIGN(&t) == ZPOS)
|
| + SIGN(&v) = NEG;
|
| + else
|
| + SIGN(&v) = ZPOS;
|
| + }
|
| +
|
| + if((res = mp_sub(&u, &v, &t)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + if(s_mp_cmp_d(&t, 0) == MP_EQ)
|
| + break;
|
| + }
|
| +
|
| + s_mp_2expt(&v, k); /* v = 2^k */
|
| + res = mp_mul(&u, &v, c); /* c = u * v */
|
| +
|
| + CLEANUP:
|
| + mp_clear(&v);
|
| + V:
|
| + mp_clear(&u);
|
| + U:
|
| + mp_clear(&t);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_gcd() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_lcm(a, b, c) */
|
| +
|
| +/* We compute the least common multiple using the rule:
|
| +
|
| + ab = [a, b](a, b)
|
| +
|
| + ... by computing the product, and dividing out the gcd.
|
| + */
|
| +
|
| +mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c)
|
| +{
|
| + mp_int gcd, prod;
|
| + mp_err res;
|
| +
|
| + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
|
| +
|
| + /* Set up temporaries */
|
| + if((res = mp_init(&gcd)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_init(&prod)) != MP_OKAY)
|
| + goto GCD;
|
| +
|
| + if((res = mp_mul(a, b, &prod)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + if((res = mp_gcd(a, b, &gcd)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + res = mp_div(&prod, &gcd, c, NULL);
|
| +
|
| + CLEANUP:
|
| + mp_clear(&prod);
|
| + GCD:
|
| + mp_clear(&gcd);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_lcm() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_xgcd(a, b, g, x, y) */
|
| +
|
| +/*
|
| + mp_xgcd(a, b, g, x, y)
|
| +
|
| + Compute g = (a, b) and values x and y satisfying Bezout's identity
|
| + (that is, ax + by = g). This uses the binary extended GCD algorithm
|
| + based on the Stein algorithm used for mp_gcd()
|
| + See algorithm 14.61 in Handbook of Applied Cryptogrpahy.
|
| + */
|
| +
|
| +mp_err mp_xgcd(const mp_int *a, const mp_int *b, mp_int *g, mp_int *x, mp_int *y)
|
| +{
|
| + mp_int gx, xc, yc, u, v, A, B, C, D;
|
| + mp_int *clean[9];
|
| + mp_err res;
|
| + int last = -1;
|
| +
|
| + if(mp_cmp_z(b) == 0)
|
| + return MP_RANGE;
|
| +
|
| + /* Initialize all these variables we need */
|
| + MP_CHECKOK( mp_init(&u) );
|
| + clean[++last] = &u;
|
| + MP_CHECKOK( mp_init(&v) );
|
| + clean[++last] = &v;
|
| + MP_CHECKOK( mp_init(&gx) );
|
| + clean[++last] = &gx;
|
| + MP_CHECKOK( mp_init(&A) );
|
| + clean[++last] = &A;
|
| + MP_CHECKOK( mp_init(&B) );
|
| + clean[++last] = &B;
|
| + MP_CHECKOK( mp_init(&C) );
|
| + clean[++last] = &C;
|
| + MP_CHECKOK( mp_init(&D) );
|
| + clean[++last] = &D;
|
| + MP_CHECKOK( mp_init_copy(&xc, a) );
|
| + clean[++last] = &xc;
|
| + mp_abs(&xc, &xc);
|
| + MP_CHECKOK( mp_init_copy(&yc, b) );
|
| + clean[++last] = &yc;
|
| + mp_abs(&yc, &yc);
|
| +
|
| + mp_set(&gx, 1);
|
| +
|
| + /* Divide by two until at least one of them is odd */
|
| + while(mp_iseven(&xc) && mp_iseven(&yc)) {
|
| + mp_size nx = mp_trailing_zeros(&xc);
|
| + mp_size ny = mp_trailing_zeros(&yc);
|
| + mp_size n = MP_MIN(nx, ny);
|
| + s_mp_div_2d(&xc,n);
|
| + s_mp_div_2d(&yc,n);
|
| + MP_CHECKOK( s_mp_mul_2d(&gx,n) );
|
| + }
|
| +
|
| + mp_copy(&xc, &u);
|
| + mp_copy(&yc, &v);
|
| + mp_set(&A, 1); mp_set(&D, 1);
|
| +
|
| + /* Loop through binary GCD algorithm */
|
| + do {
|
| + while(mp_iseven(&u)) {
|
| + s_mp_div_2(&u);
|
| +
|
| + if(mp_iseven(&A) && mp_iseven(&B)) {
|
| + s_mp_div_2(&A); s_mp_div_2(&B);
|
| + } else {
|
| + MP_CHECKOK( mp_add(&A, &yc, &A) );
|
| + s_mp_div_2(&A);
|
| + MP_CHECKOK( mp_sub(&B, &xc, &B) );
|
| + s_mp_div_2(&B);
|
| + }
|
| + }
|
| +
|
| + while(mp_iseven(&v)) {
|
| + s_mp_div_2(&v);
|
| +
|
| + if(mp_iseven(&C) && mp_iseven(&D)) {
|
| + s_mp_div_2(&C); s_mp_div_2(&D);
|
| + } else {
|
| + MP_CHECKOK( mp_add(&C, &yc, &C) );
|
| + s_mp_div_2(&C);
|
| + MP_CHECKOK( mp_sub(&D, &xc, &D) );
|
| + s_mp_div_2(&D);
|
| + }
|
| + }
|
| +
|
| + if(mp_cmp(&u, &v) >= 0) {
|
| + MP_CHECKOK( mp_sub(&u, &v, &u) );
|
| + MP_CHECKOK( mp_sub(&A, &C, &A) );
|
| + MP_CHECKOK( mp_sub(&B, &D, &B) );
|
| + } else {
|
| + MP_CHECKOK( mp_sub(&v, &u, &v) );
|
| + MP_CHECKOK( mp_sub(&C, &A, &C) );
|
| + MP_CHECKOK( mp_sub(&D, &B, &D) );
|
| + }
|
| + } while (mp_cmp_z(&u) != 0);
|
| +
|
| + /* copy results to output */
|
| + if(x)
|
| + MP_CHECKOK( mp_copy(&C, x) );
|
| +
|
| + if(y)
|
| + MP_CHECKOK( mp_copy(&D, y) );
|
| +
|
| + if(g)
|
| + MP_CHECKOK( mp_mul(&gx, &v, g) );
|
| +
|
| + CLEANUP:
|
| + while(last >= 0)
|
| + mp_clear(clean[last--]);
|
| +
|
| + return res;
|
| +
|
| +} /* end mp_xgcd() */
|
| +
|
| +/* }}} */
|
| +
|
| +mp_size mp_trailing_zeros(const mp_int *mp)
|
| +{
|
| + mp_digit d;
|
| + mp_size n = 0;
|
| + int ix;
|
| +
|
| + if (!mp || !MP_DIGITS(mp) || !mp_cmp_z(mp))
|
| + return n;
|
| +
|
| + for (ix = 0; !(d = MP_DIGIT(mp,ix)) && (ix < MP_USED(mp)); ++ix)
|
| + n += MP_DIGIT_BIT;
|
| + if (!d)
|
| + return 0; /* shouldn't happen, but ... */
|
| +#if !defined(MP_USE_UINT_DIGIT)
|
| + if (!(d & 0xffffffffU)) {
|
| + d >>= 32;
|
| + n += 32;
|
| + }
|
| +#endif
|
| + if (!(d & 0xffffU)) {
|
| + d >>= 16;
|
| + n += 16;
|
| + }
|
| + if (!(d & 0xffU)) {
|
| + d >>= 8;
|
| + n += 8;
|
| + }
|
| + if (!(d & 0xfU)) {
|
| + d >>= 4;
|
| + n += 4;
|
| + }
|
| + if (!(d & 0x3U)) {
|
| + d >>= 2;
|
| + n += 2;
|
| + }
|
| + if (!(d & 0x1U)) {
|
| + d >>= 1;
|
| + n += 1;
|
| + }
|
| +#if MP_ARGCHK == 2
|
| + assert(0 != (d & 1));
|
| +#endif
|
| + return n;
|
| +}
|
| +
|
| +/* Given a and prime p, computes c and k such that a*c == 2**k (mod p).
|
| +** Returns k (positive) or error (negative).
|
| +** This technique from the paper "Fast Modular Reciprocals" (unpublished)
|
| +** by Richard Schroeppel (a.k.a. Captain Nemo).
|
| +*/
|
| +mp_err s_mp_almost_inverse(const mp_int *a, const mp_int *p, mp_int *c)
|
| +{
|
| + mp_err res;
|
| + mp_err k = 0;
|
| + mp_int d, f, g;
|
| +
|
| + ARGCHK(a && p && c, MP_BADARG);
|
| +
|
| + MP_DIGITS(&d) = 0;
|
| + MP_DIGITS(&f) = 0;
|
| + MP_DIGITS(&g) = 0;
|
| + MP_CHECKOK( mp_init(&d) );
|
| + MP_CHECKOK( mp_init_copy(&f, a) ); /* f = a */
|
| + MP_CHECKOK( mp_init_copy(&g, p) ); /* g = p */
|
| +
|
| + mp_set(c, 1);
|
| + mp_zero(&d);
|
| +
|
| + if (mp_cmp_z(&f) == 0) {
|
| + res = MP_UNDEF;
|
| + } else
|
| + for (;;) {
|
| + int diff_sign;
|
| + while (mp_iseven(&f)) {
|
| + mp_size n = mp_trailing_zeros(&f);
|
| + if (!n) {
|
| + res = MP_UNDEF;
|
| + goto CLEANUP;
|
| + }
|
| + s_mp_div_2d(&f, n);
|
| + MP_CHECKOK( s_mp_mul_2d(&d, n) );
|
| + k += n;
|
| + }
|
| + if (mp_cmp_d(&f, 1) == MP_EQ) { /* f == 1 */
|
| + res = k;
|
| + break;
|
| + }
|
| + diff_sign = mp_cmp(&f, &g);
|
| + if (diff_sign < 0) { /* f < g */
|
| + s_mp_exch(&f, &g);
|
| + s_mp_exch(c, &d);
|
| + } else if (diff_sign == 0) { /* f == g */
|
| + res = MP_UNDEF; /* a and p are not relatively prime */
|
| + break;
|
| + }
|
| + if ((MP_DIGIT(&f,0) % 4) == (MP_DIGIT(&g,0) % 4)) {
|
| + MP_CHECKOK( mp_sub(&f, &g, &f) ); /* f = f - g */
|
| + MP_CHECKOK( mp_sub(c, &d, c) ); /* c = c - d */
|
| + } else {
|
| + MP_CHECKOK( mp_add(&f, &g, &f) ); /* f = f + g */
|
| + MP_CHECKOK( mp_add(c, &d, c) ); /* c = c + d */
|
| + }
|
| + }
|
| + if (res >= 0) {
|
| + while (MP_SIGN(c) != MP_ZPOS) {
|
| + MP_CHECKOK( mp_add(c, p, c) );
|
| + }
|
| + res = k;
|
| + }
|
| +
|
| +CLEANUP:
|
| + mp_clear(&d);
|
| + mp_clear(&f);
|
| + mp_clear(&g);
|
| + return res;
|
| +}
|
| +
|
| +/* Compute T = (P ** -1) mod MP_RADIX. Also works for 16-bit mp_digits.
|
| +** This technique from the paper "Fast Modular Reciprocals" (unpublished)
|
| +** by Richard Schroeppel (a.k.a. Captain Nemo).
|
| +*/
|
| +mp_digit s_mp_invmod_radix(mp_digit P)
|
| +{
|
| + mp_digit T = P;
|
| + T *= 2 - (P * T);
|
| + T *= 2 - (P * T);
|
| + T *= 2 - (P * T);
|
| + T *= 2 - (P * T);
|
| +#if !defined(MP_USE_UINT_DIGIT)
|
| + T *= 2 - (P * T);
|
| + T *= 2 - (P * T);
|
| +#endif
|
| + return T;
|
| +}
|
| +
|
| +/* Given c, k, and prime p, where a*c == 2**k (mod p),
|
| +** Compute x = (a ** -1) mod p. This is similar to Montgomery reduction.
|
| +** This technique from the paper "Fast Modular Reciprocals" (unpublished)
|
| +** by Richard Schroeppel (a.k.a. Captain Nemo).
|
| +*/
|
| +mp_err s_mp_fixup_reciprocal(const mp_int *c, const mp_int *p, int k, mp_int *x)
|
| +{
|
| + int k_orig = k;
|
| + mp_digit r;
|
| + mp_size ix;
|
| + mp_err res;
|
| +
|
| + if (mp_cmp_z(c) < 0) { /* c < 0 */
|
| + MP_CHECKOK( mp_add(c, p, x) ); /* x = c + p */
|
| + } else {
|
| + MP_CHECKOK( mp_copy(c, x) ); /* x = c */
|
| + }
|
| +
|
| + /* make sure x is large enough */
|
| + ix = MP_HOWMANY(k, MP_DIGIT_BIT) + MP_USED(p) + 1;
|
| + ix = MP_MAX(ix, MP_USED(x));
|
| + MP_CHECKOK( s_mp_pad(x, ix) );
|
| +
|
| + r = 0 - s_mp_invmod_radix(MP_DIGIT(p,0));
|
| +
|
| + for (ix = 0; k > 0; ix++) {
|
| + int j = MP_MIN(k, MP_DIGIT_BIT);
|
| + mp_digit v = r * MP_DIGIT(x, ix);
|
| + if (j < MP_DIGIT_BIT) {
|
| + v &= ((mp_digit)1 << j) - 1; /* v = v mod (2 ** j) */
|
| + }
|
| + s_mp_mul_d_add_offset(p, v, x, ix); /* x += p * v * (RADIX ** ix) */
|
| + k -= j;
|
| + }
|
| + s_mp_clamp(x);
|
| + s_mp_div_2d(x, k_orig);
|
| + res = MP_OKAY;
|
| +
|
| +CLEANUP:
|
| + return res;
|
| +}
|
| +
|
| +/* compute mod inverse using Schroeppel's method, only if m is odd */
|
| +mp_err s_mp_invmod_odd_m(const mp_int *a, const mp_int *m, mp_int *c)
|
| +{
|
| + int k;
|
| + mp_err res;
|
| + mp_int x;
|
| +
|
| + ARGCHK(a && m && c, MP_BADARG);
|
| +
|
| + if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0)
|
| + return MP_RANGE;
|
| + if (mp_iseven(m))
|
| + return MP_UNDEF;
|
| +
|
| + MP_DIGITS(&x) = 0;
|
| +
|
| + if (a == c) {
|
| + if ((res = mp_init_copy(&x, a)) != MP_OKAY)
|
| + return res;
|
| + if (a == m)
|
| + m = &x;
|
| + a = &x;
|
| + } else if (m == c) {
|
| + if ((res = mp_init_copy(&x, m)) != MP_OKAY)
|
| + return res;
|
| + m = &x;
|
| + } else {
|
| + MP_DIGITS(&x) = 0;
|
| + }
|
| +
|
| + MP_CHECKOK( s_mp_almost_inverse(a, m, c) );
|
| + k = res;
|
| + MP_CHECKOK( s_mp_fixup_reciprocal(c, m, k, c) );
|
| +CLEANUP:
|
| + mp_clear(&x);
|
| + return res;
|
| +}
|
| +
|
| +/* Known good algorithm for computing modular inverse. But slow. */
|
| +mp_err mp_invmod_xgcd(const mp_int *a, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_int g, x;
|
| + mp_err res;
|
| +
|
| + ARGCHK(a && m && c, MP_BADARG);
|
| +
|
| + if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0)
|
| + return MP_RANGE;
|
| +
|
| + MP_DIGITS(&g) = 0;
|
| + MP_DIGITS(&x) = 0;
|
| + MP_CHECKOK( mp_init(&x) );
|
| + MP_CHECKOK( mp_init(&g) );
|
| +
|
| + MP_CHECKOK( mp_xgcd(a, m, &g, &x, NULL) );
|
| +
|
| + if (mp_cmp_d(&g, 1) != MP_EQ) {
|
| + res = MP_UNDEF;
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + res = mp_mod(&x, m, c);
|
| + SIGN(c) = SIGN(a);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&x);
|
| + mp_clear(&g);
|
| +
|
| + return res;
|
| +}
|
| +
|
| +/* modular inverse where modulus is 2**k. */
|
| +/* c = a**-1 mod 2**k */
|
| +mp_err s_mp_invmod_2d(const mp_int *a, mp_size k, mp_int *c)
|
| +{
|
| + mp_err res;
|
| + mp_size ix = k + 4;
|
| + mp_int t0, t1, val, tmp, two2k;
|
| +
|
| + static const mp_digit d2 = 2;
|
| + static const mp_int two = { MP_ZPOS, 1, 1, (mp_digit *)&d2 };
|
| +
|
| + if (mp_iseven(a))
|
| + return MP_UNDEF;
|
| + if (k <= MP_DIGIT_BIT) {
|
| + mp_digit i = s_mp_invmod_radix(MP_DIGIT(a,0));
|
| + if (k < MP_DIGIT_BIT)
|
| + i &= ((mp_digit)1 << k) - (mp_digit)1;
|
| + mp_set(c, i);
|
| + return MP_OKAY;
|
| + }
|
| + MP_DIGITS(&t0) = 0;
|
| + MP_DIGITS(&t1) = 0;
|
| + MP_DIGITS(&val) = 0;
|
| + MP_DIGITS(&tmp) = 0;
|
| + MP_DIGITS(&two2k) = 0;
|
| + MP_CHECKOK( mp_init_copy(&val, a) );
|
| + s_mp_mod_2d(&val, k);
|
| + MP_CHECKOK( mp_init_copy(&t0, &val) );
|
| + MP_CHECKOK( mp_init_copy(&t1, &t0) );
|
| + MP_CHECKOK( mp_init(&tmp) );
|
| + MP_CHECKOK( mp_init(&two2k) );
|
| + MP_CHECKOK( s_mp_2expt(&two2k, k) );
|
| + do {
|
| + MP_CHECKOK( mp_mul(&val, &t1, &tmp) );
|
| + MP_CHECKOK( mp_sub(&two, &tmp, &tmp) );
|
| + MP_CHECKOK( mp_mul(&t1, &tmp, &t1) );
|
| + s_mp_mod_2d(&t1, k);
|
| + while (MP_SIGN(&t1) != MP_ZPOS) {
|
| + MP_CHECKOK( mp_add(&t1, &two2k, &t1) );
|
| + }
|
| + if (mp_cmp(&t1, &t0) == MP_EQ)
|
| + break;
|
| + MP_CHECKOK( mp_copy(&t1, &t0) );
|
| + } while (--ix > 0);
|
| + if (!ix) {
|
| + res = MP_UNDEF;
|
| + } else {
|
| + mp_exch(c, &t1);
|
| + }
|
| +
|
| +CLEANUP:
|
| + mp_clear(&t0);
|
| + mp_clear(&t1);
|
| + mp_clear(&val);
|
| + mp_clear(&tmp);
|
| + mp_clear(&two2k);
|
| + return res;
|
| +}
|
| +
|
| +mp_err s_mp_invmod_even_m(const mp_int *a, const mp_int *m, mp_int *c)
|
| +{
|
| + mp_err res;
|
| + mp_size k;
|
| + mp_int oddFactor, evenFactor; /* factors of the modulus */
|
| + mp_int oddPart, evenPart; /* parts to combine via CRT. */
|
| + mp_int C2, tmp1, tmp2;
|
| +
|
| + /*static const mp_digit d1 = 1; */
|
| + /*static const mp_int one = { MP_ZPOS, 1, 1, (mp_digit *)&d1 }; */
|
| +
|
| + if ((res = s_mp_ispow2(m)) >= 0) {
|
| + k = res;
|
| + return s_mp_invmod_2d(a, k, c);
|
| + }
|
| + MP_DIGITS(&oddFactor) = 0;
|
| + MP_DIGITS(&evenFactor) = 0;
|
| + MP_DIGITS(&oddPart) = 0;
|
| + MP_DIGITS(&evenPart) = 0;
|
| + MP_DIGITS(&C2) = 0;
|
| + MP_DIGITS(&tmp1) = 0;
|
| + MP_DIGITS(&tmp2) = 0;
|
| +
|
| + MP_CHECKOK( mp_init_copy(&oddFactor, m) ); /* oddFactor = m */
|
| + MP_CHECKOK( mp_init(&evenFactor) );
|
| + MP_CHECKOK( mp_init(&oddPart) );
|
| + MP_CHECKOK( mp_init(&evenPart) );
|
| + MP_CHECKOK( mp_init(&C2) );
|
| + MP_CHECKOK( mp_init(&tmp1) );
|
| + MP_CHECKOK( mp_init(&tmp2) );
|
| +
|
| + k = mp_trailing_zeros(m);
|
| + s_mp_div_2d(&oddFactor, k);
|
| + MP_CHECKOK( s_mp_2expt(&evenFactor, k) );
|
| +
|
| + /* compute a**-1 mod oddFactor. */
|
| + MP_CHECKOK( s_mp_invmod_odd_m(a, &oddFactor, &oddPart) );
|
| + /* compute a**-1 mod evenFactor, where evenFactor == 2**k. */
|
| + MP_CHECKOK( s_mp_invmod_2d( a, k, &evenPart) );
|
| +
|
| + /* Use Chinese Remainer theorem to compute a**-1 mod m. */
|
| + /* let m1 = oddFactor, v1 = oddPart,
|
| + * let m2 = evenFactor, v2 = evenPart.
|
| + */
|
| +
|
| + /* Compute C2 = m1**-1 mod m2. */
|
| + MP_CHECKOK( s_mp_invmod_2d(&oddFactor, k, &C2) );
|
| +
|
| + /* compute u = (v2 - v1)*C2 mod m2 */
|
| + MP_CHECKOK( mp_sub(&evenPart, &oddPart, &tmp1) );
|
| + MP_CHECKOK( mp_mul(&tmp1, &C2, &tmp2) );
|
| + s_mp_mod_2d(&tmp2, k);
|
| + while (MP_SIGN(&tmp2) != MP_ZPOS) {
|
| + MP_CHECKOK( mp_add(&tmp2, &evenFactor, &tmp2) );
|
| + }
|
| +
|
| + /* compute answer = v1 + u*m1 */
|
| + MP_CHECKOK( mp_mul(&tmp2, &oddFactor, c) );
|
| + MP_CHECKOK( mp_add(&oddPart, c, c) );
|
| + /* not sure this is necessary, but it's low cost if not. */
|
| + MP_CHECKOK( mp_mod(c, m, c) );
|
| +
|
| +CLEANUP:
|
| + mp_clear(&oddFactor);
|
| + mp_clear(&evenFactor);
|
| + mp_clear(&oddPart);
|
| + mp_clear(&evenPart);
|
| + mp_clear(&C2);
|
| + mp_clear(&tmp1);
|
| + mp_clear(&tmp2);
|
| + return res;
|
| +}
|
| +
|
| +
|
| +/* {{{ mp_invmod(a, m, c) */
|
| +
|
| +/*
|
| + mp_invmod(a, m, c)
|
| +
|
| + Compute c = a^-1 (mod m), if there is an inverse for a (mod m).
|
| + This is equivalent to the question of whether (a, m) = 1. If not,
|
| + MP_UNDEF is returned, and there is no inverse.
|
| + */
|
| +
|
| +mp_err mp_invmod(const mp_int *a, const mp_int *m, mp_int *c)
|
| +{
|
| +
|
| + ARGCHK(a && m && c, MP_BADARG);
|
| +
|
| + if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0)
|
| + return MP_RANGE;
|
| +
|
| + if (mp_isodd(m)) {
|
| + return s_mp_invmod_odd_m(a, m, c);
|
| + }
|
| + if (mp_iseven(a))
|
| + return MP_UNDEF; /* not invertable */
|
| +
|
| + return s_mp_invmod_even_m(a, m, c);
|
| +
|
| +} /* end mp_invmod() */
|
| +
|
| +/* }}} */
|
| +#endif /* if MP_NUMTH */
|
| +
|
| +/* }}} */
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* {{{ mp_print(mp, ofp) */
|
| +
|
| +#if MP_IOFUNC
|
| +/*
|
| + mp_print(mp, ofp)
|
| +
|
| + Print a textual representation of the given mp_int on the output
|
| + stream 'ofp'. Output is generated using the internal radix.
|
| + */
|
| +
|
| +void mp_print(mp_int *mp, FILE *ofp)
|
| +{
|
| + int ix;
|
| +
|
| + if(mp == NULL || ofp == NULL)
|
| + return;
|
| +
|
| + fputc((SIGN(mp) == NEG) ? '-' : '+', ofp);
|
| +
|
| + for(ix = USED(mp) - 1; ix >= 0; ix--) {
|
| + fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix));
|
| + }
|
| +
|
| +} /* end mp_print() */
|
| +
|
| +#endif /* if MP_IOFUNC */
|
| +
|
| +/* }}} */
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* {{{ More I/O Functions */
|
| +
|
| +/* {{{ mp_read_raw(mp, str, len) */
|
| +
|
| +/*
|
| + mp_read_raw(mp, str, len)
|
| +
|
| + Read in a raw value (base 256) into the given mp_int
|
| + */
|
| +
|
| +mp_err mp_read_raw(mp_int *mp, char *str, int len)
|
| +{
|
| + int ix;
|
| + mp_err res;
|
| + unsigned char *ustr = (unsigned char *)str;
|
| +
|
| + ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
|
| +
|
| + mp_zero(mp);
|
| +
|
| + /* Get sign from first byte */
|
| + if(ustr[0])
|
| + SIGN(mp) = NEG;
|
| + else
|
| + SIGN(mp) = ZPOS;
|
| +
|
| + /* Read the rest of the digits */
|
| + for(ix = 1; ix < len; ix++) {
|
| + if((res = mp_mul_d(mp, 256, mp)) != MP_OKAY)
|
| + return res;
|
| + if((res = mp_add_d(mp, ustr[ix], mp)) != MP_OKAY)
|
| + return res;
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_read_raw() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_raw_size(mp) */
|
| +
|
| +int mp_raw_size(mp_int *mp)
|
| +{
|
| + ARGCHK(mp != NULL, 0);
|
| +
|
| + return (USED(mp) * sizeof(mp_digit)) + 1;
|
| +
|
| +} /* end mp_raw_size() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_toraw(mp, str) */
|
| +
|
| +mp_err mp_toraw(mp_int *mp, char *str)
|
| +{
|
| + int ix, jx, pos = 1;
|
| +
|
| + ARGCHK(mp != NULL && str != NULL, MP_BADARG);
|
| +
|
| + str[0] = (char)SIGN(mp);
|
| +
|
| + /* Iterate over each digit... */
|
| + for(ix = USED(mp) - 1; ix >= 0; ix--) {
|
| + mp_digit d = DIGIT(mp, ix);
|
| +
|
| + /* Unpack digit bytes, high order first */
|
| + for(jx = sizeof(mp_digit) - 1; jx >= 0; jx--) {
|
| + str[pos++] = (char)(d >> (jx * CHAR_BIT));
|
| + }
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_toraw() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_read_radix(mp, str, radix) */
|
| +
|
| +/*
|
| + mp_read_radix(mp, str, radix)
|
| +
|
| + Read an integer from the given string, and set mp to the resulting
|
| + value. The input is presumed to be in base 10. Leading non-digit
|
| + characters are ignored, and the function reads until a non-digit
|
| + character or the end of the string.
|
| + */
|
| +
|
| +mp_err mp_read_radix(mp_int *mp, const char *str, int radix)
|
| +{
|
| + int ix = 0, val = 0;
|
| + mp_err res;
|
| + mp_sign sig = ZPOS;
|
| +
|
| + ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX,
|
| + MP_BADARG);
|
| +
|
| + mp_zero(mp);
|
| +
|
| + /* Skip leading non-digit characters until a digit or '-' or '+' */
|
| + while(str[ix] &&
|
| + (s_mp_tovalue(str[ix], radix) < 0) &&
|
| + str[ix] != '-' &&
|
| + str[ix] != '+') {
|
| + ++ix;
|
| + }
|
| +
|
| + if(str[ix] == '-') {
|
| + sig = NEG;
|
| + ++ix;
|
| + } else if(str[ix] == '+') {
|
| + sig = ZPOS; /* this is the default anyway... */
|
| + ++ix;
|
| + }
|
| +
|
| + while((val = s_mp_tovalue(str[ix], radix)) >= 0) {
|
| + if((res = s_mp_mul_d(mp, radix)) != MP_OKAY)
|
| + return res;
|
| + if((res = s_mp_add_d(mp, val)) != MP_OKAY)
|
| + return res;
|
| + ++ix;
|
| + }
|
| +
|
| + if(s_mp_cmp_d(mp, 0) == MP_EQ)
|
| + SIGN(mp) = ZPOS;
|
| + else
|
| + SIGN(mp) = sig;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_read_radix() */
|
| +
|
| +mp_err mp_read_variable_radix(mp_int *a, const char * str, int default_radix)
|
| +{
|
| + int radix = default_radix;
|
| + int cx;
|
| + mp_sign sig = ZPOS;
|
| + mp_err res;
|
| +
|
| + /* Skip leading non-digit characters until a digit or '-' or '+' */
|
| + while ((cx = *str) != 0 &&
|
| + (s_mp_tovalue(cx, radix) < 0) &&
|
| + cx != '-' &&
|
| + cx != '+') {
|
| + ++str;
|
| + }
|
| +
|
| + if (cx == '-') {
|
| + sig = NEG;
|
| + ++str;
|
| + } else if (cx == '+') {
|
| + sig = ZPOS; /* this is the default anyway... */
|
| + ++str;
|
| + }
|
| +
|
| + if (str[0] == '0') {
|
| + if ((str[1] | 0x20) == 'x') {
|
| + radix = 16;
|
| + str += 2;
|
| + } else {
|
| + radix = 8;
|
| + str++;
|
| + }
|
| + }
|
| + res = mp_read_radix(a, str, radix);
|
| + if (res == MP_OKAY) {
|
| + MP_SIGN(a) = (s_mp_cmp_d(a, 0) == MP_EQ) ? ZPOS : sig;
|
| + }
|
| + return res;
|
| +}
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_radix_size(mp, radix) */
|
| +
|
| +int mp_radix_size(mp_int *mp, int radix)
|
| +{
|
| + int bits;
|
| +
|
| + if(!mp || radix < 2 || radix > MAX_RADIX)
|
| + return 0;
|
| +
|
| + bits = USED(mp) * DIGIT_BIT - 1;
|
| +
|
| + return s_mp_outlen(bits, radix);
|
| +
|
| +} /* end mp_radix_size() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_toradix(mp, str, radix) */
|
| +
|
| +mp_err mp_toradix(mp_int *mp, char *str, int radix)
|
| +{
|
| + int ix, pos = 0;
|
| +
|
| + ARGCHK(mp != NULL && str != NULL, MP_BADARG);
|
| + ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE);
|
| +
|
| + if(mp_cmp_z(mp) == MP_EQ) {
|
| + str[0] = '0';
|
| + str[1] = '\0';
|
| + } else {
|
| + mp_err res;
|
| + mp_int tmp;
|
| + mp_sign sgn;
|
| + mp_digit rem, rdx = (mp_digit)radix;
|
| + char ch;
|
| +
|
| + if((res = mp_init_copy(&tmp, mp)) != MP_OKAY)
|
| + return res;
|
| +
|
| + /* Save sign for later, and take absolute value */
|
| + sgn = SIGN(&tmp); SIGN(&tmp) = ZPOS;
|
| +
|
| + /* Generate output digits in reverse order */
|
| + while(mp_cmp_z(&tmp) != 0) {
|
| + if((res = mp_div_d(&tmp, rdx, &tmp, &rem)) != MP_OKAY) {
|
| + mp_clear(&tmp);
|
| + return res;
|
| + }
|
| +
|
| + /* Generate digits, use capital letters */
|
| + ch = s_mp_todigit(rem, radix, 0);
|
| +
|
| + str[pos++] = ch;
|
| + }
|
| +
|
| + /* Add - sign if original value was negative */
|
| + if(sgn == NEG)
|
| + str[pos++] = '-';
|
| +
|
| + /* Add trailing NUL to end the string */
|
| + str[pos--] = '\0';
|
| +
|
| + /* Reverse the digits and sign indicator */
|
| + ix = 0;
|
| + while(ix < pos) {
|
| + char tmp = str[ix];
|
| +
|
| + str[ix] = str[pos];
|
| + str[pos] = tmp;
|
| + ++ix;
|
| + --pos;
|
| + }
|
| +
|
| + mp_clear(&tmp);
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end mp_toradix() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_tovalue(ch, r) */
|
| +
|
| +int mp_tovalue(char ch, int r)
|
| +{
|
| + return s_mp_tovalue(ch, r);
|
| +
|
| +} /* end mp_tovalue() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_strerror(ec) */
|
| +
|
| +/*
|
| + mp_strerror(ec)
|
| +
|
| + Return a string describing the meaning of error code 'ec'. The
|
| + string returned is allocated in static memory, so the caller should
|
| + not attempt to modify or free the memory associated with this
|
| + string.
|
| + */
|
| +const char *mp_strerror(mp_err ec)
|
| +{
|
| + int aec = (ec < 0) ? -ec : ec;
|
| +
|
| + /* Code values are negative, so the senses of these comparisons
|
| + are accurate */
|
| + if(ec < MP_LAST_CODE || ec > MP_OKAY) {
|
| + return mp_err_string[0]; /* unknown error code */
|
| + } else {
|
| + return mp_err_string[aec + 1];
|
| + }
|
| +
|
| +} /* end mp_strerror() */
|
| +
|
| +/* }}} */
|
| +
|
| +/*========================================================================*/
|
| +/*------------------------------------------------------------------------*/
|
| +/* Static function definitions (internal use only) */
|
| +
|
| +/* {{{ Memory management */
|
| +
|
| +/* {{{ s_mp_grow(mp, min) */
|
| +
|
| +/* Make sure there are at least 'min' digits allocated to mp */
|
| +mp_err s_mp_grow(mp_int *mp, mp_size min)
|
| +{
|
| + if(min > ALLOC(mp)) {
|
| + mp_digit *tmp;
|
| +
|
| + /* Set min to next nearest default precision block size */
|
| + min = MP_ROUNDUP(min, s_mp_defprec);
|
| +
|
| + if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL)
|
| + return MP_MEM;
|
| +
|
| + s_mp_copy(DIGITS(mp), tmp, USED(mp));
|
| +
|
| +#if MP_CRYPTO
|
| + s_mp_setz(DIGITS(mp), ALLOC(mp));
|
| +#endif
|
| + s_mp_free(DIGITS(mp));
|
| + DIGITS(mp) = tmp;
|
| + ALLOC(mp) = min;
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end s_mp_grow() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_pad(mp, min) */
|
| +
|
| +/* Make sure the used size of mp is at least 'min', growing if needed */
|
| +mp_err s_mp_pad(mp_int *mp, mp_size min)
|
| +{
|
| + if(min > USED(mp)) {
|
| + mp_err res;
|
| +
|
| + /* Make sure there is room to increase precision */
|
| + if (min > ALLOC(mp)) {
|
| + if ((res = s_mp_grow(mp, min)) != MP_OKAY)
|
| + return res;
|
| + } else {
|
| + s_mp_setz(DIGITS(mp) + USED(mp), min - USED(mp));
|
| + }
|
| +
|
| + /* Increase precision; should already be 0-filled */
|
| + USED(mp) = min;
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end s_mp_pad() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_setz(dp, count) */
|
| +
|
| +#if MP_MACRO == 0
|
| +/* Set 'count' digits pointed to by dp to be zeroes */
|
| +void s_mp_setz(mp_digit *dp, mp_size count)
|
| +{
|
| +#if MP_MEMSET == 0
|
| + int ix;
|
| +
|
| + for(ix = 0; ix < count; ix++)
|
| + dp[ix] = 0;
|
| +#else
|
| + memset(dp, 0, count * sizeof(mp_digit));
|
| +#endif
|
| +
|
| +} /* end s_mp_setz() */
|
| +#endif
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_copy(sp, dp, count) */
|
| +
|
| +#if MP_MACRO == 0
|
| +/* Copy 'count' digits from sp to dp */
|
| +void s_mp_copy(const mp_digit *sp, mp_digit *dp, mp_size count)
|
| +{
|
| +#if MP_MEMCPY == 0
|
| + int ix;
|
| +
|
| + for(ix = 0; ix < count; ix++)
|
| + dp[ix] = sp[ix];
|
| +#else
|
| + memcpy(dp, sp, count * sizeof(mp_digit));
|
| +#endif
|
| +
|
| +} /* end s_mp_copy() */
|
| +#endif
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_alloc(nb, ni) */
|
| +
|
| +#if MP_MACRO == 0
|
| +/* Allocate ni records of nb bytes each, and return a pointer to that */
|
| +void *s_mp_alloc(size_t nb, size_t ni)
|
| +{
|
| + ++mp_allocs;
|
| + return calloc(nb, ni);
|
| +
|
| +} /* end s_mp_alloc() */
|
| +#endif
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_free(ptr) */
|
| +
|
| +#if MP_MACRO == 0
|
| +/* Free the memory pointed to by ptr */
|
| +void s_mp_free(void *ptr)
|
| +{
|
| + if(ptr) {
|
| + ++mp_frees;
|
| + free(ptr);
|
| + }
|
| +} /* end s_mp_free() */
|
| +#endif
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_clamp(mp) */
|
| +
|
| +#if MP_MACRO == 0
|
| +/* Remove leading zeroes from the given value */
|
| +void s_mp_clamp(mp_int *mp)
|
| +{
|
| + mp_size used = MP_USED(mp);
|
| + while (used > 1 && DIGIT(mp, used - 1) == 0)
|
| + --used;
|
| + MP_USED(mp) = used;
|
| +} /* end s_mp_clamp() */
|
| +#endif
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_exch(a, b) */
|
| +
|
| +/* Exchange the data for a and b; (b, a) = (a, b) */
|
| +void s_mp_exch(mp_int *a, mp_int *b)
|
| +{
|
| + mp_int tmp;
|
| +
|
| + tmp = *a;
|
| + *a = *b;
|
| + *b = tmp;
|
| +
|
| +} /* end s_mp_exch() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ Arithmetic helpers */
|
| +
|
| +/* {{{ s_mp_lshd(mp, p) */
|
| +
|
| +/*
|
| + Shift mp leftward by p digits, growing if needed, and zero-filling
|
| + the in-shifted digits at the right end. This is a convenient
|
| + alternative to multiplication by powers of the radix
|
| + The value of USED(mp) must already have been set to the value for
|
| + the shifted result.
|
| + */
|
| +
|
| +mp_err s_mp_lshd(mp_int *mp, mp_size p)
|
| +{
|
| + mp_err res;
|
| + mp_size pos;
|
| + int ix;
|
| +
|
| + if(p == 0)
|
| + return MP_OKAY;
|
| +
|
| + if (MP_USED(mp) == 1 && MP_DIGIT(mp, 0) == 0)
|
| + return MP_OKAY;
|
| +
|
| + if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY)
|
| + return res;
|
| +
|
| + pos = USED(mp) - 1;
|
| +
|
| + /* Shift all the significant figures over as needed */
|
| + for(ix = pos - p; ix >= 0; ix--)
|
| + DIGIT(mp, ix + p) = DIGIT(mp, ix);
|
| +
|
| + /* Fill the bottom digits with zeroes */
|
| + for(ix = 0; ix < p; ix++)
|
| + DIGIT(mp, ix) = 0;
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end s_mp_lshd() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_mul_2d(mp, d) */
|
| +
|
| +/*
|
| + Multiply the integer by 2^d, where d is a number of bits. This
|
| + amounts to a bitwise shift of the value.
|
| + */
|
| +mp_err s_mp_mul_2d(mp_int *mp, mp_digit d)
|
| +{
|
| + mp_err res;
|
| + mp_digit dshift, bshift;
|
| + mp_digit mask;
|
| +
|
| + ARGCHK(mp != NULL, MP_BADARG);
|
| +
|
| + dshift = d / MP_DIGIT_BIT;
|
| + bshift = d % MP_DIGIT_BIT;
|
| + /* bits to be shifted out of the top word */
|
| + mask = ((mp_digit)~0 << (MP_DIGIT_BIT - bshift));
|
| + mask &= MP_DIGIT(mp, MP_USED(mp) - 1);
|
| +
|
| + if (MP_OKAY != (res = s_mp_pad(mp, MP_USED(mp) + dshift + (mask != 0) )))
|
| + return res;
|
| +
|
| + if (dshift && MP_OKAY != (res = s_mp_lshd(mp, dshift)))
|
| + return res;
|
| +
|
| + if (bshift) {
|
| + mp_digit *pa = MP_DIGITS(mp);
|
| + mp_digit *alim = pa + MP_USED(mp);
|
| + mp_digit prev = 0;
|
| +
|
| + for (pa += dshift; pa < alim; ) {
|
| + mp_digit x = *pa;
|
| + *pa++ = (x << bshift) | prev;
|
| + prev = x >> (DIGIT_BIT - bshift);
|
| + }
|
| + }
|
| +
|
| + s_mp_clamp(mp);
|
| + return MP_OKAY;
|
| +} /* end s_mp_mul_2d() */
|
| +
|
| +/* {{{ s_mp_rshd(mp, p) */
|
| +
|
| +/*
|
| + Shift mp rightward by p digits. Maintains the invariant that
|
| + digits above the precision are all zero. Digits shifted off the
|
| + end are lost. Cannot fail.
|
| + */
|
| +
|
| +void s_mp_rshd(mp_int *mp, mp_size p)
|
| +{
|
| + mp_size ix;
|
| + mp_digit *src, *dst;
|
| +
|
| + if(p == 0)
|
| + return;
|
| +
|
| + /* Shortcut when all digits are to be shifted off */
|
| + if(p >= USED(mp)) {
|
| + s_mp_setz(DIGITS(mp), ALLOC(mp));
|
| + USED(mp) = 1;
|
| + SIGN(mp) = ZPOS;
|
| + return;
|
| + }
|
| +
|
| + /* Shift all the significant figures over as needed */
|
| + dst = MP_DIGITS(mp);
|
| + src = dst + p;
|
| + for (ix = USED(mp) - p; ix > 0; ix--)
|
| + *dst++ = *src++;
|
| +
|
| + MP_USED(mp) -= p;
|
| + /* Fill the top digits with zeroes */
|
| + while (p-- > 0)
|
| + *dst++ = 0;
|
| +
|
| +#if 0
|
| + /* Strip off any leading zeroes */
|
| + s_mp_clamp(mp);
|
| +#endif
|
| +
|
| +} /* end s_mp_rshd() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_div_2(mp) */
|
| +
|
| +/* Divide by two -- take advantage of radix properties to do it fast */
|
| +void s_mp_div_2(mp_int *mp)
|
| +{
|
| + s_mp_div_2d(mp, 1);
|
| +
|
| +} /* end s_mp_div_2() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_mul_2(mp) */
|
| +
|
| +mp_err s_mp_mul_2(mp_int *mp)
|
| +{
|
| + mp_digit *pd;
|
| + int ix, used;
|
| + mp_digit kin = 0;
|
| +
|
| + /* Shift digits leftward by 1 bit */
|
| + used = MP_USED(mp);
|
| + pd = MP_DIGITS(mp);
|
| + for (ix = 0; ix < used; ix++) {
|
| + mp_digit d = *pd;
|
| + *pd++ = (d << 1) | kin;
|
| + kin = (d >> (DIGIT_BIT - 1));
|
| + }
|
| +
|
| + /* Deal with rollover from last digit */
|
| + if (kin) {
|
| + if (ix >= ALLOC(mp)) {
|
| + mp_err res;
|
| + if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY)
|
| + return res;
|
| + }
|
| +
|
| + DIGIT(mp, ix) = kin;
|
| + USED(mp) += 1;
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end s_mp_mul_2() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_mod_2d(mp, d) */
|
| +
|
| +/*
|
| + Remainder the integer by 2^d, where d is a number of bits. This
|
| + amounts to a bitwise AND of the value, and does not require the full
|
| + division code
|
| + */
|
| +void s_mp_mod_2d(mp_int *mp, mp_digit d)
|
| +{
|
| + mp_size ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT);
|
| + mp_size ix;
|
| + mp_digit dmask;
|
| +
|
| + if(ndig >= USED(mp))
|
| + return;
|
| +
|
| + /* Flush all the bits above 2^d in its digit */
|
| + dmask = ((mp_digit)1 << nbit) - 1;
|
| + DIGIT(mp, ndig) &= dmask;
|
| +
|
| + /* Flush all digits above the one with 2^d in it */
|
| + for(ix = ndig + 1; ix < USED(mp); ix++)
|
| + DIGIT(mp, ix) = 0;
|
| +
|
| + s_mp_clamp(mp);
|
| +
|
| +} /* end s_mp_mod_2d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_div_2d(mp, d) */
|
| +
|
| +/*
|
| + Divide the integer by 2^d, where d is a number of bits. This
|
| + amounts to a bitwise shift of the value, and does not require the
|
| + full division code (used in Barrett reduction, see below)
|
| + */
|
| +void s_mp_div_2d(mp_int *mp, mp_digit d)
|
| +{
|
| + int ix;
|
| + mp_digit save, next, mask;
|
| +
|
| + s_mp_rshd(mp, d / DIGIT_BIT);
|
| + d %= DIGIT_BIT;
|
| + if (d) {
|
| + mask = ((mp_digit)1 << d) - 1;
|
| + save = 0;
|
| + for(ix = USED(mp) - 1; ix >= 0; ix--) {
|
| + next = DIGIT(mp, ix) & mask;
|
| + DIGIT(mp, ix) = (DIGIT(mp, ix) >> d) | (save << (DIGIT_BIT - d));
|
| + save = next;
|
| + }
|
| + }
|
| + s_mp_clamp(mp);
|
| +
|
| +} /* end s_mp_div_2d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_norm(a, b, *d) */
|
| +
|
| +/*
|
| + s_mp_norm(a, b, *d)
|
| +
|
| + Normalize a and b for division, where b is the divisor. In order
|
| + that we might make good guesses for quotient digits, we want the
|
| + leading digit of b to be at least half the radix, which we
|
| + accomplish by multiplying a and b by a power of 2. The exponent
|
| + (shift count) is placed in *pd, so that the remainder can be shifted
|
| + back at the end of the division process.
|
| + */
|
| +
|
| +mp_err s_mp_norm(mp_int *a, mp_int *b, mp_digit *pd)
|
| +{
|
| + mp_digit d;
|
| + mp_digit mask;
|
| + mp_digit b_msd;
|
| + mp_err res = MP_OKAY;
|
| +
|
| + d = 0;
|
| + mask = DIGIT_MAX & ~(DIGIT_MAX >> 1); /* mask is msb of digit */
|
| + b_msd = DIGIT(b, USED(b) - 1);
|
| + while (!(b_msd & mask)) {
|
| + b_msd <<= 1;
|
| + ++d;
|
| + }
|
| +
|
| + if (d) {
|
| + MP_CHECKOK( s_mp_mul_2d(a, d) );
|
| + MP_CHECKOK( s_mp_mul_2d(b, d) );
|
| + }
|
| +
|
| + *pd = d;
|
| +CLEANUP:
|
| + return res;
|
| +
|
| +} /* end s_mp_norm() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ Primitive digit arithmetic */
|
| +
|
| +/* {{{ s_mp_add_d(mp, d) */
|
| +
|
| +/* Add d to |mp| in place */
|
| +mp_err s_mp_add_d(mp_int *mp, mp_digit d) /* unsigned digit addition */
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + mp_word w, k = 0;
|
| + mp_size ix = 1;
|
| +
|
| + w = (mp_word)DIGIT(mp, 0) + d;
|
| + DIGIT(mp, 0) = ACCUM(w);
|
| + k = CARRYOUT(w);
|
| +
|
| + while(ix < USED(mp) && k) {
|
| + w = (mp_word)DIGIT(mp, ix) + k;
|
| + DIGIT(mp, ix) = ACCUM(w);
|
| + k = CARRYOUT(w);
|
| + ++ix;
|
| + }
|
| +
|
| + if(k != 0) {
|
| + mp_err res;
|
| +
|
| + if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY)
|
| + return res;
|
| +
|
| + DIGIT(mp, ix) = (mp_digit)k;
|
| + }
|
| +
|
| + return MP_OKAY;
|
| +#else
|
| + mp_digit * pmp = MP_DIGITS(mp);
|
| + mp_digit sum, mp_i, carry = 0;
|
| + mp_err res = MP_OKAY;
|
| + int used = (int)MP_USED(mp);
|
| +
|
| + mp_i = *pmp;
|
| + *pmp++ = sum = d + mp_i;
|
| + carry = (sum < d);
|
| + while (carry && --used > 0) {
|
| + mp_i = *pmp;
|
| + *pmp++ = sum = carry + mp_i;
|
| + carry = !sum;
|
| + }
|
| + if (carry && !used) {
|
| + /* mp is growing */
|
| + used = MP_USED(mp);
|
| + MP_CHECKOK( s_mp_pad(mp, used + 1) );
|
| + MP_DIGIT(mp, used) = carry;
|
| + }
|
| +CLEANUP:
|
| + return res;
|
| +#endif
|
| +} /* end s_mp_add_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_sub_d(mp, d) */
|
| +
|
| +/* Subtract d from |mp| in place, assumes |mp| > d */
|
| +mp_err s_mp_sub_d(mp_int *mp, mp_digit d) /* unsigned digit subtract */
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + mp_word w, b = 0;
|
| + mp_size ix = 1;
|
| +
|
| + /* Compute initial subtraction */
|
| + w = (RADIX + (mp_word)DIGIT(mp, 0)) - d;
|
| + b = CARRYOUT(w) ? 0 : 1;
|
| + DIGIT(mp, 0) = ACCUM(w);
|
| +
|
| + /* Propagate borrows leftward */
|
| + while(b && ix < USED(mp)) {
|
| + w = (RADIX + (mp_word)DIGIT(mp, ix)) - b;
|
| + b = CARRYOUT(w) ? 0 : 1;
|
| + DIGIT(mp, ix) = ACCUM(w);
|
| + ++ix;
|
| + }
|
| +
|
| + /* Remove leading zeroes */
|
| + s_mp_clamp(mp);
|
| +
|
| + /* If we have a borrow out, it's a violation of the input invariant */
|
| + if(b)
|
| + return MP_RANGE;
|
| + else
|
| + return MP_OKAY;
|
| +#else
|
| + mp_digit *pmp = MP_DIGITS(mp);
|
| + mp_digit mp_i, diff, borrow;
|
| + mp_size used = MP_USED(mp);
|
| +
|
| + mp_i = *pmp;
|
| + *pmp++ = diff = mp_i - d;
|
| + borrow = (diff > mp_i);
|
| + while (borrow && --used) {
|
| + mp_i = *pmp;
|
| + *pmp++ = diff = mp_i - borrow;
|
| + borrow = (diff > mp_i);
|
| + }
|
| + s_mp_clamp(mp);
|
| + return (borrow && !used) ? MP_RANGE : MP_OKAY;
|
| +#endif
|
| +} /* end s_mp_sub_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_mul_d(a, d) */
|
| +
|
| +/* Compute a = a * d, single digit multiplication */
|
| +mp_err s_mp_mul_d(mp_int *a, mp_digit d)
|
| +{
|
| + mp_err res;
|
| + mp_size used;
|
| + int pow;
|
| +
|
| + if (!d) {
|
| + mp_zero(a);
|
| + return MP_OKAY;
|
| + }
|
| + if (d == 1)
|
| + return MP_OKAY;
|
| + if (0 <= (pow = s_mp_ispow2d(d))) {
|
| + return s_mp_mul_2d(a, (mp_digit)pow);
|
| + }
|
| +
|
| + used = MP_USED(a);
|
| + MP_CHECKOK( s_mp_pad(a, used + 1) );
|
| +
|
| + s_mpv_mul_d(MP_DIGITS(a), used, d, MP_DIGITS(a));
|
| +
|
| + s_mp_clamp(a);
|
| +
|
| +CLEANUP:
|
| + return res;
|
| +
|
| +} /* end s_mp_mul_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_div_d(mp, d, r) */
|
| +
|
| +/*
|
| + s_mp_div_d(mp, d, r)
|
| +
|
| + Compute the quotient mp = mp / d and remainder r = mp mod d, for a
|
| + single digit d. If r is null, the remainder will be discarded.
|
| + */
|
| +
|
| +mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r)
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_DIV_WORD)
|
| + mp_word w = 0, q;
|
| +#else
|
| + mp_digit w, q;
|
| +#endif
|
| + int ix;
|
| + mp_err res;
|
| + mp_int quot;
|
| + mp_int rem;
|
| +
|
| + if(d == 0)
|
| + return MP_RANGE;
|
| + if (d == 1) {
|
| + if (r)
|
| + *r = 0;
|
| + return MP_OKAY;
|
| + }
|
| + /* could check for power of 2 here, but mp_div_d does that. */
|
| + if (MP_USED(mp) == 1) {
|
| + mp_digit n = MP_DIGIT(mp,0);
|
| + mp_digit rem;
|
| +
|
| + q = n / d;
|
| + rem = n % d;
|
| + MP_DIGIT(mp,0) = q;
|
| + if (r)
|
| + *r = rem;
|
| + return MP_OKAY;
|
| + }
|
| +
|
| + MP_DIGITS(&rem) = 0;
|
| + MP_DIGITS(") = 0;
|
| + /* Make room for the quotient */
|
| + MP_CHECKOK( mp_init_size(", USED(mp)) );
|
| +
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_DIV_WORD)
|
| + for(ix = USED(mp) - 1; ix >= 0; ix--) {
|
| + w = (w << DIGIT_BIT) | DIGIT(mp, ix);
|
| +
|
| + if(w >= d) {
|
| + q = w / d;
|
| + w = w % d;
|
| + } else {
|
| + q = 0;
|
| + }
|
| +
|
| + s_mp_lshd(", 1);
|
| + DIGIT(", 0) = (mp_digit)q;
|
| + }
|
| +#else
|
| + {
|
| + mp_digit p;
|
| +#if !defined(MP_ASSEMBLY_DIV_2DX1D)
|
| + mp_digit norm;
|
| +#endif
|
| +
|
| + MP_CHECKOK( mp_init_copy(&rem, mp) );
|
| +
|
| +#if !defined(MP_ASSEMBLY_DIV_2DX1D)
|
| + MP_DIGIT(", 0) = d;
|
| + MP_CHECKOK( s_mp_norm(&rem, ", &norm) );
|
| + if (norm)
|
| + d <<= norm;
|
| + MP_DIGIT(", 0) = 0;
|
| +#endif
|
| +
|
| + p = 0;
|
| + for (ix = USED(&rem) - 1; ix >= 0; ix--) {
|
| + w = DIGIT(&rem, ix);
|
| +
|
| + if (p) {
|
| + MP_CHECKOK( s_mpv_div_2dx1d(p, w, d, &q, &w) );
|
| + } else if (w >= d) {
|
| + q = w / d;
|
| + w = w % d;
|
| + } else {
|
| + q = 0;
|
| + }
|
| +
|
| + MP_CHECKOK( s_mp_lshd(", 1) );
|
| + DIGIT(", 0) = q;
|
| + p = w;
|
| + }
|
| +#if !defined(MP_ASSEMBLY_DIV_2DX1D)
|
| + if (norm)
|
| + w >>= norm;
|
| +#endif
|
| + }
|
| +#endif
|
| +
|
| + /* Deliver the remainder, if desired */
|
| + if(r)
|
| + *r = (mp_digit)w;
|
| +
|
| + s_mp_clamp(");
|
| + mp_exch(", mp);
|
| +CLEANUP:
|
| + mp_clear(");
|
| + mp_clear(&rem);
|
| +
|
| + return res;
|
| +} /* end s_mp_div_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ Primitive full arithmetic */
|
| +
|
| +/* {{{ s_mp_add(a, b) */
|
| +
|
| +/* Compute a = |a| + |b| */
|
| +mp_err s_mp_add(mp_int *a, const mp_int *b) /* magnitude addition */
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + mp_word w = 0;
|
| +#else
|
| + mp_digit d, sum, carry = 0;
|
| +#endif
|
| + mp_digit *pa, *pb;
|
| + mp_size ix;
|
| + mp_size used;
|
| + mp_err res;
|
| +
|
| + /* Make sure a has enough precision for the output value */
|
| + if((USED(b) > USED(a)) && (res = s_mp_pad(a, USED(b))) != MP_OKAY)
|
| + return res;
|
| +
|
| + /*
|
| + Add up all digits up to the precision of b. If b had initially
|
| + the same precision as a, or greater, we took care of it by the
|
| + padding step above, so there is no problem. If b had initially
|
| + less precision, we'll have to make sure the carry out is duly
|
| + propagated upward among the higher-order digits of the sum.
|
| + */
|
| + pa = MP_DIGITS(a);
|
| + pb = MP_DIGITS(b);
|
| + used = MP_USED(b);
|
| + for(ix = 0; ix < used; ix++) {
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + w = w + *pa + *pb++;
|
| + *pa++ = ACCUM(w);
|
| + w = CARRYOUT(w);
|
| +#else
|
| + d = *pa;
|
| + sum = d + *pb++;
|
| + d = (sum < d); /* detect overflow */
|
| + *pa++ = sum += carry;
|
| + carry = d + (sum < carry); /* detect overflow */
|
| +#endif
|
| + }
|
| +
|
| + /* If we run out of 'b' digits before we're actually done, make
|
| + sure the carries get propagated upward...
|
| + */
|
| + used = MP_USED(a);
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + while (w && ix < used) {
|
| + w = w + *pa;
|
| + *pa++ = ACCUM(w);
|
| + w = CARRYOUT(w);
|
| + ++ix;
|
| + }
|
| +#else
|
| + while (carry && ix < used) {
|
| + sum = carry + *pa;
|
| + *pa++ = sum;
|
| + carry = !sum;
|
| + ++ix;
|
| + }
|
| +#endif
|
| +
|
| + /* If there's an overall carry out, increase precision and include
|
| + it. We could have done this initially, but why touch the memory
|
| + allocator unless we're sure we have to?
|
| + */
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + if (w) {
|
| + if((res = s_mp_pad(a, used + 1)) != MP_OKAY)
|
| + return res;
|
| +
|
| + DIGIT(a, ix) = (mp_digit)w;
|
| + }
|
| +#else
|
| + if (carry) {
|
| + if((res = s_mp_pad(a, used + 1)) != MP_OKAY)
|
| + return res;
|
| +
|
| + DIGIT(a, used) = carry;
|
| + }
|
| +#endif
|
| +
|
| + return MP_OKAY;
|
| +} /* end s_mp_add() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* Compute c = |a| + |b| */ /* magnitude addition */
|
| +mp_err s_mp_add_3arg(const mp_int *a, const mp_int *b, mp_int *c)
|
| +{
|
| + mp_digit *pa, *pb, *pc;
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + mp_word w = 0;
|
| +#else
|
| + mp_digit sum, carry = 0, d;
|
| +#endif
|
| + mp_size ix;
|
| + mp_size used;
|
| + mp_err res;
|
| +
|
| + MP_SIGN(c) = MP_SIGN(a);
|
| + if (MP_USED(a) < MP_USED(b)) {
|
| + const mp_int *xch = a;
|
| + a = b;
|
| + b = xch;
|
| + }
|
| +
|
| + /* Make sure a has enough precision for the output value */
|
| + if (MP_OKAY != (res = s_mp_pad(c, MP_USED(a))))
|
| + return res;
|
| +
|
| + /*
|
| + Add up all digits up to the precision of b. If b had initially
|
| + the same precision as a, or greater, we took care of it by the
|
| + exchange step above, so there is no problem. If b had initially
|
| + less precision, we'll have to make sure the carry out is duly
|
| + propagated upward among the higher-order digits of the sum.
|
| + */
|
| + pa = MP_DIGITS(a);
|
| + pb = MP_DIGITS(b);
|
| + pc = MP_DIGITS(c);
|
| + used = MP_USED(b);
|
| + for (ix = 0; ix < used; ix++) {
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + w = w + *pa++ + *pb++;
|
| + *pc++ = ACCUM(w);
|
| + w = CARRYOUT(w);
|
| +#else
|
| + d = *pa++;
|
| + sum = d + *pb++;
|
| + d = (sum < d); /* detect overflow */
|
| + *pc++ = sum += carry;
|
| + carry = d + (sum < carry); /* detect overflow */
|
| +#endif
|
| + }
|
| +
|
| + /* If we run out of 'b' digits before we're actually done, make
|
| + sure the carries get propagated upward...
|
| + */
|
| + for (used = MP_USED(a); ix < used; ++ix) {
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + w = w + *pa++;
|
| + *pc++ = ACCUM(w);
|
| + w = CARRYOUT(w);
|
| +#else
|
| + *pc++ = sum = carry + *pa++;
|
| + carry = (sum < carry);
|
| +#endif
|
| + }
|
| +
|
| + /* If there's an overall carry out, increase precision and include
|
| + it. We could have done this initially, but why touch the memory
|
| + allocator unless we're sure we have to?
|
| + */
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + if (w) {
|
| + if((res = s_mp_pad(c, used + 1)) != MP_OKAY)
|
| + return res;
|
| +
|
| + DIGIT(c, used) = (mp_digit)w;
|
| + ++used;
|
| + }
|
| +#else
|
| + if (carry) {
|
| + if((res = s_mp_pad(c, used + 1)) != MP_OKAY)
|
| + return res;
|
| +
|
| + DIGIT(c, used) = carry;
|
| + ++used;
|
| + }
|
| +#endif
|
| + MP_USED(c) = used;
|
| + return MP_OKAY;
|
| +}
|
| +/* {{{ s_mp_add_offset(a, b, offset) */
|
| +
|
| +/* Compute a = |a| + ( |b| * (RADIX ** offset) ) */
|
| +mp_err s_mp_add_offset(mp_int *a, mp_int *b, mp_size offset)
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + mp_word w, k = 0;
|
| +#else
|
| + mp_digit d, sum, carry = 0;
|
| +#endif
|
| + mp_size ib;
|
| + mp_size ia;
|
| + mp_size lim;
|
| + mp_err res;
|
| +
|
| + /* Make sure a has enough precision for the output value */
|
| + lim = MP_USED(b) + offset;
|
| + if((lim > USED(a)) && (res = s_mp_pad(a, lim)) != MP_OKAY)
|
| + return res;
|
| +
|
| + /*
|
| + Add up all digits up to the precision of b. If b had initially
|
| + the same precision as a, or greater, we took care of it by the
|
| + padding step above, so there is no problem. If b had initially
|
| + less precision, we'll have to make sure the carry out is duly
|
| + propagated upward among the higher-order digits of the sum.
|
| + */
|
| + lim = USED(b);
|
| + for(ib = 0, ia = offset; ib < lim; ib++, ia++) {
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + w = (mp_word)DIGIT(a, ia) + DIGIT(b, ib) + k;
|
| + DIGIT(a, ia) = ACCUM(w);
|
| + k = CARRYOUT(w);
|
| +#else
|
| + d = MP_DIGIT(a, ia);
|
| + sum = d + MP_DIGIT(b, ib);
|
| + d = (sum < d);
|
| + MP_DIGIT(a,ia) = sum += carry;
|
| + carry = d + (sum < carry);
|
| +#endif
|
| + }
|
| +
|
| + /* If we run out of 'b' digits before we're actually done, make
|
| + sure the carries get propagated upward...
|
| + */
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + for (lim = MP_USED(a); k && (ia < lim); ++ia) {
|
| + w = (mp_word)DIGIT(a, ia) + k;
|
| + DIGIT(a, ia) = ACCUM(w);
|
| + k = CARRYOUT(w);
|
| + }
|
| +#else
|
| + for (lim = MP_USED(a); carry && (ia < lim); ++ia) {
|
| + d = MP_DIGIT(a, ia);
|
| + MP_DIGIT(a,ia) = sum = d + carry;
|
| + carry = (sum < d);
|
| + }
|
| +#endif
|
| +
|
| + /* If there's an overall carry out, increase precision and include
|
| + it. We could have done this initially, but why touch the memory
|
| + allocator unless we're sure we have to?
|
| + */
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD)
|
| + if(k) {
|
| + if((res = s_mp_pad(a, USED(a) + 1)) != MP_OKAY)
|
| + return res;
|
| +
|
| + DIGIT(a, ia) = (mp_digit)k;
|
| + }
|
| +#else
|
| + if (carry) {
|
| + if((res = s_mp_pad(a, lim + 1)) != MP_OKAY)
|
| + return res;
|
| +
|
| + DIGIT(a, lim) = carry;
|
| + }
|
| +#endif
|
| + s_mp_clamp(a);
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end s_mp_add_offset() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_sub(a, b) */
|
| +
|
| +/* Compute a = |a| - |b|, assumes |a| >= |b| */
|
| +mp_err s_mp_sub(mp_int *a, const mp_int *b) /* magnitude subtract */
|
| +{
|
| + mp_digit *pa, *pb, *limit;
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + mp_sword w = 0;
|
| +#else
|
| + mp_digit d, diff, borrow = 0;
|
| +#endif
|
| +
|
| + /*
|
| + Subtract and propagate borrow. Up to the precision of b, this
|
| + accounts for the digits of b; after that, we just make sure the
|
| + carries get to the right place. This saves having to pad b out to
|
| + the precision of a just to make the loops work right...
|
| + */
|
| + pa = MP_DIGITS(a);
|
| + pb = MP_DIGITS(b);
|
| + limit = pb + MP_USED(b);
|
| + while (pb < limit) {
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + w = w + *pa - *pb++;
|
| + *pa++ = ACCUM(w);
|
| + w >>= MP_DIGIT_BIT;
|
| +#else
|
| + d = *pa;
|
| + diff = d - *pb++;
|
| + d = (diff > d); /* detect borrow */
|
| + if (borrow && --diff == MP_DIGIT_MAX)
|
| + ++d;
|
| + *pa++ = diff;
|
| + borrow = d;
|
| +#endif
|
| + }
|
| + limit = MP_DIGITS(a) + MP_USED(a);
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + while (w && pa < limit) {
|
| + w = w + *pa;
|
| + *pa++ = ACCUM(w);
|
| + w >>= MP_DIGIT_BIT;
|
| + }
|
| +#else
|
| + while (borrow && pa < limit) {
|
| + d = *pa;
|
| + *pa++ = diff = d - borrow;
|
| + borrow = (diff > d);
|
| + }
|
| +#endif
|
| +
|
| + /* Clobber any leading zeroes we created */
|
| + s_mp_clamp(a);
|
| +
|
| + /*
|
| + If there was a borrow out, then |b| > |a| in violation
|
| + of our input invariant. We've already done the work,
|
| + but we'll at least complain about it...
|
| + */
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + return w ? MP_RANGE : MP_OKAY;
|
| +#else
|
| + return borrow ? MP_RANGE : MP_OKAY;
|
| +#endif
|
| +} /* end s_mp_sub() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* Compute c = |a| - |b|, assumes |a| >= |b| */ /* magnitude subtract */
|
| +mp_err s_mp_sub_3arg(const mp_int *a, const mp_int *b, mp_int *c)
|
| +{
|
| + mp_digit *pa, *pb, *pc;
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + mp_sword w = 0;
|
| +#else
|
| + mp_digit d, diff, borrow = 0;
|
| +#endif
|
| + int ix, limit;
|
| + mp_err res;
|
| +
|
| + MP_SIGN(c) = MP_SIGN(a);
|
| +
|
| + /* Make sure a has enough precision for the output value */
|
| + if (MP_OKAY != (res = s_mp_pad(c, MP_USED(a))))
|
| + return res;
|
| +
|
| + /*
|
| + Subtract and propagate borrow. Up to the precision of b, this
|
| + accounts for the digits of b; after that, we just make sure the
|
| + carries get to the right place. This saves having to pad b out to
|
| + the precision of a just to make the loops work right...
|
| + */
|
| + pa = MP_DIGITS(a);
|
| + pb = MP_DIGITS(b);
|
| + pc = MP_DIGITS(c);
|
| + limit = MP_USED(b);
|
| + for (ix = 0; ix < limit; ++ix) {
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + w = w + *pa++ - *pb++;
|
| + *pc++ = ACCUM(w);
|
| + w >>= MP_DIGIT_BIT;
|
| +#else
|
| + d = *pa++;
|
| + diff = d - *pb++;
|
| + d = (diff > d);
|
| + if (borrow && --diff == MP_DIGIT_MAX)
|
| + ++d;
|
| + *pc++ = diff;
|
| + borrow = d;
|
| +#endif
|
| + }
|
| + for (limit = MP_USED(a); ix < limit; ++ix) {
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + w = w + *pa++;
|
| + *pc++ = ACCUM(w);
|
| + w >>= MP_DIGIT_BIT;
|
| +#else
|
| + d = *pa++;
|
| + *pc++ = diff = d - borrow;
|
| + borrow = (diff > d);
|
| +#endif
|
| + }
|
| +
|
| + /* Clobber any leading zeroes we created */
|
| + MP_USED(c) = ix;
|
| + s_mp_clamp(c);
|
| +
|
| + /*
|
| + If there was a borrow out, then |b| > |a| in violation
|
| + of our input invariant. We've already done the work,
|
| + but we'll at least complain about it...
|
| + */
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD)
|
| + return w ? MP_RANGE : MP_OKAY;
|
| +#else
|
| + return borrow ? MP_RANGE : MP_OKAY;
|
| +#endif
|
| +}
|
| +/* {{{ s_mp_mul(a, b) */
|
| +
|
| +/* Compute a = |a| * |b| */
|
| +mp_err s_mp_mul(mp_int *a, const mp_int *b)
|
| +{
|
| + return mp_mul(a, b, a);
|
| +} /* end s_mp_mul() */
|
| +
|
| +/* }}} */
|
| +
|
| +#if defined(MP_USE_UINT_DIGIT) && defined(MP_USE_LONG_LONG_MULTIPLY)
|
| +/* This trick works on Sparc V8 CPUs with the Workshop compilers. */
|
| +#define MP_MUL_DxD(a, b, Phi, Plo) \
|
| + { unsigned long long product = (unsigned long long)a * b; \
|
| + Plo = (mp_digit)product; \
|
| + Phi = (mp_digit)(product >> MP_DIGIT_BIT); }
|
| +#elif defined(OSF1)
|
| +#define MP_MUL_DxD(a, b, Phi, Plo) \
|
| + { Plo = asm ("mulq %a0, %a1, %v0", a, b);\
|
| + Phi = asm ("umulh %a0, %a1, %v0", a, b); }
|
| +#else
|
| +#define MP_MUL_DxD(a, b, Phi, Plo) \
|
| + { mp_digit a0b1, a1b0; \
|
| + Plo = (a & MP_HALF_DIGIT_MAX) * (b & MP_HALF_DIGIT_MAX); \
|
| + Phi = (a >> MP_HALF_DIGIT_BIT) * (b >> MP_HALF_DIGIT_BIT); \
|
| + a0b1 = (a & MP_HALF_DIGIT_MAX) * (b >> MP_HALF_DIGIT_BIT); \
|
| + a1b0 = (a >> MP_HALF_DIGIT_BIT) * (b & MP_HALF_DIGIT_MAX); \
|
| + a1b0 += a0b1; \
|
| + Phi += a1b0 >> MP_HALF_DIGIT_BIT; \
|
| + if (a1b0 < a0b1) \
|
| + Phi += MP_HALF_RADIX; \
|
| + a1b0 <<= MP_HALF_DIGIT_BIT; \
|
| + Plo += a1b0; \
|
| + if (Plo < a1b0) \
|
| + ++Phi; \
|
| + }
|
| +#endif
|
| +
|
| +#if !defined(MP_ASSEMBLY_MULTIPLY)
|
| +/* c = a * b */
|
| +void s_mpv_mul_d(const mp_digit *a, mp_size a_len, mp_digit b, mp_digit *c)
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_MUL_WORD)
|
| + mp_digit d = 0;
|
| +
|
| + /* Inner product: Digits of a */
|
| + while (a_len--) {
|
| + mp_word w = ((mp_word)b * *a++) + d;
|
| + *c++ = ACCUM(w);
|
| + d = CARRYOUT(w);
|
| + }
|
| + *c = d;
|
| +#else
|
| + mp_digit carry = 0;
|
| + while (a_len--) {
|
| + mp_digit a_i = *a++;
|
| + mp_digit a0b0, a1b1;
|
| +
|
| + MP_MUL_DxD(a_i, b, a1b1, a0b0);
|
| +
|
| + a0b0 += carry;
|
| + if (a0b0 < carry)
|
| + ++a1b1;
|
| + *c++ = a0b0;
|
| + carry = a1b1;
|
| + }
|
| + *c = carry;
|
| +#endif
|
| +}
|
| +
|
| +/* c += a * b */
|
| +void s_mpv_mul_d_add(const mp_digit *a, mp_size a_len, mp_digit b,
|
| + mp_digit *c)
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_MUL_WORD)
|
| + mp_digit d = 0;
|
| +
|
| + /* Inner product: Digits of a */
|
| + while (a_len--) {
|
| + mp_word w = ((mp_word)b * *a++) + *c + d;
|
| + *c++ = ACCUM(w);
|
| + d = CARRYOUT(w);
|
| + }
|
| + *c = d;
|
| +#else
|
| + mp_digit carry = 0;
|
| + while (a_len--) {
|
| + mp_digit a_i = *a++;
|
| + mp_digit a0b0, a1b1;
|
| +
|
| + MP_MUL_DxD(a_i, b, a1b1, a0b0);
|
| +
|
| + a0b0 += carry;
|
| + if (a0b0 < carry)
|
| + ++a1b1;
|
| + a0b0 += a_i = *c;
|
| + if (a0b0 < a_i)
|
| + ++a1b1;
|
| + *c++ = a0b0;
|
| + carry = a1b1;
|
| + }
|
| + *c = carry;
|
| +#endif
|
| +}
|
| +
|
| +/* Presently, this is only used by the Montgomery arithmetic code. */
|
| +/* c += a * b */
|
| +void s_mpv_mul_d_add_prop(const mp_digit *a, mp_size a_len, mp_digit b, mp_digit *c)
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_MUL_WORD)
|
| + mp_digit d = 0;
|
| +
|
| + /* Inner product: Digits of a */
|
| + while (a_len--) {
|
| + mp_word w = ((mp_word)b * *a++) + *c + d;
|
| + *c++ = ACCUM(w);
|
| + d = CARRYOUT(w);
|
| + }
|
| +
|
| + while (d) {
|
| + mp_word w = (mp_word)*c + d;
|
| + *c++ = ACCUM(w);
|
| + d = CARRYOUT(w);
|
| + }
|
| +#else
|
| + mp_digit carry = 0;
|
| + while (a_len--) {
|
| + mp_digit a_i = *a++;
|
| + mp_digit a0b0, a1b1;
|
| +
|
| + MP_MUL_DxD(a_i, b, a1b1, a0b0);
|
| +
|
| + a0b0 += carry;
|
| + if (a0b0 < carry)
|
| + ++a1b1;
|
| +
|
| + a0b0 += a_i = *c;
|
| + if (a0b0 < a_i)
|
| + ++a1b1;
|
| +
|
| + *c++ = a0b0;
|
| + carry = a1b1;
|
| + }
|
| + while (carry) {
|
| + mp_digit c_i = *c;
|
| + carry += c_i;
|
| + *c++ = carry;
|
| + carry = carry < c_i;
|
| + }
|
| +#endif
|
| +}
|
| +#endif
|
| +
|
| +#if defined(MP_USE_UINT_DIGIT) && defined(MP_USE_LONG_LONG_MULTIPLY)
|
| +/* This trick works on Sparc V8 CPUs with the Workshop compilers. */
|
| +#define MP_SQR_D(a, Phi, Plo) \
|
| + { unsigned long long square = (unsigned long long)a * a; \
|
| + Plo = (mp_digit)square; \
|
| + Phi = (mp_digit)(square >> MP_DIGIT_BIT); }
|
| +#elif defined(OSF1)
|
| +#define MP_SQR_D(a, Phi, Plo) \
|
| + { Plo = asm ("mulq %a0, %a0, %v0", a);\
|
| + Phi = asm ("umulh %a0, %a0, %v0", a); }
|
| +#else
|
| +#define MP_SQR_D(a, Phi, Plo) \
|
| + { mp_digit Pmid; \
|
| + Plo = (a & MP_HALF_DIGIT_MAX) * (a & MP_HALF_DIGIT_MAX); \
|
| + Phi = (a >> MP_HALF_DIGIT_BIT) * (a >> MP_HALF_DIGIT_BIT); \
|
| + Pmid = (a & MP_HALF_DIGIT_MAX) * (a >> MP_HALF_DIGIT_BIT); \
|
| + Phi += Pmid >> (MP_HALF_DIGIT_BIT - 1); \
|
| + Pmid <<= (MP_HALF_DIGIT_BIT + 1); \
|
| + Plo += Pmid; \
|
| + if (Plo < Pmid) \
|
| + ++Phi; \
|
| + }
|
| +#endif
|
| +
|
| +#if !defined(MP_ASSEMBLY_SQUARE)
|
| +/* Add the squares of the digits of a to the digits of b. */
|
| +void s_mpv_sqr_add_prop(const mp_digit *pa, mp_size a_len, mp_digit *ps)
|
| +{
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_MUL_WORD)
|
| + mp_word w;
|
| + mp_digit d;
|
| + mp_size ix;
|
| +
|
| + w = 0;
|
| +#define ADD_SQUARE(n) \
|
| + d = pa[n]; \
|
| + w += (d * (mp_word)d) + ps[2*n]; \
|
| + ps[2*n] = ACCUM(w); \
|
| + w = (w >> DIGIT_BIT) + ps[2*n+1]; \
|
| + ps[2*n+1] = ACCUM(w); \
|
| + w = (w >> DIGIT_BIT)
|
| +
|
| + for (ix = a_len; ix >= 4; ix -= 4) {
|
| + ADD_SQUARE(0);
|
| + ADD_SQUARE(1);
|
| + ADD_SQUARE(2);
|
| + ADD_SQUARE(3);
|
| + pa += 4;
|
| + ps += 8;
|
| + }
|
| + if (ix) {
|
| + ps += 2*ix;
|
| + pa += ix;
|
| + switch (ix) {
|
| + case 3: ADD_SQUARE(-3); /* FALLTHRU */
|
| + case 2: ADD_SQUARE(-2); /* FALLTHRU */
|
| + case 1: ADD_SQUARE(-1); /* FALLTHRU */
|
| + case 0: break;
|
| + }
|
| + }
|
| + while (w) {
|
| + w += *ps;
|
| + *ps++ = ACCUM(w);
|
| + w = (w >> DIGIT_BIT);
|
| + }
|
| +#else
|
| + mp_digit carry = 0;
|
| + while (a_len--) {
|
| + mp_digit a_i = *pa++;
|
| + mp_digit a0a0, a1a1;
|
| +
|
| + MP_SQR_D(a_i, a1a1, a0a0);
|
| +
|
| + /* here a1a1 and a0a0 constitute a_i ** 2 */
|
| + a0a0 += carry;
|
| + if (a0a0 < carry)
|
| + ++a1a1;
|
| +
|
| + /* now add to ps */
|
| + a0a0 += a_i = *ps;
|
| + if (a0a0 < a_i)
|
| + ++a1a1;
|
| + *ps++ = a0a0;
|
| + a1a1 += a_i = *ps;
|
| + carry = (a1a1 < a_i);
|
| + *ps++ = a1a1;
|
| + }
|
| + while (carry) {
|
| + mp_digit s_i = *ps;
|
| + carry += s_i;
|
| + *ps++ = carry;
|
| + carry = carry < s_i;
|
| + }
|
| +#endif
|
| +}
|
| +#endif
|
| +
|
| +#if (defined(MP_NO_MP_WORD) || defined(MP_NO_DIV_WORD)) \
|
| +&& !defined(MP_ASSEMBLY_DIV_2DX1D)
|
| +/*
|
| +** Divide 64-bit (Nhi,Nlo) by 32-bit divisor, which must be normalized
|
| +** so its high bit is 1. This code is from NSPR.
|
| +*/
|
| +mp_err s_mpv_div_2dx1d(mp_digit Nhi, mp_digit Nlo, mp_digit divisor,
|
| + mp_digit *qp, mp_digit *rp)
|
| +{
|
| + mp_digit d1, d0, q1, q0;
|
| + mp_digit r1, r0, m;
|
| +
|
| + d1 = divisor >> MP_HALF_DIGIT_BIT;
|
| + d0 = divisor & MP_HALF_DIGIT_MAX;
|
| + r1 = Nhi % d1;
|
| + q1 = Nhi / d1;
|
| + m = q1 * d0;
|
| + r1 = (r1 << MP_HALF_DIGIT_BIT) | (Nlo >> MP_HALF_DIGIT_BIT);
|
| + if (r1 < m) {
|
| + q1--, r1 += divisor;
|
| + if (r1 >= divisor && r1 < m) {
|
| + q1--, r1 += divisor;
|
| + }
|
| + }
|
| + r1 -= m;
|
| + r0 = r1 % d1;
|
| + q0 = r1 / d1;
|
| + m = q0 * d0;
|
| + r0 = (r0 << MP_HALF_DIGIT_BIT) | (Nlo & MP_HALF_DIGIT_MAX);
|
| + if (r0 < m) {
|
| + q0--, r0 += divisor;
|
| + if (r0 >= divisor && r0 < m) {
|
| + q0--, r0 += divisor;
|
| + }
|
| + }
|
| + if (qp)
|
| + *qp = (q1 << MP_HALF_DIGIT_BIT) | q0;
|
| + if (rp)
|
| + *rp = r0 - m;
|
| + return MP_OKAY;
|
| +}
|
| +#endif
|
| +
|
| +#if MP_SQUARE
|
| +/* {{{ s_mp_sqr(a) */
|
| +
|
| +mp_err s_mp_sqr(mp_int *a)
|
| +{
|
| + mp_err res;
|
| + mp_int tmp;
|
| +
|
| + if((res = mp_init_size(&tmp, 2 * USED(a))) != MP_OKAY)
|
| + return res;
|
| + res = mp_sqr(a, &tmp);
|
| + if (res == MP_OKAY) {
|
| + s_mp_exch(&tmp, a);
|
| + }
|
| + mp_clear(&tmp);
|
| + return res;
|
| +}
|
| +
|
| +/* }}} */
|
| +#endif
|
| +
|
| +/* {{{ s_mp_div(a, b) */
|
| +
|
| +/*
|
| + s_mp_div(a, b)
|
| +
|
| + Compute a = a / b and b = a mod b. Assumes b > a.
|
| + */
|
| +
|
| +mp_err s_mp_div(mp_int *rem, /* i: dividend, o: remainder */
|
| + mp_int *div, /* i: divisor */
|
| + mp_int *quot) /* i: 0; o: quotient */
|
| +{
|
| + mp_int part, t;
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_DIV_WORD)
|
| + mp_word q_msd;
|
| +#else
|
| + mp_digit q_msd;
|
| +#endif
|
| + mp_err res;
|
| + mp_digit d;
|
| + mp_digit div_msd;
|
| + int ix;
|
| +
|
| + if(mp_cmp_z(div) == 0)
|
| + return MP_RANGE;
|
| +
|
| + /* Shortcut if divisor is power of two */
|
| + if((ix = s_mp_ispow2(div)) >= 0) {
|
| + MP_CHECKOK( mp_copy(rem, quot) );
|
| + s_mp_div_2d(quot, (mp_digit)ix);
|
| + s_mp_mod_2d(rem, (mp_digit)ix);
|
| +
|
| + return MP_OKAY;
|
| + }
|
| +
|
| + DIGITS(&t) = 0;
|
| + MP_SIGN(rem) = ZPOS;
|
| + MP_SIGN(div) = ZPOS;
|
| +
|
| + /* A working temporary for division */
|
| + MP_CHECKOK( mp_init_size(&t, MP_ALLOC(rem)));
|
| +
|
| + /* Normalize to optimize guessing */
|
| + MP_CHECKOK( s_mp_norm(rem, div, &d) );
|
| +
|
| + part = *rem;
|
| +
|
| + /* Perform the division itself...woo! */
|
| + MP_USED(quot) = MP_ALLOC(quot);
|
| +
|
| + /* Find a partial substring of rem which is at least div */
|
| + /* If we didn't find one, we're finished dividing */
|
| + while (MP_USED(rem) > MP_USED(div) || s_mp_cmp(rem, div) >= 0) {
|
| + int i;
|
| + int unusedRem;
|
| +
|
| + unusedRem = MP_USED(rem) - MP_USED(div);
|
| + MP_DIGITS(&part) = MP_DIGITS(rem) + unusedRem;
|
| + MP_ALLOC(&part) = MP_ALLOC(rem) - unusedRem;
|
| + MP_USED(&part) = MP_USED(div);
|
| + if (s_mp_cmp(&part, div) < 0) {
|
| + -- unusedRem;
|
| +#if MP_ARGCHK == 2
|
| + assert(unusedRem >= 0);
|
| +#endif
|
| + -- MP_DIGITS(&part);
|
| + ++ MP_USED(&part);
|
| + ++ MP_ALLOC(&part);
|
| + }
|
| +
|
| + /* Compute a guess for the next quotient digit */
|
| + q_msd = MP_DIGIT(&part, MP_USED(&part) - 1);
|
| + div_msd = MP_DIGIT(div, MP_USED(div) - 1);
|
| + if (q_msd >= div_msd) {
|
| + q_msd = 1;
|
| + } else if (MP_USED(&part) > 1) {
|
| +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_DIV_WORD)
|
| + q_msd = (q_msd << MP_DIGIT_BIT) | MP_DIGIT(&part, MP_USED(&part) - 2);
|
| + q_msd /= div_msd;
|
| + if (q_msd == RADIX)
|
| + --q_msd;
|
| +#else
|
| + mp_digit r;
|
| + MP_CHECKOK( s_mpv_div_2dx1d(q_msd, MP_DIGIT(&part, MP_USED(&part) - 2),
|
| + div_msd, &q_msd, &r) );
|
| +#endif
|
| + } else {
|
| + q_msd = 0;
|
| + }
|
| +#if MP_ARGCHK == 2
|
| + assert(q_msd > 0); /* This case should never occur any more. */
|
| +#endif
|
| + if (q_msd <= 0)
|
| + break;
|
| +
|
| + /* See what that multiplies out to */
|
| + mp_copy(div, &t);
|
| + MP_CHECKOK( s_mp_mul_d(&t, (mp_digit)q_msd) );
|
| +
|
| + /*
|
| + If it's too big, back it off. We should not have to do this
|
| + more than once, or, in rare cases, twice. Knuth describes a
|
| + method by which this could be reduced to a maximum of once, but
|
| + I didn't implement that here.
|
| + * When using s_mpv_div_2dx1d, we may have to do this 3 times.
|
| + */
|
| + for (i = 4; s_mp_cmp(&t, &part) > 0 && i > 0; --i) {
|
| + --q_msd;
|
| + s_mp_sub(&t, div); /* t -= div */
|
| + }
|
| + if (i < 0) {
|
| + res = MP_RANGE;
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + /* At this point, q_msd should be the right next digit */
|
| + MP_CHECKOK( s_mp_sub(&part, &t) ); /* part -= t */
|
| + s_mp_clamp(rem);
|
| +
|
| + /*
|
| + Include the digit in the quotient. We allocated enough memory
|
| + for any quotient we could ever possibly get, so we should not
|
| + have to check for failures here
|
| + */
|
| + MP_DIGIT(quot, unusedRem) = (mp_digit)q_msd;
|
| + }
|
| +
|
| + /* Denormalize remainder */
|
| + if (d) {
|
| + s_mp_div_2d(rem, d);
|
| + }
|
| +
|
| + s_mp_clamp(quot);
|
| +
|
| +CLEANUP:
|
| + mp_clear(&t);
|
| +
|
| + return res;
|
| +
|
| +} /* end s_mp_div() */
|
| +
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_2expt(a, k) */
|
| +
|
| +mp_err s_mp_2expt(mp_int *a, mp_digit k)
|
| +{
|
| + mp_err res;
|
| + mp_size dig, bit;
|
| +
|
| + dig = k / DIGIT_BIT;
|
| + bit = k % DIGIT_BIT;
|
| +
|
| + mp_zero(a);
|
| + if((res = s_mp_pad(a, dig + 1)) != MP_OKAY)
|
| + return res;
|
| +
|
| + DIGIT(a, dig) |= ((mp_digit)1 << bit);
|
| +
|
| + return MP_OKAY;
|
| +
|
| +} /* end s_mp_2expt() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_reduce(x, m, mu) */
|
| +
|
| +/*
|
| + Compute Barrett reduction, x (mod m), given a precomputed value for
|
| + mu = b^2k / m, where b = RADIX and k = #digits(m). This should be
|
| + faster than straight division, when many reductions by the same
|
| + value of m are required (such as in modular exponentiation). This
|
| + can nearly halve the time required to do modular exponentiation,
|
| + as compared to using the full integer divide to reduce.
|
| +
|
| + This algorithm was derived from the _Handbook of Applied
|
| + Cryptography_ by Menezes, Oorschot and VanStone, Ch. 14,
|
| + pp. 603-604.
|
| + */
|
| +
|
| +mp_err s_mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu)
|
| +{
|
| + mp_int q;
|
| + mp_err res;
|
| +
|
| + if((res = mp_init_copy(&q, x)) != MP_OKAY)
|
| + return res;
|
| +
|
| + s_mp_rshd(&q, USED(m) - 1); /* q1 = x / b^(k-1) */
|
| + s_mp_mul(&q, mu); /* q2 = q1 * mu */
|
| + s_mp_rshd(&q, USED(m) + 1); /* q3 = q2 / b^(k+1) */
|
| +
|
| + /* x = x mod b^(k+1), quick (no division) */
|
| + s_mp_mod_2d(x, DIGIT_BIT * (USED(m) + 1));
|
| +
|
| + /* q = q * m mod b^(k+1), quick (no division) */
|
| + s_mp_mul(&q, m);
|
| + s_mp_mod_2d(&q, DIGIT_BIT * (USED(m) + 1));
|
| +
|
| + /* x = x - q */
|
| + if((res = mp_sub(x, &q, x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| +
|
| + /* If x < 0, add b^(k+1) to it */
|
| + if(mp_cmp_z(x) < 0) {
|
| + mp_set(&q, 1);
|
| + if((res = s_mp_lshd(&q, USED(m) + 1)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + if((res = mp_add(x, &q, x)) != MP_OKAY)
|
| + goto CLEANUP;
|
| + }
|
| +
|
| + /* Back off if it's too big */
|
| + while(mp_cmp(x, m) >= 0) {
|
| + if((res = s_mp_sub(x, m)) != MP_OKAY)
|
| + break;
|
| + }
|
| +
|
| + CLEANUP:
|
| + mp_clear(&q);
|
| +
|
| + return res;
|
| +
|
| +} /* end s_mp_reduce() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ Primitive comparisons */
|
| +
|
| +/* {{{ s_mp_cmp(a, b) */
|
| +
|
| +/* Compare |a| <=> |b|, return 0 if equal, <0 if a<b, >0 if a>b */
|
| +int s_mp_cmp(const mp_int *a, const mp_int *b)
|
| +{
|
| + mp_size used_a = MP_USED(a);
|
| + {
|
| + mp_size used_b = MP_USED(b);
|
| +
|
| + if (used_a > used_b)
|
| + goto IS_GT;
|
| + if (used_a < used_b)
|
| + goto IS_LT;
|
| + }
|
| + {
|
| + mp_digit *pa, *pb;
|
| + mp_digit da = 0, db = 0;
|
| +
|
| +#define CMP_AB(n) if ((da = pa[n]) != (db = pb[n])) goto done
|
| +
|
| + pa = MP_DIGITS(a) + used_a;
|
| + pb = MP_DIGITS(b) + used_a;
|
| + while (used_a >= 4) {
|
| + pa -= 4;
|
| + pb -= 4;
|
| + used_a -= 4;
|
| + CMP_AB(3);
|
| + CMP_AB(2);
|
| + CMP_AB(1);
|
| + CMP_AB(0);
|
| + }
|
| + while (used_a-- > 0 && ((da = *--pa) == (db = *--pb)))
|
| + /* do nothing */;
|
| +done:
|
| + if (da > db)
|
| + goto IS_GT;
|
| + if (da < db)
|
| + goto IS_LT;
|
| + }
|
| + return MP_EQ;
|
| +IS_LT:
|
| + return MP_LT;
|
| +IS_GT:
|
| + return MP_GT;
|
| +} /* end s_mp_cmp() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_cmp_d(a, d) */
|
| +
|
| +/* Compare |a| <=> d, return 0 if equal, <0 if a<d, >0 if a>d */
|
| +int s_mp_cmp_d(const mp_int *a, mp_digit d)
|
| +{
|
| + if(USED(a) > 1)
|
| + return MP_GT;
|
| +
|
| + if(DIGIT(a, 0) < d)
|
| + return MP_LT;
|
| + else if(DIGIT(a, 0) > d)
|
| + return MP_GT;
|
| + else
|
| + return MP_EQ;
|
| +
|
| +} /* end s_mp_cmp_d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_ispow2(v) */
|
| +
|
| +/*
|
| + Returns -1 if the value is not a power of two; otherwise, it returns
|
| + k such that v = 2^k, i.e. lg(v).
|
| + */
|
| +int s_mp_ispow2(const mp_int *v)
|
| +{
|
| + mp_digit d;
|
| + int extra = 0, ix;
|
| +
|
| + ix = MP_USED(v) - 1;
|
| + d = MP_DIGIT(v, ix); /* most significant digit of v */
|
| +
|
| + extra = s_mp_ispow2d(d);
|
| + if (extra < 0 || ix == 0)
|
| + return extra;
|
| +
|
| + while (--ix >= 0) {
|
| + if (DIGIT(v, ix) != 0)
|
| + return -1; /* not a power of two */
|
| + extra += MP_DIGIT_BIT;
|
| + }
|
| +
|
| + return extra;
|
| +
|
| +} /* end s_mp_ispow2() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_ispow2d(d) */
|
| +
|
| +int s_mp_ispow2d(mp_digit d)
|
| +{
|
| + if ((d != 0) && ((d & (d-1)) == 0)) { /* d is a power of 2 */
|
| + int pow = 0;
|
| +#if defined (MP_USE_UINT_DIGIT)
|
| + if (d & 0xffff0000U)
|
| + pow += 16;
|
| + if (d & 0xff00ff00U)
|
| + pow += 8;
|
| + if (d & 0xf0f0f0f0U)
|
| + pow += 4;
|
| + if (d & 0xccccccccU)
|
| + pow += 2;
|
| + if (d & 0xaaaaaaaaU)
|
| + pow += 1;
|
| +#elif defined(MP_USE_LONG_LONG_DIGIT)
|
| + if (d & 0xffffffff00000000ULL)
|
| + pow += 32;
|
| + if (d & 0xffff0000ffff0000ULL)
|
| + pow += 16;
|
| + if (d & 0xff00ff00ff00ff00ULL)
|
| + pow += 8;
|
| + if (d & 0xf0f0f0f0f0f0f0f0ULL)
|
| + pow += 4;
|
| + if (d & 0xccccccccccccccccULL)
|
| + pow += 2;
|
| + if (d & 0xaaaaaaaaaaaaaaaaULL)
|
| + pow += 1;
|
| +#elif defined(MP_USE_LONG_DIGIT)
|
| + if (d & 0xffffffff00000000UL)
|
| + pow += 32;
|
| + if (d & 0xffff0000ffff0000UL)
|
| + pow += 16;
|
| + if (d & 0xff00ff00ff00ff00UL)
|
| + pow += 8;
|
| + if (d & 0xf0f0f0f0f0f0f0f0UL)
|
| + pow += 4;
|
| + if (d & 0xccccccccccccccccUL)
|
| + pow += 2;
|
| + if (d & 0xaaaaaaaaaaaaaaaaUL)
|
| + pow += 1;
|
| +#else
|
| +#error "unknown type for mp_digit"
|
| +#endif
|
| + return pow;
|
| + }
|
| + return -1;
|
| +
|
| +} /* end s_mp_ispow2d() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ Primitive I/O helpers */
|
| +
|
| +/* {{{ s_mp_tovalue(ch, r) */
|
| +
|
| +/*
|
| + Convert the given character to its digit value, in the given radix.
|
| + If the given character is not understood in the given radix, -1 is
|
| + returned. Otherwise the digit's numeric value is returned.
|
| +
|
| + The results will be odd if you use a radix < 2 or > 62, you are
|
| + expected to know what you're up to.
|
| + */
|
| +int s_mp_tovalue(char ch, int r)
|
| +{
|
| + int val, xch;
|
| +
|
| + if(r > 36)
|
| + xch = ch;
|
| + else
|
| + xch = toupper(ch);
|
| +
|
| + if(isdigit(xch))
|
| + val = xch - '0';
|
| + else if(isupper(xch))
|
| + val = xch - 'A' + 10;
|
| + else if(islower(xch))
|
| + val = xch - 'a' + 36;
|
| + else if(xch == '+')
|
| + val = 62;
|
| + else if(xch == '/')
|
| + val = 63;
|
| + else
|
| + return -1;
|
| +
|
| + if(val < 0 || val >= r)
|
| + return -1;
|
| +
|
| + return val;
|
| +
|
| +} /* end s_mp_tovalue() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_todigit(val, r, low) */
|
| +
|
| +/*
|
| + Convert val to a radix-r digit, if possible. If val is out of range
|
| + for r, returns zero. Otherwise, returns an ASCII character denoting
|
| + the value in the given radix.
|
| +
|
| + The results may be odd if you use a radix < 2 or > 64, you are
|
| + expected to know what you're doing.
|
| + */
|
| +
|
| +char s_mp_todigit(mp_digit val, int r, int low)
|
| +{
|
| + char ch;
|
| +
|
| + if(val >= r)
|
| + return 0;
|
| +
|
| + ch = s_dmap_1[val];
|
| +
|
| + if(r <= 36 && low)
|
| + ch = tolower(ch);
|
| +
|
| + return ch;
|
| +
|
| +} /* end s_mp_todigit() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ s_mp_outlen(bits, radix) */
|
| +
|
| +/*
|
| + Return an estimate for how long a string is needed to hold a radix
|
| + r representation of a number with 'bits' significant bits, plus an
|
| + extra for a zero terminator (assuming C style strings here)
|
| + */
|
| +int s_mp_outlen(int bits, int r)
|
| +{
|
| + return (int)((double)bits * LOG_V_2(r) + 1.5) + 1;
|
| +
|
| +} /* end s_mp_outlen() */
|
| +
|
| +/* }}} */
|
| +
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_read_unsigned_octets(mp, str, len) */
|
| +/* mp_read_unsigned_octets(mp, str, len)
|
| + Read in a raw value (base 256) into the given mp_int
|
| + No sign bit, number is positive. Leading zeros ignored.
|
| + */
|
| +
|
| +mp_err
|
| +mp_read_unsigned_octets(mp_int *mp, const unsigned char *str, mp_size len)
|
| +{
|
| + int count;
|
| + mp_err res;
|
| + mp_digit d;
|
| +
|
| + ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
|
| +
|
| + mp_zero(mp);
|
| +
|
| + count = len % sizeof(mp_digit);
|
| + if (count) {
|
| + for (d = 0; count-- > 0; --len) {
|
| + d = (d << 8) | *str++;
|
| + }
|
| + MP_DIGIT(mp, 0) = d;
|
| + }
|
| +
|
| + /* Read the rest of the digits */
|
| + for(; len > 0; len -= sizeof(mp_digit)) {
|
| + for (d = 0, count = sizeof(mp_digit); count > 0; --count) {
|
| + d = (d << 8) | *str++;
|
| + }
|
| + if (MP_EQ == mp_cmp_z(mp)) {
|
| + if (!d)
|
| + continue;
|
| + } else {
|
| + if((res = s_mp_lshd(mp, 1)) != MP_OKAY)
|
| + return res;
|
| + }
|
| + MP_DIGIT(mp, 0) = d;
|
| + }
|
| + return MP_OKAY;
|
| +} /* end mp_read_unsigned_octets() */
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_unsigned_octet_size(mp) */
|
| +int
|
| +mp_unsigned_octet_size(const mp_int *mp)
|
| +{
|
| + int bytes;
|
| + int ix;
|
| + mp_digit d = 0;
|
| +
|
| + ARGCHK(mp != NULL, MP_BADARG);
|
| + ARGCHK(MP_ZPOS == SIGN(mp), MP_BADARG);
|
| +
|
| + bytes = (USED(mp) * sizeof(mp_digit));
|
| +
|
| + /* subtract leading zeros. */
|
| + /* Iterate over each digit... */
|
| + for(ix = USED(mp) - 1; ix >= 0; ix--) {
|
| + d = DIGIT(mp, ix);
|
| + if (d)
|
| + break;
|
| + bytes -= sizeof(d);
|
| + }
|
| + if (!bytes)
|
| + return 1;
|
| +
|
| + /* Have MSD, check digit bytes, high order first */
|
| + for(ix = sizeof(mp_digit) - 1; ix >= 0; ix--) {
|
| + unsigned char x = (unsigned char)(d >> (ix * CHAR_BIT));
|
| + if (x)
|
| + break;
|
| + --bytes;
|
| + }
|
| + return bytes;
|
| +} /* end mp_unsigned_octet_size() */
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_to_unsigned_octets(mp, str) */
|
| +/* output a buffer of big endian octets no longer than specified. */
|
| +mp_err
|
| +mp_to_unsigned_octets(const mp_int *mp, unsigned char *str, mp_size maxlen)
|
| +{
|
| + int ix, pos = 0;
|
| + int bytes;
|
| +
|
| + ARGCHK(mp != NULL && str != NULL && !SIGN(mp), MP_BADARG);
|
| +
|
| + bytes = mp_unsigned_octet_size(mp);
|
| + ARGCHK(bytes <= maxlen, MP_BADARG);
|
| +
|
| + /* Iterate over each digit... */
|
| + for(ix = USED(mp) - 1; ix >= 0; ix--) {
|
| + mp_digit d = DIGIT(mp, ix);
|
| + int jx;
|
| +
|
| + /* Unpack digit bytes, high order first */
|
| + for(jx = sizeof(mp_digit) - 1; jx >= 0; jx--) {
|
| + unsigned char x = (unsigned char)(d >> (jx * CHAR_BIT));
|
| + if (!pos && !x) /* suppress leading zeros */
|
| + continue;
|
| + str[pos++] = x;
|
| + }
|
| + }
|
| + if (!pos)
|
| + str[pos++] = 0;
|
| + return pos;
|
| +} /* end mp_to_unsigned_octets() */
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_to_signed_octets(mp, str) */
|
| +/* output a buffer of big endian octets no longer than specified. */
|
| +mp_err
|
| +mp_to_signed_octets(const mp_int *mp, unsigned char *str, mp_size maxlen)
|
| +{
|
| + int ix, pos = 0;
|
| + int bytes;
|
| +
|
| + ARGCHK(mp != NULL && str != NULL && !SIGN(mp), MP_BADARG);
|
| +
|
| + bytes = mp_unsigned_octet_size(mp);
|
| + ARGCHK(bytes <= maxlen, MP_BADARG);
|
| +
|
| + /* Iterate over each digit... */
|
| + for(ix = USED(mp) - 1; ix >= 0; ix--) {
|
| + mp_digit d = DIGIT(mp, ix);
|
| + int jx;
|
| +
|
| + /* Unpack digit bytes, high order first */
|
| + for(jx = sizeof(mp_digit) - 1; jx >= 0; jx--) {
|
| + unsigned char x = (unsigned char)(d >> (jx * CHAR_BIT));
|
| + if (!pos) {
|
| + if (!x) /* suppress leading zeros */
|
| + continue;
|
| + if (x & 0x80) { /* add one leading zero to make output positive. */
|
| + ARGCHK(bytes + 1 <= maxlen, MP_BADARG);
|
| + if (bytes + 1 > maxlen)
|
| + return MP_BADARG;
|
| + str[pos++] = 0;
|
| + }
|
| + }
|
| + str[pos++] = x;
|
| + }
|
| + }
|
| + if (!pos)
|
| + str[pos++] = 0;
|
| + return pos;
|
| +} /* end mp_to_signed_octets() */
|
| +/* }}} */
|
| +
|
| +/* {{{ mp_to_fixlen_octets(mp, str) */
|
| +/* output a buffer of big endian octets exactly as long as requested. */
|
| +mp_err
|
| +mp_to_fixlen_octets(const mp_int *mp, unsigned char *str, mp_size length)
|
| +{
|
| + int ix, pos = 0;
|
| + int bytes;
|
| +
|
| + ARGCHK(mp != NULL && str != NULL && !SIGN(mp), MP_BADARG);
|
| +
|
| + bytes = mp_unsigned_octet_size(mp);
|
| + ARGCHK(bytes <= length, MP_BADARG);
|
| +
|
| + /* place any needed leading zeros */
|
| + for (;length > bytes; --length) {
|
| + *str++ = 0;
|
| + }
|
| +
|
| + /* Iterate over each digit... */
|
| + for(ix = USED(mp) - 1; ix >= 0; ix--) {
|
| + mp_digit d = DIGIT(mp, ix);
|
| + int jx;
|
| +
|
| + /* Unpack digit bytes, high order first */
|
| + for(jx = sizeof(mp_digit) - 1; jx >= 0; jx--) {
|
| + unsigned char x = (unsigned char)(d >> (jx * CHAR_BIT));
|
| + if (!pos && !x) /* suppress leading zeros */
|
| + continue;
|
| + str[pos++] = x;
|
| + }
|
| + }
|
| + if (!pos)
|
| + str[pos++] = 0;
|
| + return MP_OKAY;
|
| +} /* end mp_to_fixlen_octets() */
|
| +/* }}} */
|
| +
|
| +
|
| +/*------------------------------------------------------------------------*/
|
| +/* HERE THERE BE DRAGONS */
|
| +
|
|
|
Chromium Code Reviews
Issue 6804032:
Add TLS-SRP (RFC 5054) support
Base URL: http://git.chromium.org/git/chromium.git@trunk