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authorMatt A. Tobin <mattatobin@localhost.localdomain>2018-02-02 04:16:08 -0500
committerMatt A. Tobin <mattatobin@localhost.localdomain>2018-02-02 04:16:08 -0500
commit5f8de423f190bbb79a62f804151bc24824fa32d8 (patch)
tree10027f336435511475e392454359edea8e25895d /security/nss/lib/freebl/mpi/mpi.c
parent49ee0794b5d912db1f95dce6eb52d781dc210db5 (diff)
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Add m-esr52 at 52.6.0
Diffstat (limited to 'security/nss/lib/freebl/mpi/mpi.c')
-rw-r--r--security/nss/lib/freebl/mpi/mpi.c4839
1 files changed, 4839 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/mpi/mpi.c b/security/nss/lib/freebl/mpi/mpi.c
new file mode 100644
index 000000000..f6f75439c
--- /dev/null
+++ b/security/nss/lib/freebl/mpi/mpi.c
@@ -0,0 +1,4839 @@
+/*
+ * mpi.c
+ *
+ * Arbitrary precision integer arithmetic library
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
+
+#include "mpi-priv.h"
+#if defined(OSF1)
+#include <c_asm.h>
+#endif
+
+#if defined(__arm__) && \
+ ((defined(__thumb__) && !defined(__thumb2__)) || defined(__ARM_ARCH_3__))
+/* 16-bit thumb or ARM v3 doesn't work inlined assember version */
+#undef MP_ASSEMBLY_MULTIPLY
+#undef MP_ASSEMBLY_SQUARE
+#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
+
+#ifdef CT_VERIF
+#include <valgrind/memcheck.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+/";
+
+/* }}} */
+
+/* {{{ 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() */
+
+/* }}} */
+
+#ifdef CT_VERIF
+void
+mp_taint(mp_int *mp)
+{
+ size_t i;
+ for (i = 0; i < mp->used; ++i) {
+ VALGRIND_MAKE_MEM_UNDEFINED(&(mp->dp[i]), sizeof(mp_digit));
+ }
+}
+
+void
+mp_untaint(mp_int *mp)
+{
+ size_t i;
+ for (i = 0; i < mp->used; ++i) {
+ VALGRIND_MAKE_MEM_DEFINED(&(mp->dp[i]), sizeof(mp_digit));
+ }
+}
+#endif
+
+/*------------------------------------------------------------------------*/
+/* {{{ 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;
+
+ { /* 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) {
+ s_mp_setz(DIGITS(to), ALLOC(to));
+ 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) {
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+ 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 = 0;
+ 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) {
+ if ((res = mp_copy(a, q)) != MP_OKAY) {
+ return res;
+ }
+ 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;
+ unsigned 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() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ 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;
+ unsigned 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 */
+ if ((res = s_mp_add_d(&mu, 1)) != MP_OKAY)
+ goto CLEANUP;
+ if ((res = s_mp_lshd(&mu, 2 * USED(m))) != MP_OKAY)
+ goto CLEANUP;
+ 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(const mp_int *a, const mp_int *b)
+{
+ ARGCHK(a != NULL && b != NULL, MP_EQ);
+
+ return s_mp_cmp(a, b);
+
+} /* end mp_cmp_mag() */
+
+/* }}} */
+
+/* {{{ 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_CHECKOK(mp_copy(&xc, &u));
+ MP_CHECKOK(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;
+ unsigned 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));
+
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+ 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) */
+
+/* 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() */
+
+/* }}} */
+
+/* {{{ s_mp_copy(sp, dp, count) */
+
+/* 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() */
+
+/* }}} */
+
+/* {{{ s_mp_alloc(nb, ni) */
+
+/* Allocate ni records of nb bytes each, and return a pointer to that */
+void *
+s_mp_alloc(size_t nb, size_t ni)
+{
+ return calloc(nb, ni);
+
+} /* end s_mp_alloc() */
+
+/* }}} */
+
+/* {{{ s_mp_free(ptr) */
+
+/* Free the memory pointed to by ptr */
+void
+s_mp_free(void *ptr)
+{
+ if (ptr) {
+ free(ptr);
+ }
+} /* end s_mp_free() */
+
+/* }}} */
+
+/* {{{ s_mp_clamp(mp) */
+
+/* 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() */
+
+/* }}} */
+
+/* {{{ 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
+ */
+
+mp_err
+s_mp_lshd(mp_int *mp, mp_size p)
+{
+ mp_err res;
+ unsigned 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;
+
+ /* Shift all the significant figures over as needed */
+ for (ix = USED(mp) - p; ix-- > 0;) {
+ DIGIT(mp, ix + p) = DIGIT(mp, ix);
+ }
+
+ /* Fill the bottom digits with zeroes */
+ for (ix = 0; (mp_size)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 */
+ if (bshift) {
+ mask = (mp_digit)~0 << (MP_DIGIT_BIT - bshift);
+ mask &= MP_DIGIT(mp, MP_USED(mp) - 1);
+ } else {
+ mask = 0;
+ }
+
+ 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;
+
+} /* 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;
+ unsigned 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 = 0, 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(&quot) = 0;
+ /* Make room for the quotient */
+ MP_CHECKOK(mp_init_size(&quot, 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(&quot, 1);
+ DIGIT(&quot, 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(&quot, 0) = d;
+ MP_CHECKOK(s_mp_norm(&rem, &quot, &norm));
+ if (norm)
+ d <<= norm;
+ MP_DIGIT(&quot, 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(&quot, 1));
+ DIGIT(&quot, 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(&quot);
+ mp_exch(&quot, mp);
+CLEANUP:
+ mp_clear(&quot);
+ 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;
+
+ DIGITS(&t) = 0;
+ /* 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;
+ }
+
+ MP_SIGN(rem) = ZPOS;
+ MP_SIGN(div) = ZPOS;
+ MP_SIGN(&part) = 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));
+
+ /* 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;
+ int partExtended = 0; /* set to true if we need to extend part */
+
+ 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);
+
+ /* We have now truncated the part of the remainder to the same length as
+ * the divisor. If part is smaller than div, extend part by one digit. */
+ 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);
+ partExtended = 1;
+ }
+
+ /* 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 (!partExtended) {
+ /* In this case, q_msd /= div_msd is always 1. First, since div_msd is
+ * normalized to have the high bit set, 2*div_msd > MP_DIGIT_MAX. Since
+ * we didn't extend part, q_msd >= div_msd. Therefore we know that
+ * div_msd <= q_msd <= MP_DIGIT_MAX < 2*div_msd. Dividing by div_msd we
+ * get 1 <= q_msd/div_msd < 2. So q_msd /= div_msd must be 1. */
+ q_msd = 1;
+ } else {
+#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
+ if (q_msd == div_msd) {
+ q_msd = MP_DIGIT_MAX;
+ } 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
+ }
+#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;
+ MP_CHECKOK(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) */
+unsigned int
+mp_unsigned_octet_size(const mp_int *mp)
+{
+ unsigned 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;
+ unsigned 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;
+ unsigned 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;
+ unsigned 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 */