diff options
Diffstat (limited to 'security/nss/lib/freebl/mpi/mpi.c')
| -rw-r--r-- | security/nss/lib/freebl/mpi/mpi.c | 4975 |
1 files changed, 4975 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 0000000000..2e6cd84664 --- /dev/null +++ b/security/nss/lib/freebl/mpi/mpi.c @@ -0,0 +1,4975 @@ +/* + * 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" +#include "mplogic.h" + +#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) +{ + unsigned long v = labs(z); + mp_err res; + + ARGCHK(mp != NULL, MP_BADARG); + + /* https://bugzilla.mozilla.org/show_bug.cgi?id=1509432 */ + if ((res = mp_set_ulong(mp, v)) != MP_OKAY) { /* avoids duplicated code */ + 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 && m != 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 && m != 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) +{ + ARGMPCHK(a != NULL); + + 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) +{ + ARGMPCHK(a != NULL); + + 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 */ + +/* {{{ mp_gcd(a, b, c) */ + +/* + Computes the GCD using the constant-time algorithm + by Bernstein and Yang (https://eprint.iacr.org/2019/266) + "Fast constant-time gcd computation and modular inversion" + */ +mp_err +mp_gcd(mp_int *a, mp_int *b, mp_int *c) +{ + mp_err res; + mp_digit cond = 0, mask = 0; + mp_int g, temp, f; + int i, j, m, bit = 1, delta = 1, shifts = 0, last = -1; + mp_size top, flen, glen; + mp_int *clear[3]; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + /* + Early exit if either of the inputs is zero. + Caller is responsible for the proper handling of inputs. + */ + if (mp_cmp_z(a) == MP_EQ) { + res = mp_copy(b, c); + SIGN(c) = ZPOS; + return res; + } else if (mp_cmp_z(b) == MP_EQ) { + res = mp_copy(a, c); + SIGN(c) = ZPOS; + return res; + } + + MP_CHECKOK(mp_init(&temp)); + clear[++last] = &temp; + MP_CHECKOK(mp_init_copy(&g, a)); + clear[++last] = &g; + MP_CHECKOK(mp_init_copy(&f, b)); + clear[++last] = &f; + + /* + For even case compute the number of + shared powers of 2 in f and g. + */ + for (i = 0; i < USED(&f) && i < USED(&g); i++) { + mask = ~(DIGIT(&f, i) | DIGIT(&g, i)); + for (j = 0; j < MP_DIGIT_BIT; j++) { + bit &= mask; + shifts += bit; + mask >>= 1; + } + } + /* Reduce to the odd case by removing the powers of 2. */ + s_mp_div_2d(&f, shifts); + s_mp_div_2d(&g, shifts); + + /* Allocate to the size of largest mp_int. */ + top = (mp_size)1 + ((USED(&f) >= USED(&g)) ? USED(&f) : USED(&g)); + MP_CHECKOK(s_mp_grow(&f, top)); + MP_CHECKOK(s_mp_grow(&g, top)); + MP_CHECKOK(s_mp_grow(&temp, top)); + + /* Make sure f contains the odd value. */ + MP_CHECKOK(mp_cswap((~DIGIT(&f, 0) & 1), &f, &g, top)); + + /* Upper bound for the total iterations. */ + flen = mpl_significant_bits(&f); + glen = mpl_significant_bits(&g); + m = 4 + 3 * ((flen >= glen) ? flen : glen); + +#if defined(_MSC_VER) +#pragma warning(push) +#pragma warning(disable : 4146) // Thanks MSVC, we know what we're negating an unsigned mp_digit +#endif + + for (i = 0; i < m; i++) { + /* Step 1: conditional swap. */ + /* Set cond if delta > 0 and g is odd. */ + cond = (-delta >> (8 * sizeof(delta) - 1)) & DIGIT(&g, 0) & 1; + /* If cond is set replace (delta,f) with (-delta,-f). */ + delta = (-cond & -delta) | ((cond - 1) & delta); + SIGN(&f) ^= cond; + /* If cond is set swap f with g. */ + MP_CHECKOK(mp_cswap(cond, &f, &g, top)); + + /* Step 2: elemination. */ + /* Update delta. */ + delta++; + /* If g is odd, right shift (g+f) else right shift g. */ + MP_CHECKOK(mp_add(&g, &f, &temp)); + MP_CHECKOK(mp_cswap((DIGIT(&g, 0) & 1), &g, &temp, top)); + s_mp_div_2(&g); + } + +#if defined(_MSC_VER) +#pragma warning(pop) +#endif + + /* GCD is in f, take the absolute value. */ + SIGN(&f) = ZPOS; + + /* Add back the removed powers of 2. */ + MP_CHECKOK(s_mp_mul_2d(&f, shifts)); + + MP_CHECKOK(mp_copy(&f, c)); + +CLEANUP: + while (last >= 0) + mp_clear(clear[last--]); + 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 != NULL && p != NULL && c != NULL, 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) { + if (mp_cmp_mag(c, p) >= 0) { + MP_CHECKOK(mp_div(c, p, NULL, c)); + } + if (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; +} + +/* + Computes the modular inverse using the constant-time algorithm + by Bernstein and Yang (https://eprint.iacr.org/2019/266) + "Fast constant-time gcd computation and modular inversion" + */ +mp_err +s_mp_invmod_odd_m(const mp_int *a, const mp_int *m, mp_int *c) +{ + mp_err res; + mp_digit cond = 0; + mp_int g, f, v, r, temp; + int i, its, delta = 1, last = -1; + mp_size top, flen, glen; + mp_int *clear[6]; + + ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG); + /* Check for invalid inputs. */ + if (mp_cmp_z(a) == MP_EQ || mp_cmp_d(m, 2) == MP_LT) + return MP_RANGE; + + if (a == m || mp_iseven(m)) + return MP_UNDEF; + + MP_CHECKOK(mp_init(&temp)); + clear[++last] = &temp; + MP_CHECKOK(mp_init(&v)); + clear[++last] = &v; + MP_CHECKOK(mp_init(&r)); + clear[++last] = &r; + MP_CHECKOK(mp_init_copy(&g, a)); + clear[++last] = &g; + MP_CHECKOK(mp_init_copy(&f, m)); + clear[++last] = &f; + + mp_set(&v, 0); + mp_set(&r, 1); + + /* Allocate to the size of largest mp_int. */ + top = (mp_size)1 + ((USED(&f) >= USED(&g)) ? USED(&f) : USED(&g)); + MP_CHECKOK(s_mp_grow(&f, top)); + MP_CHECKOK(s_mp_grow(&g, top)); + MP_CHECKOK(s_mp_grow(&temp, top)); + MP_CHECKOK(s_mp_grow(&v, top)); + MP_CHECKOK(s_mp_grow(&r, top)); + + /* Upper bound for the total iterations. */ + flen = mpl_significant_bits(&f); + glen = mpl_significant_bits(&g); + its = 4 + 3 * ((flen >= glen) ? flen : glen); + +#if defined(_MSC_VER) +#pragma warning(push) +#pragma warning(disable : 4146) // Thanks MSVC, we know what we're negating an unsigned mp_digit +#endif + + for (i = 0; i < its; i++) { + /* Step 1: conditional swap. */ + /* Set cond if delta > 0 and g is odd. */ + cond = (-delta >> (8 * sizeof(delta) - 1)) & DIGIT(&g, 0) & 1; + /* If cond is set replace (delta,f,v) with (-delta,-f,-v). */ + delta = (-cond & -delta) | ((cond - 1) & delta); + SIGN(&f) ^= cond; + SIGN(&v) ^= cond; + /* If cond is set swap (f,v) with (g,r). */ + MP_CHECKOK(mp_cswap(cond, &f, &g, top)); + MP_CHECKOK(mp_cswap(cond, &v, &r, top)); + + /* Step 2: elemination. */ + /* Update delta */ + delta++; + /* If g is odd replace r with (r+v). */ + MP_CHECKOK(mp_add(&r, &v, &temp)); + MP_CHECKOK(mp_cswap((DIGIT(&g, 0) & 1), &r, &temp, top)); + /* If g is odd, right shift (g+f) else right shift g. */ + MP_CHECKOK(mp_add(&g, &f, &temp)); + MP_CHECKOK(mp_cswap((DIGIT(&g, 0) & 1), &g, &temp, top)); + s_mp_div_2(&g); + /* + If r is even, right shift it. + If r is odd, right shift (r+m) which is even because m is odd. + We want the result modulo m so adding in multiples of m here vanish. + */ + MP_CHECKOK(mp_add(&r, m, &temp)); + MP_CHECKOK(mp_cswap((DIGIT(&r, 0) & 1), &r, &temp, top)); + s_mp_div_2(&r); + } + +#if defined(_MSC_VER) +#pragma warning(pop) +#endif + + /* We have the inverse in v, propagate sign from f. */ + SIGN(&v) ^= SIGN(&f); + /* GCD is in f, take the absolute value. */ + SIGN(&f) = ZPOS; + + /* If gcd != 1, not invertible. */ + if (mp_cmp_d(&f, 1) != MP_EQ) { + res = MP_UNDEF; + goto CLEANUP; + } + + /* Return inverse modulo m. */ + MP_CHECKOK(mp_mod(&v, m, c)); + +CLEANUP: + while (last >= 0) + mp_clear(clear[last--]); + 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 != NULL && m != NULL && c != NULL, 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 defined(_MSC_VER) +#pragma warning(push) +#pragma warning(disable : 4146) // Thanks MSVC, we know what we're negating an unsigned mp_digit +#endif + if (k <= MP_DIGIT_BIT) { + mp_digit i = s_mp_invmod_radix(MP_DIGIT(a, 0)); + /* propagate the sign from mp_int */ + i = (i ^ -(mp_digit)SIGN(a)) + (mp_digit)SIGN(a); + if (k < MP_DIGIT_BIT) + i &= ((mp_digit)1 << k) - (mp_digit)1; + mp_set(c, i); + return MP_OKAY; + } +#if defined(_MSC_VER) +#pragma warning(pop) +#endif + + 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; + + ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG); + + /*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 != NULL && m != NULL && c != NULL, 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() */ + +/* }}} */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ 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); + + /* 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; + } + + /* Get sign from first byte */ + if (ustr[0]) + SIGN(mp) = NEG; + else + SIGN(mp) = ZPOS; + + 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 SIGN(mp) + 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 tmpc = str[ix]; + + str[ix] = str[pos]; + str[pos] = tmpc; + ++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) +{ + ARGCHK(mp != NULL, MP_BADARG); + + 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) +{ + ARGCHK(mp != NULL, MP_BADARG); + + 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) +{ + memset(dp, 0, count * sizeof(mp_digit)); +} /* 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) +{ + memcpy(dp, sp, count * sizeof(mp_digit)); +} /* 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; + if (used == 1 && DIGIT(mp, 0) == 0) + MP_SIGN(mp) = ZPOS; +} /* 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; + if (!a || !b) { + return; + } + + 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; + + ARGCHK(mp != NULL, MP_BADARG); + + 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, rshift, mask, x, prev = 0; + mp_digit *pa = NULL; + int i; + + ARGCHK(mp != NULL, MP_BADARG); + + dshift = d / MP_DIGIT_BIT; + d %= MP_DIGIT_BIT; + /* mp_digit >> rshift is undefined behavior for rshift >= MP_DIGIT_BIT */ + /* mod and corresponding mask logic avoid that when d = 0 */ + rshift = MP_DIGIT_BIT - d; + rshift %= MP_DIGIT_BIT; + /* mask = (2**d - 1) * 2**(w-d) mod 2**w */ + mask = (DIGIT_MAX << rshift) + 1; + mask &= DIGIT_MAX - 1; + /* bits to be shifted out of the top word */ + x = MP_DIGIT(mp, MP_USED(mp) - 1) & mask; + + if (MP_OKAY != (res = s_mp_pad(mp, MP_USED(mp) + dshift + (x != 0)))) + return res; + + if (dshift && MP_OKAY != (res = s_mp_lshd(mp, dshift))) + return res; + + pa = MP_DIGITS(mp) + dshift; + + for (i = MP_USED(mp) - dshift; i > 0; i--) { + x = *pa; + *pa++ = (x << d) | prev; + prev = (x & mask) >> rshift; + } + + 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; + + ARGCHK(mp != NULL, MP_BADARG); + + /* 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, lshift; + + s_mp_rshd(mp, d / DIGIT_BIT); + d %= DIGIT_BIT; + /* mp_digit << lshift is undefined behavior for lshift >= MP_DIGIT_BIT */ + /* mod and corresponding mask logic avoid that when d = 0 */ + lshift = DIGIT_BIT - d; + lshift %= DIGIT_BIT; + mask = ((mp_digit)1 << d) - 1; + save = 0; + for (ix = USED(mp) - 1; ix >= 0; ix--) { + next = DIGIT(mp, ix) & mask; + DIGIT(mp, ix) = (save << lshift) | (DIGIT(mp, ix) >> 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; + + ARGCHK(a != NULL && b != NULL && pd != NULL, MP_BADARG); + + 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 remdig; + + q = n / d; + remdig = n % d; + MP_DIGIT(mp, 0) = q; + if (r) { + *r = remdig; + } + return MP_OKAY; + } + + MP_DIGITS(&rem) = 0; + MP_DIGITS(") = 0; + /* Make room for the quotient */ + MP_CHECKOK(mp_init_size(", USED(mp))); + +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_DIV_WORD) + for (ix = USED(mp) - 1; ix >= 0; ix--) { + w = (w << DIGIT_BIT) | DIGIT(mp, ix); + + if (w >= d) { + q = w / d; + w = w % d; + } else { + q = 0; + } + + s_mp_lshd(", 1); + DIGIT(", 0) = (mp_digit)q; + } +#else + { + mp_digit p; +#if !defined(MP_ASSEMBLY_DIV_2DX1D) + mp_digit norm; +#endif + + MP_CHECKOK(mp_init_copy(&rem, mp)); + +#if !defined(MP_ASSEMBLY_DIV_2DX1D) + MP_DIGIT(", 0) = d; + MP_CHECKOK(s_mp_norm(&rem, ", &norm)); + if (norm) + d <<= norm; + MP_DIGIT(", 0) = 0; +#endif + + p = 0; + for (ix = USED(&rem) - 1; ix >= 0; ix--) { + w = DIGIT(&rem, ix); + + if (p) { + MP_CHECKOK(s_mpv_div_2dx1d(p, w, d, &q, &w)); + } else if (w >= d) { + q = w / d; + w = w % d; + } else { + q = 0; + } + + MP_CHECKOK(s_mp_lshd(", 1)); + DIGIT(", 0) = q; + p = w; + } +#if !defined(MP_ASSEMBLY_DIV_2DX1D) + if (norm) + w >>= norm; +#endif + } +#endif + + /* Deliver the remainder, if desired */ + if (r) { + *r = (mp_digit)w; + } + + s_mp_clamp("); + mp_exch(", mp); +CLEANUP: + mp_clear("); + mp_clear(&rem); + + return res; +} /* end s_mp_div_d() */ + +/* }}} */ + +/* }}} */ + +/* {{{ Primitive full arithmetic */ + +/* {{{ s_mp_add(a, b) */ + +/* Compute a = |a| + |b| */ +mp_err +s_mp_add(mp_int *a, const mp_int *b) /* magnitude addition */ +{ +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + mp_word w = 0; +#else + mp_digit d, sum, carry = 0; +#endif + mp_digit *pa, *pb; + mp_size ix; + mp_size used; + mp_err res; + + /* Make sure a has enough precision for the output value */ + if ((USED(b) > USED(a)) && (res = s_mp_pad(a, USED(b))) != MP_OKAY) + return res; + + /* + Add up all digits up to the precision of b. If b had initially + the same precision as a, or greater, we took care of it by the + padding step above, so there is no problem. If b had initially + less precision, we'll have to make sure the carry out is duly + propagated upward among the higher-order digits of the sum. + */ + pa = MP_DIGITS(a); + pb = MP_DIGITS(b); + used = MP_USED(b); + for (ix = 0; ix < used; ix++) { +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + w = w + *pa + *pb++; + *pa++ = ACCUM(w); + w = CARRYOUT(w); +#else + d = *pa; + sum = d + *pb++; + d = (sum < d); /* detect overflow */ + *pa++ = sum += carry; + carry = d + (sum < carry); /* detect overflow */ +#endif + } + + /* If we run out of 'b' digits before we're actually done, make + sure the carries get propagated upward... + */ + used = MP_USED(a); +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + while (w && ix < used) { + w = w + *pa; + *pa++ = ACCUM(w); + w = CARRYOUT(w); + ++ix; + } +#else + while (carry && ix < used) { + sum = carry + *pa; + *pa++ = sum; + carry = !sum; + ++ix; + } +#endif + +/* If there's an overall carry out, increase precision and include + it. We could have done this initially, but why touch the memory + allocator unless we're sure we have to? + */ +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + if (w) { + if ((res = s_mp_pad(a, used + 1)) != MP_OKAY) + return res; + + DIGIT(a, ix) = (mp_digit)w; + } +#else + if (carry) { + if ((res = s_mp_pad(a, used + 1)) != MP_OKAY) + return res; + + DIGIT(a, used) = carry; + } +#endif + + return MP_OKAY; +} /* end s_mp_add() */ + +/* }}} */ + +/* Compute c = |a| + |b| */ /* magnitude addition */ +mp_err +s_mp_add_3arg(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_digit *pa, *pb, *pc; +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + mp_word w = 0; +#else + mp_digit sum, carry = 0, d; +#endif + mp_size ix; + mp_size used; + mp_err res; + + MP_SIGN(c) = MP_SIGN(a); + if (MP_USED(a) < MP_USED(b)) { + const mp_int *xch = a; + a = b; + b = xch; + } + + /* Make sure a has enough precision for the output value */ + if (MP_OKAY != (res = s_mp_pad(c, MP_USED(a)))) + return res; + + /* + Add up all digits up to the precision of b. If b had initially + the same precision as a, or greater, we took care of it by the + exchange step above, so there is no problem. If b had initially + less precision, we'll have to make sure the carry out is duly + propagated upward among the higher-order digits of the sum. + */ + pa = MP_DIGITS(a); + pb = MP_DIGITS(b); + pc = MP_DIGITS(c); + used = MP_USED(b); + for (ix = 0; ix < used; ix++) { +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + w = w + *pa++ + *pb++; + *pc++ = ACCUM(w); + w = CARRYOUT(w); +#else + d = *pa++; + sum = d + *pb++; + d = (sum < d); /* detect overflow */ + *pc++ = sum += carry; + carry = d + (sum < carry); /* detect overflow */ +#endif + } + + /* If we run out of 'b' digits before we're actually done, make + sure the carries get propagated upward... + */ + for (used = MP_USED(a); ix < used; ++ix) { +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + w = w + *pa++; + *pc++ = ACCUM(w); + w = CARRYOUT(w); +#else + *pc++ = sum = carry + *pa++; + carry = (sum < carry); +#endif + } + +/* If there's an overall carry out, increase precision and include + it. We could have done this initially, but why touch the memory + allocator unless we're sure we have to? + */ +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + if (w) { + if ((res = s_mp_pad(c, used + 1)) != MP_OKAY) + return res; + + DIGIT(c, used) = (mp_digit)w; + ++used; + } +#else + if (carry) { + if ((res = s_mp_pad(c, used + 1)) != MP_OKAY) + return res; + + DIGIT(c, used) = carry; + ++used; + } +#endif + MP_USED(c) = used; + return MP_OKAY; +} +/* {{{ s_mp_add_offset(a, b, offset) */ + +/* Compute a = |a| + ( |b| * (RADIX ** offset) ) */ +mp_err +s_mp_add_offset(mp_int *a, mp_int *b, mp_size offset) +{ +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + mp_word w, k = 0; +#else + mp_digit d, sum, carry = 0; +#endif + mp_size ib; + mp_size ia; + mp_size lim; + mp_err res; + + /* Make sure a has enough precision for the output value */ + lim = MP_USED(b) + offset; + if ((lim > USED(a)) && (res = s_mp_pad(a, lim)) != MP_OKAY) + return res; + + /* + Add up all digits up to the precision of b. If b had initially + the same precision as a, or greater, we took care of it by the + padding step above, so there is no problem. If b had initially + less precision, we'll have to make sure the carry out is duly + propagated upward among the higher-order digits of the sum. + */ + lim = USED(b); + for (ib = 0, ia = offset; ib < lim; ib++, ia++) { +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + w = (mp_word)DIGIT(a, ia) + DIGIT(b, ib) + k; + DIGIT(a, ia) = ACCUM(w); + k = CARRYOUT(w); +#else + d = MP_DIGIT(a, ia); + sum = d + MP_DIGIT(b, ib); + d = (sum < d); + MP_DIGIT(a, ia) = sum += carry; + carry = d + (sum < carry); +#endif + } + +/* If we run out of 'b' digits before we're actually done, make + sure the carries get propagated upward... + */ +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + for (lim = MP_USED(a); k && (ia < lim); ++ia) { + w = (mp_word)DIGIT(a, ia) + k; + DIGIT(a, ia) = ACCUM(w); + k = CARRYOUT(w); + } +#else + for (lim = MP_USED(a); carry && (ia < lim); ++ia) { + d = MP_DIGIT(a, ia); + MP_DIGIT(a, ia) = sum = d + carry; + carry = (sum < d); + } +#endif + +/* If there's an overall carry out, increase precision and include + it. We could have done this initially, but why touch the memory + allocator unless we're sure we have to? + */ +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_ADD_WORD) + if (k) { + if ((res = s_mp_pad(a, USED(a) + 1)) != MP_OKAY) + return res; + + DIGIT(a, ia) = (mp_digit)k; + } +#else + if (carry) { + if ((res = s_mp_pad(a, lim + 1)) != MP_OKAY) + return res; + + DIGIT(a, lim) = carry; + } +#endif + s_mp_clamp(a); + + return MP_OKAY; + +} /* end s_mp_add_offset() */ + +/* }}} */ + +/* {{{ s_mp_sub(a, b) */ + +/* Compute a = |a| - |b|, assumes |a| >= |b| */ +mp_err +s_mp_sub(mp_int *a, const mp_int *b) /* magnitude subtract */ +{ + mp_digit *pa, *pb, *limit; +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD) + mp_sword w = 0; +#else + mp_digit d, diff, borrow = 0; +#endif + + /* + Subtract and propagate borrow. Up to the precision of b, this + accounts for the digits of b; after that, we just make sure the + carries get to the right place. This saves having to pad b out to + the precision of a just to make the loops work right... + */ + pa = MP_DIGITS(a); + pb = MP_DIGITS(b); + limit = pb + MP_USED(b); + while (pb < limit) { +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD) + w = w + *pa - *pb++; + *pa++ = ACCUM(w); + w >>= MP_DIGIT_BIT; +#else + d = *pa; + diff = d - *pb++; + d = (diff > d); /* detect borrow */ + if (borrow && --diff == MP_DIGIT_MAX) + ++d; + *pa++ = diff; + borrow = d; +#endif + } + limit = MP_DIGITS(a) + MP_USED(a); +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD) + while (w && pa < limit) { + w = w + *pa; + *pa++ = ACCUM(w); + w >>= MP_DIGIT_BIT; + } +#else + while (borrow && pa < limit) { + d = *pa; + *pa++ = diff = d - borrow; + borrow = (diff > d); + } +#endif + + /* Clobber any leading zeroes we created */ + s_mp_clamp(a); + +/* + If there was a borrow out, then |b| > |a| in violation + of our input invariant. We've already done the work, + but we'll at least complain about it... + */ +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD) + return w ? MP_RANGE : MP_OKAY; +#else + return borrow ? MP_RANGE : MP_OKAY; +#endif +} /* end s_mp_sub() */ + +/* }}} */ + +/* Compute c = |a| - |b|, assumes |a| >= |b| */ /* magnitude subtract */ +mp_err +s_mp_sub_3arg(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_digit *pa, *pb, *pc; +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD) + mp_sword w = 0; +#else + mp_digit d, diff, borrow = 0; +#endif + int ix, limit; + mp_err res; + + MP_SIGN(c) = MP_SIGN(a); + + /* Make sure a has enough precision for the output value */ + if (MP_OKAY != (res = s_mp_pad(c, MP_USED(a)))) + return res; + + /* + Subtract and propagate borrow. Up to the precision of b, this + accounts for the digits of b; after that, we just make sure the + carries get to the right place. This saves having to pad b out to + the precision of a just to make the loops work right... + */ + pa = MP_DIGITS(a); + pb = MP_DIGITS(b); + pc = MP_DIGITS(c); + limit = MP_USED(b); + for (ix = 0; ix < limit; ++ix) { +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD) + w = w + *pa++ - *pb++; + *pc++ = ACCUM(w); + w >>= MP_DIGIT_BIT; +#else + d = *pa++; + diff = d - *pb++; + d = (diff > d); + if (borrow && --diff == MP_DIGIT_MAX) + ++d; + *pc++ = diff; + borrow = d; +#endif + } + for (limit = MP_USED(a); ix < limit; ++ix) { +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD) + w = w + *pa++; + *pc++ = ACCUM(w); + w >>= MP_DIGIT_BIT; +#else + d = *pa++; + *pc++ = diff = d - borrow; + borrow = (diff > d); +#endif + } + + /* Clobber any leading zeroes we created */ + MP_USED(c) = ix; + s_mp_clamp(c); + +/* + If there was a borrow out, then |b| > |a| in violation + of our input invariant. We've already done the work, + but we'll at least complain about it... + */ +#if !defined(MP_NO_MP_WORD) && !defined(MP_NO_SUB_WORD) + return w ? MP_RANGE : MP_OKAY; +#else + return borrow ? MP_RANGE : MP_OKAY; +#endif +} +/* {{{ s_mp_mul(a, b) */ + +/* Compute a = |a| * |b| */ +mp_err +s_mp_mul(mp_int *a, const mp_int *b) +{ + return mp_mul(a, b, a); +} /* end s_mp_mul() */ + +/* }}} */ + +#if defined(MP_USE_UINT_DIGIT) && defined(MP_USE_LONG_LONG_MULTIPLY) +/* This trick works on Sparc V8 CPUs with the Workshop compilers. */ +#define MP_MUL_DxD(a, b, Phi, Plo) \ + { \ + unsigned long long product = (unsigned long long)a * b; \ + Plo = (mp_digit)product; \ + Phi = (mp_digit)(product >> MP_DIGIT_BIT); \ + } +#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); \ + } +#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_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; + mp_digit q_msd; + 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 (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)); + } + } +#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, 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) = 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) +{ + ARGMPCHK(a != NULL && b != NULL); + + 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) +{ + ARGMPCHK(a != NULL); + + 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; + + ARGMPCHK(v != NULL); + + 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. + constant time on the value of mp. */ +mp_err +mp_to_fixlen_octets(const mp_int *mp, unsigned char *str, mp_size length) +{ + int ix, jx; + unsigned int bytes; + + ARGCHK(mp != NULL && str != NULL && !SIGN(mp) && length > 0, MP_BADARG); + + /* Constant time on the value of mp. Don't use mp_unsigned_octet_size. */ + bytes = USED(mp) * MP_DIGIT_SIZE; + + /* If the output is shorter than the native size of mp, then check that any + * bytes not written have zero values. This check isn't constant time on + * the assumption that timing-sensitive callers can guarantee that mp fits + * in the allocated space. */ + ix = USED(mp) - 1; + if (bytes > length) { + unsigned int zeros = bytes - length; + + while (zeros >= MP_DIGIT_SIZE) { + ARGCHK(DIGIT(mp, ix) == 0, MP_BADARG); + zeros -= MP_DIGIT_SIZE; + ix--; + } + + if (zeros > 0) { + mp_digit d = DIGIT(mp, ix); + mp_digit m = ~0ULL << ((MP_DIGIT_SIZE - zeros) * CHAR_BIT); + ARGCHK((d & m) == 0, MP_BADARG); + for (jx = MP_DIGIT_SIZE - zeros - 1; jx >= 0; jx--) { + *str++ = d >> (jx * CHAR_BIT); + } + ix--; + } + } else if (bytes < length) { + /* Place any needed leading zeros. */ + unsigned int zeros = length - bytes; + memset(str, 0, zeros); + str += zeros; + } + + /* Iterate over each whole digit... */ + for (; ix >= 0; ix--) { + mp_digit d = DIGIT(mp, ix); + + /* Unpack digit bytes, high order first */ + for (jx = MP_DIGIT_SIZE - 1; jx >= 0; jx--) { + *str++ = d >> (jx * CHAR_BIT); + } + } + return MP_OKAY; +} /* end mp_to_fixlen_octets() */ +/* }}} */ + +/* {{{ mp_cswap(condition, a, b, numdigits) */ +/* performs a conditional swap between mp_int. */ +mp_err +mp_cswap(mp_digit condition, mp_int *a, mp_int *b, mp_size numdigits) +{ + mp_digit x; + unsigned int i; + mp_err res = 0; + + /* if pointers are equal return */ + if (a == b) + return res; + + if (MP_ALLOC(a) < numdigits || MP_ALLOC(b) < numdigits) { + MP_CHECKOK(s_mp_grow(a, numdigits)); + MP_CHECKOK(s_mp_grow(b, numdigits)); + } + + condition = ((~condition & ((condition - 1))) >> (MP_DIGIT_BIT - 1)) - 1; + + x = (USED(a) ^ USED(b)) & condition; + USED(a) ^= x; + USED(b) ^= x; + + x = (SIGN(a) ^ SIGN(b)) & condition; + SIGN(a) ^= x; + SIGN(b) ^= x; + + for (i = 0; i < numdigits; i++) { + x = (DIGIT(a, i) ^ DIGIT(b, i)) & condition; + DIGIT(a, i) ^= x; + DIGIT(b, i) ^= x; + } + +CLEANUP: + return res; +} /* end mp_cswap() */ +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* HERE THERE BE DRAGONS */ |