[patch 9/9] Include code for bignum math

Include BSD-licensed bignum library 'iMath' by Michael J. Fromberger
in pgcrypto. Thus the standalone build has equal functionality
to the OpenSSL build.

Index: pgsql/contrib/pgcrypto/Makefile
===================================================================
*** pgsql.orig/contrib/pgcrypto/Makefile
--- pgsql/contrib/pgcrypto/Makefile
***************
*** 3,9 ****
#

INT_SRCS = md5.c sha1.c sha2.c internal.c internal-sha2.c blf.c rijndael.c \
! fortuna.c random.c pgp-mpi-internal.c
INT_TESTS = sha2

OSSL_SRCS = openssl.c pgp-mpi-openssl.c
--- 3,9 ----
#

INT_SRCS = md5.c sha1.c sha2.c internal.c internal-sha2.c blf.c rijndael.c \
! fortuna.c random.c pgp-mpi-internal.c imath.c
INT_TESTS = sha2

OSSL_SRCS = openssl.c pgp-mpi-openssl.c
*************** OSSL_TESTS = sha2 des 3des cast5
*** 12,25 ****
ZLIB_OFF_CFLAGS = -DDISABLE_ZLIB
ZLIB_TST = pgp-compression
ZLIB_OFF_TST = pgp-zlib-DISABLED
- PUBENC_ON = pgp-pubkey-decrypt pgp-pubkey-encrypt pgp-info
- PUBENC_OFF = pgp-pubkey-DISABLED

CF_SRCS = $(if $(subst no,,$(with_openssl)), $(OSSL_SRCS), $(INT_SRCS))
CF_TESTS = $(if $(subst no,,$(with_openssl)), $(OSSL_TESTS), $(INT_TESTS))
CF_CFLAGS = $(if $(subst yes,,$(with_zlib)), $(ZLIB_OFF_CFLAGS))
! CF_PGP_TESTS = $(if $(subst no,,$(with_zlib)), $(ZLIB_TST), $(ZLIB_OFF_TST)) \
! $(if $(subst no,,$(with_openssl)), $(PUBENC_ON), $(PUBENC_OFF))

PG_CPPFLAGS = $(CF_CFLAGS)

--- 12,22 ----
ZLIB_OFF_CFLAGS = -DDISABLE_ZLIB
ZLIB_TST = pgp-compression
ZLIB_OFF_TST = pgp-zlib-DISABLED

CF_SRCS = $(if $(subst no,,$(with_openssl)), $(OSSL_SRCS), $(INT_SRCS))
CF_TESTS = $(if $(subst no,,$(with_openssl)), $(OSSL_TESTS), $(INT_TESTS))
CF_CFLAGS = $(if $(subst yes,,$(with_zlib)), $(ZLIB_OFF_CFLAGS))
! CF_PGP_TESTS = $(if $(subst no,,$(with_zlib)), $(ZLIB_TST), $(ZLIB_OFF_TST))

PG_CPPFLAGS = $(CF_CFLAGS)

*************** EXTRA_CLEAN = gen-rtab
*** 41,47 ****
REGRESS = init md5 sha1 hmac-md5 hmac-sha1 blowfish rijndael \
$(CF_TESTS) \
crypt-des crypt-md5 crypt-blowfish crypt-xdes \
! pgp-armor pgp-decrypt pgp-encrypt $(CF_PGP_TESTS)


ifdef USE_PGXS
--- 38,45 ----
REGRESS = init md5 sha1 hmac-md5 hmac-sha1 blowfish rijndael \
$(CF_TESTS) \
crypt-des crypt-md5 crypt-blowfish crypt-xdes \
! pgp-armor pgp-decrypt pgp-encrypt $(CF_PGP_TESTS) \
! pgp-pubkey-decrypt pgp-pubkey-encrypt pgp-info


ifdef USE_PGXS
Index: pgsql/contrib/pgcrypto/README.pgcrypto
===================================================================
*** pgsql.orig/contrib/pgcrypto/README.pgcrypto
--- pgsql/contrib/pgcrypto/README.pgcrypto
*************** There are some other differences with an
*** 56,62 ****
DES/3DES/CAST5 no yes
Raw encryption yes yes
PGP Symmetric encryption yes yes
! PGP Public-Key encryption no yes
----------------------------------------------------

1. Any digest algorithm OpenSSL supports is automatically picked up.
--- 56,62 ----
DES/3DES/CAST5 no yes
Raw encryption yes yes
PGP Symmetric encryption yes yes
! PGP Public-Key encryption yes yes
----------------------------------------------------

1. Any digest algorithm OpenSSL supports is automatically picked up.
*************** draining the randomness generator pool.
*** 639,647 ****

I have used code from following sources:

! `--------------------`-------------------------`----------------------
Algorithm Author Source origin
! ----------------------------------------------------------------------
DES crypt() David Burren and others FreeBSD libcrypt
MD5 crypt() Poul-Henning Kamp FreeBSD libcrypt
Blowfish crypt() Solar Designer www.openwall.com
--- 639,647 ----

I have used code from following sources:

! `--------------------`-------------------------`-------------------------------
Algorithm Author Source origin
! -------------------------------------------------------------------------------
DES crypt() David Burren and others FreeBSD libcrypt
MD5 crypt() Poul-Henning Kamp FreeBSD libcrypt
Blowfish crypt() Solar Designer www.openwall.com
*************** I have used code from following sources:
*** 649,655 ****
Rijndael cipher Brian Gladman OpenBSD sys/crypto
MD5 and SHA1 WIDE Project KAME kame/sys/crypto
SHA256/384/512 Aaron D. Gifford OpenBSD sys/crypto
! ----------------------------------------------------------------------


9. Legalese
--- 649,656 ----
Rijndael cipher Brian Gladman OpenBSD sys/crypto
MD5 and SHA1 WIDE Project KAME kame/sys/crypto
SHA256/384/512 Aaron D. Gifford OpenBSD sys/crypto
! BIGNUM math Michael J. Fromberger dartmouth.edu/~sting/sw/imath
! -------------------------------------------------------------------------------


9. Legalese
Index: pgsql/contrib/pgcrypto/pgp-mpi-internal.c
===================================================================
*** pgsql.orig/contrib/pgcrypto/pgp-mpi-internal.c
--- pgsql/contrib/pgcrypto/pgp-mpi-internal.c
***************
*** 30,61 ****
*/
#include "postgres.h"

#include "px.h"
#include "mbuf.h"
#include "pgp.h"

int
pgp_elgamal_encrypt(PGP_PubKey * pk, PGP_MPI * _m,
PGP_MPI ** c1_p, PGP_MPI ** c2_p)
{
! return PXE_PGP_NO_BIGNUM;
}

int
pgp_elgamal_decrypt(PGP_PubKey * pk, PGP_MPI * _c1, PGP_MPI * _c2,
PGP_MPI ** msg_p)
{
! return PXE_PGP_NO_BIGNUM;
}

int
! pgp_rsa_encrypt(PGP_PubKey * pk, PGP_MPI * m, PGP_MPI ** c)
{
! return PXE_PGP_NO_BIGNUM;
}

int
! pgp_rsa_decrypt(PGP_PubKey * pk, PGP_MPI * c, PGP_MPI ** m)
{
! return PXE_PGP_NO_BIGNUM;
}
--- 30,298 ----
*/
#include "postgres.h"

+ #include "imath.h"
+
#include "px.h"
#include "mbuf.h"
#include "pgp.h"

+ static mpz_t *mp_new()
+ {
+ mpz_t *mp = mp_int_alloc();
+ mp_int_init_size(mp, 256);
+ return mp;
+ }
+
+ static void mp_clear_free(mpz_t *a)
+ {
+ if (!a)
+ return;
+ // fixme: no clear?
+ mp_int_free(a);
+ }
+
+
+ static int mp_px_rand(uint32 bits, mpz_t *res)
+ {
+ int err;
+ unsigned bytes = (bits + 7) / 8;
+ int last_bits = bits & 7;
+ uint8 *buf;
+
+ buf = px_alloc(bytes);
+ err = px_get_random_bytes(buf, bytes);
+ if (err < 0) {
+ px_free(buf);
+ return err;
+ }
+
+ /* clear unnecessary bits and set last bit to one */
+ if (last_bits) {
+ buf[0] >>= 8 - last_bits;
+ buf[0] |= 1 << (last_bits - 1);
+ } else
+ buf[0] |= 1 << 7;
+
+ mp_int_read_unsigned(res, buf, bytes);
+
+ px_free(buf);
+
+ return 0;
+ }
+
+ static void mp_modmul(mpz_t *a, mpz_t *b, mpz_t *p, mpz_t *res)
+ {
+ mpz_t *tmp = mp_new();
+ mp_int_mul(a, b, tmp);
+ mp_int_mod(tmp, p, res);
+ mp_clear_free(tmp);
+ }
+
+ static mpz_t *
+ mpi_to_bn(PGP_MPI * n)
+ {
+ mpz_t *bn = mp_new();
+ mp_int_read_unsigned(bn, n->data, n->bytes);
+
+ if (!bn)
+ return NULL;
+ if (mp_int_count_bits(bn) != n->bits)
+ {
+ px_debug("mpi_to_bn: bignum conversion failed: mpi=%d, bn=%d",
+ n->bits, mp_int_count_bits(bn));
+ mp_clear_free(bn);
+ return NULL;
+ }
+ return bn;
+ }
+
+ static PGP_MPI *
+ bn_to_mpi(mpz_t *bn)
+ {
+ int res;
+ PGP_MPI *n;
+ int bytes;
+
+ res = pgp_mpi_alloc(mp_int_count_bits(bn), &n);
+ if (res < 0)
+ return NULL;
+
+ bytes = (mp_int_count_bits(bn) + 7) / 8;
+ if (bytes != n->bytes)
+ {
+ px_debug("bn_to_mpi: bignum conversion failed: bn=%d, mpi=%d",
+ bytes, n->bytes);
+ pgp_mpi_free(n);
+ return NULL;
+ }
+ mp_int_to_unsigned(bn, n->data, n->bytes);
+ return n;
+ }
+
+ /*
+ * Decide the number of bits in the random componont k
+ *
+ * It should be in the same range as p for signing (which
+ * is deprecated), but can be much smaller for encrypting.
+ *
+ * Until I research it further, I just mimic gpg behaviour.
+ * It has a special mapping table, for values <= 5120,
+ * above that it uses 'arbitrary high number'. Following
+ * algorihm hovers 10-70 bits above gpg values. And for
+ * larger p, it uses gpg's algorihm.
+ *
+ * The point is - if k gets large, encryption will be
+ * really slow. It does not matter for decryption.
+ */
+ static int
+ decide_k_bits(int p_bits)
+ {
+ if (p_bits <= 5120)
+ return p_bits / 10 + 160;
+ else
+ return (p_bits / 8 + 200) * 3 / 2;
+ }
+
int
pgp_elgamal_encrypt(PGP_PubKey * pk, PGP_MPI * _m,
PGP_MPI ** c1_p, PGP_MPI ** c2_p)
{
! int res = PXE_PGP_MATH_FAILED;
! int k_bits;
! mpz_t *m = mpi_to_bn(_m);
! mpz_t *p = mpi_to_bn(pk->pub.elg.p);
! mpz_t *g = mpi_to_bn(pk->pub.elg.g);
! mpz_t *y = mpi_to_bn(pk->pub.elg.y);
! mpz_t *k = mp_new();
! mpz_t *yk = mp_new();
! mpz_t *c1 = mp_new();
! mpz_t *c2 = mp_new();
!
! if (!m || !p || !g || !y || !k || !yk || !c1 || !c2)
! goto err;
!
! /*
! * generate k
! */
! k_bits = decide_k_bits(mp_int_count_bits(p));
! res = mp_px_rand(k_bits, k);
! if (res < 0)
! return res;
!
! /*
! * c1 = g^k c2 = m * y^k
! */
! mp_int_exptmod(g, k, p, c1);
! mp_int_exptmod(y, k, p, yk);
! mp_modmul(m, yk, p, c2);
!
! /* result */
! *c1_p = bn_to_mpi(c1);
! *c2_p = bn_to_mpi(c2);
! if (*c1_p && *c2_p)
! res = 0;
! err:
! mp_clear_free(c2);
! mp_clear_free(c1);
! mp_clear_free(yk);
! mp_clear_free(k);
! mp_clear_free(y);
! mp_clear_free(g);
! mp_clear_free(p);
! mp_clear_free(m);
! return res;
}

int
pgp_elgamal_decrypt(PGP_PubKey * pk, PGP_MPI * _c1, PGP_MPI * _c2,
PGP_MPI ** msg_p)
{
! int res = PXE_PGP_MATH_FAILED;
! mpz_t *c1 = mpi_to_bn(_c1);
! mpz_t *c2 = mpi_to_bn(_c2);
! mpz_t *p = mpi_to_bn(pk->pub.elg.p);
! mpz_t *x = mpi_to_bn(pk->sec.elg.x);
! mpz_t *c1x = mp_new();
! mpz_t *div = mp_new();
! mpz_t *m = mp_new();
!
! if (!c1 || !c2 || !p || !x || !c1x || !div || !m)
! goto err;
!
! /*
! * m = c2 / (c1^x)
! */
! mp_int_exptmod(c1, x, p, c1x);
! mp_int_invmod(c1x, p, div);
! mp_modmul(c2, div, p, m);
!
! /* result */
! *msg_p = bn_to_mpi(m);
! if (*msg_p)
! res = 0;
! err:
! mp_clear_free(m);
! mp_clear_free(div);
! mp_clear_free(c1x);
! mp_clear_free(x);
! mp_clear_free(p);
! mp_clear_free(c2);
! mp_clear_free(c1);
! return res;
}

int
! pgp_rsa_encrypt(PGP_PubKey * pk, PGP_MPI * _m, PGP_MPI ** c_p)
{
! int res = PXE_PGP_MATH_FAILED;
! mpz_t *m = mpi_to_bn(_m);
! mpz_t *e = mpi_to_bn(pk->pub.rsa.e);
! mpz_t *n = mpi_to_bn(pk->pub.rsa.n);
! mpz_t *c = mp_new();
!
! if (!m || !e || !n || !c)
! goto err;
!
! /*
! * c = m ^ e
! */
! mp_int_exptmod(m, e, n, c);
!
! *c_p = bn_to_mpi(c);
! if (*c_p)
! res = 0;
! err:
! mp_clear_free(c);
! mp_clear_free(n);
! mp_clear_free(e);
! mp_clear_free(m);
! return res;
}

int
! pgp_rsa_decrypt(PGP_PubKey * pk, PGP_MPI * _c, PGP_MPI ** m_p)
{
! int res = PXE_PGP_MATH_FAILED;
! mpz_t *c = mpi_to_bn(_c);
! mpz_t *d = mpi_to_bn(pk->sec.rsa.d);
! mpz_t *n = mpi_to_bn(pk->pub.rsa.n);
! mpz_t *m = mp_new();
!
! if (!m || !d || !n || !c)
! goto err;
!
! /*
! * m = c ^ d
! */
! mp_int_exptmod(c, d, n, m);
!
! *m_p = bn_to_mpi(m);
! if (*m_p)
! res = 0;
! err:
! mp_clear_free(m);
! mp_clear_free(n);
! mp_clear_free(d);
! mp_clear_free(c);
! return res;
}
Index: pgsql/contrib/pgcrypto/imath.c
===================================================================
*** /dev/null
--- pgsql/contrib/pgcrypto/imath.c
***************
*** 0 ****
--- 1,3261 ----
+ /* imath version 1.3 */
+ /*
+ Name: imath.c
+ Purpose: Arbitrary precision integer arithmetic routines.
+ Author: M. J. Fromberger <http://www.dartmouth.edu/~sting/>
+ Info: $Id: imath.c 21 2006-04-02 18:58:36Z sting $
+
+ Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved.
+
+ Permission is hereby granted, free of charge, to any person
+ obtaining a copy of this software and associated documentation files
+ (the "Software"), to deal in the Software without restriction,
+ including without limitation the rights to use, copy, modify, merge,
+ publish, distribute, sublicense, and/or sell copies of the Software,
+ and to permit persons to whom the Software is furnished to do so,
+ subject to the following conditions:
+
+ The above copyright notice and this permission notice shall be
+ included in all copies or substantial portions of the Software.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ SOFTWARE.
+ */
+
+ #include "postgres.h"
+ #include "px.h"
+ #include "imath.h"
+
+ #undef assert
+ #define assert(TEST)
+ #define TRACEABLE_CLAMP 0
+ #define TRACEABLE_FREE 0
+
+ /* {{{ Constants */
+
+ const mp_result MP_OK = 0; /* no error, all is well */
+ const mp_result MP_FALSE = 0; /* boolean false */
+ const mp_result MP_TRUE = -1; /* boolean true */
+ const mp_result MP_MEMORY = -2; /* out of memory */
+ const mp_result MP_RANGE = -3; /* argument out of range */
+ const mp_result MP_UNDEF = -4; /* result undefined */
+ const mp_result MP_TRUNC = -5; /* output truncated */
+ const mp_result MP_BADARG = -6; /* invalid null argument */
+
+ const mp_sign MP_NEG = 1; /* value is strictly negative */
+ const mp_sign MP_ZPOS = 0; /* value is non-negative */
+
+ static const char *s_unknown_err = "unknown result code";
+ static const char *s_error_msg[] = {
+ "error code 0",
+ "boolean true",
+ "out of memory",
+ "argument out of range",
+ "result undefined",
+ "output truncated",
+ "invalid null argument",
+ NULL
+ };
+
+ /* }}} */
+
+ /* Optional library flags */
+ #define MP_CAP_DIGITS 1 /* flag bit to capitalize letter digits */
+
+ /* Argument checking macros
+ Use CHECK() where a return value is required; NRCHECK() elsewhere */
+ #define CHECK(TEST) assert(TEST)
+ #define NRCHECK(TEST) assert(TEST)
+
+ /* {{{ Logarithm table for computing output sizes */
+
+ /* The ith entry of this table gives the value of log_i(2).
+
+ An integer value n requires ceil(log_i(n)) digits to be represented
+ in base i. Since it is easy to compute lg(n), by counting bits, we
+ can compute log_i(n) = lg(n) * log_i(2).
+ */
+ static const double s_log2[] = {
+ 0.000000000, 0.000000000, 1.000000000, 0.630929754, /* 0 1 2 3 */
+ 0.500000000, 0.430676558, 0.386852807, 0.356207187, /* 4 5 6 7 */
+ 0.333333333, 0.315464877, 0.301029996, 0.289064826, /* 8 9 10 11 */
+ 0.278942946, 0.270238154, 0.262649535, 0.255958025, /* 12 13 14 15 */
+ 0.250000000, 0.244650542, 0.239812467, 0.235408913, /* 16 17 18 19 */
+ 0.231378213, 0.227670249, 0.224243824, 0.221064729, /* 20 21 22 23 */
+ 0.218104292, 0.215338279, 0.212746054, 0.210309918, /* 24 25 26 27 */
+ 0.208014598, 0.205846832, 0.203795047, 0.201849087, /* 28 29 30 31 */
+ 0.200000000, 0.198239863, 0.196561632, 0.194959022, /* 32 33 34 35 */
+ 0.193426404, 0.191958720, 0.190551412, 0.189200360, /* 36 37 38 39 */
+ 0.187901825, 0.186652411, 0.185449023, 0.184288833, /* 40 41 42 43 */
+ 0.183169251, 0.182087900, 0.181042597, 0.180031327, /* 44 45 46 47 */
+ 0.179052232, 0.178103594, 0.177183820, 0.176291434, /* 48 49 50 51 */
+ 0.175425064, 0.174583430, 0.173765343, 0.172969690, /* 52 53 54 55 */
+ 0.172195434, 0.171441601, 0.170707280, 0.169991616, /* 56 57 58 59 */
+ 0.169293808, 0.168613099, 0.167948779, 0.167300179, /* 60 61 62 63 */
+ 0.166666667
+ };
+
+ /* }}} */
+ /* {{{ Various macros */
+
+ /* Return the number of digits needed to represent a static value */
+ #define MP_VALUE_DIGITS(V) \
+ ((sizeof(V)+(sizeof(mp_digit)-1))/sizeof(mp_digit))
+
+ /* Round precision P to nearest word boundary */
+ #define ROUND_PREC(P) ((mp_size)(2*(((P)+1)/2)))
+
+ /* Set array P of S digits to zero */
+ #define ZERO(P, S) \
+ do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P);memset(p__,0,i__);}while(0)
+
+ /* Copy S digits from array P to array Q */
+ #define COPY(P, Q, S) \
+ do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P),*q__=(Q);\
+ memcpy(q__,p__,i__);}while(0)
+
+ /* Reverse N elements of type T in array A */
+ #define REV(T, A, N) \
+ do{T *u_=(A),*v_=u_+(N)-1;while(u_<v_){T xch=*u_;*u_++=*v_;*v_--=xch;}}while(0)
+
+ #if TRACEABLE_CLAMP
+ #define CLAMP(Z) s_clamp(Z)
+ #else
+ #define CLAMP(Z) \
+ do{mp_int z_=(Z);mp_size uz_=MP_USED(z_);mp_digit *dz_=MP_DIGITS(z_)+uz_-1;\
+ while(uz_ > 1 && (*dz_-- == 0)) --uz_;MP_USED(z_)=uz_;}while(0)
+ #endif
+
+ #undef MIN
+ #undef MAX
+ #define MIN(A, B) ((B)<(A)?(B):(A))
+ #define MAX(A, B) ((B)>(A)?(B):(A))
+ #define SWAP(T, A, B) do{T t_=(A);A=(B);B=t_;}while(0)
+
+ #define TEMP(K) (temp + (K))
+ #define SETUP(E, C) \
+ do{if((res = (E)) != MP_OK) goto CLEANUP; ++(C);}while(0)
+
+ #define CMPZ(Z) \
+ (((Z)->used==1&&(Z)->digits[0]==0)?0:((Z)->sign==MP_NEG)?-1:1)
+
+ #define UMUL(X, Y, Z) \
+ do{mp_size ua_=MP_USED(X),ub_=MP_USED(Y);mp_size o_=ua_+ub_;\
+ ZERO(MP_DIGITS(Z),o_);\
+ (void) s_kmul(MP_DIGITS(X),MP_DIGITS(Y),MP_DIGITS(Z),ua_,ub_);\
+ MP_USED(Z)=o_;CLAMP(Z);}while(0)
+
+ #define USQR(X, Z) \
+ do{mp_size ua_=MP_USED(X),o_=ua_+ua_;ZERO(MP_DIGITS(Z),o_);\
+ (void) s_ksqr(MP_DIGITS(X),MP_DIGITS(Z),ua_);MP_USED(Z)=o_;CLAMP(Z);}while(0)
+
+ #define UPPER_HALF(W) ((mp_word)((W) >> MP_DIGIT_BIT))
+ #define LOWER_HALF(W) ((mp_digit)(W))
+ #define HIGH_BIT_SET(W) ((W) >> (MP_WORD_BIT - 1))
+ #define ADD_WILL_OVERFLOW(W, V) ((MP_WORD_MAX - (V)) < (W))
+
+ /* }}} */
+
+ /* Default number of digits allocated to a new mp_int */
+ static mp_size default_precision = 64;
+
+ /* Minimum number of digits to invoke recursive multiply */
+ static mp_size multiply_threshold = 32;
+
+ /* Default library configuration flags */
+ static mp_word mp_flags = MP_CAP_DIGITS;
+
+ /* Allocate a buffer of (at least) num digits, or return
+ NULL if that couldn't be done. */
+ static mp_digit *s_alloc(mp_size num);
+ #if TRACEABLE_FREE
+ static void s_free(void *ptr);
+ #else
+ #define s_free(P) px_free(P)
+ #endif
+
+ /* Insure that z has at least min digits allocated, resizing if
+ necessary. Returns true if successful, false if out of memory. */
+ static int s_pad(mp_int z, mp_size min);
+
+ /* Normalize by removing leading zeroes (except when z = 0) */
+ #if TRACEABLE_CLAMP
+ static void s_clamp(mp_int z);
+ #endif
+
+ /* Fill in a "fake" mp_int on the stack with a given value */
+ static void s_fake(mp_int z, int value, mp_digit vbuf[]);
+
+ /* Compare two runs of digits of given length, returns <0, 0, >0 */
+ static int s_cdig(mp_digit *da, mp_digit *db, mp_size len);
+
+ /* Pack the unsigned digits of v into array t */
+ static int s_vpack(int v, mp_digit t[]);
+
+ /* Compare magnitudes of a and b, returns <0, 0, >0 */
+ static int s_ucmp(mp_int a, mp_int b);
+
+ /* Compare magnitudes of a and v, returns <0, 0, >0 */
+ static int s_vcmp(mp_int a, int v);
+
+ /* Unsigned magnitude addition; assumes dc is big enough.
+ Carry out is returned (no memory allocated). */
+ static mp_digit s_uadd(mp_digit *da, mp_digit *db, mp_digit *dc,
+ mp_size size_a, mp_size size_b);
+
+ /* Unsigned magnitude subtraction. Assumes dc is big enough. */
+ static void s_usub(mp_digit *da, mp_digit *db, mp_digit *dc,
+ mp_size size_a, mp_size size_b);
+
+ /* Unsigned recursive multiplication. Assumes dc is big enough. */
+ static int s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc,
+ mp_size size_a, mp_size size_b);
+
+ /* Unsigned magnitude multiplication. Assumes dc is big enough. */
+ static void s_umul(mp_digit *da, mp_digit *db, mp_digit *dc,
+ mp_size size_a, mp_size size_b);
+
+ /* Unsigned recursive squaring. Assumes dc is big enough. */
+ static int s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a);
+
+ /* Unsigned magnitude squaring. Assumes dc is big enough. */
+ static void s_usqr(mp_digit *da, mp_digit *dc, mp_size size_a);
+
+ /* Single digit addition. Assumes a is big enough. */
+ static void s_dadd(mp_int a, mp_digit b);
+
+ /* Single digit multiplication. Assumes a is big enough. */
+ static void s_dmul(mp_int a, mp_digit b);
+
+ /* Single digit multiplication on buffers; assumes dc is big enough. */
+ static void s_dbmul(mp_digit *da, mp_digit b, mp_digit *dc,
+ mp_size size_a);
+
+ /* Single digit division. Replaces a with the quotient,
+ returns the remainder. */
+ static mp_digit s_ddiv(mp_int a, mp_digit b);
+
+ /* Quick division by a power of 2, replaces z (no allocation) */
+ static void s_qdiv(mp_int z, mp_size p2);
+
+ /* Quick remainder by a power of 2, replaces z (no allocation) */
+ static void s_qmod(mp_int z, mp_size p2);
+
+ /* Quick multiplication by a power of 2, replaces z.
+ Allocates if necessary; returns false in case this fails. */
+ static int s_qmul(mp_int z, mp_size p2);
+
+ /* Quick subtraction from a power of 2, replaces z.
+ Allocates if necessary; returns false in case this fails. */
+ static int s_qsub(mp_int z, mp_size p2);
+
+ /* Return maximum k such that 2^k divides z. */
+ static int s_dp2k(mp_int z);
+
+ /* Return k >= 0 such that z = 2^k, or -1 if there is no such k. */
+ static int s_isp2(mp_int z);
+
+ /* Set z to 2^k. May allocate; returns false in case this fails. */
+ static int s_2expt(mp_int z, int k);
+
+ /* Normalize a and b for division, returns normalization constant */
+ static int s_norm(mp_int a, mp_int b);
+
+ /* Compute constant mu for Barrett reduction, given modulus m, result
+ replaces z, m is untouched. */
+ static mp_result s_brmu(mp_int z, mp_int m);
+
+ /* Reduce a modulo m, using Barrett's algorithm. */
+ static int s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2);
+
+ /* Modular exponentiation, using Barrett reduction */
+ static mp_result s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c);
+
+ /* Unsigned magnitude division. Assumes |a| > |b|. Allocates
+ temporaries; overwrites a with quotient, b with remainder. */
+ static mp_result s_udiv(mp_int a, mp_int b);
+
+ /* Compute the number of digits in radix r required to represent the
+ given value. Does not account for sign flags, terminators, etc. */
+ static int s_outlen(mp_int z, mp_size r);
+
+ /* Guess how many digits of precision will be needed to represent a
+ radix r value of the specified number of digits. Returns a value
+ guaranteed to be no smaller than the actual number required. */
+ static mp_size s_inlen(int len, mp_size r);
+
+ /* Convert a character to a digit value in radix r, or
+ -1 if out of range */
+ static int s_ch2val(char c, int r);
+
+ /* Convert a digit value to a character */
+ static char s_val2ch(int v, int caps);
+
+ /* Take 2's complement of a buffer in place */
+ static void s_2comp(unsigned char *buf, int len);
+
+ /* Convert a value to binary, ignoring sign. On input, *limpos is the
+ bound on how many bytes should be written to buf; on output, *limpos
+ is set to the number of bytes actually written. */
+ static mp_result s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad);
+
+ #if 0
+ /* Dump a representation of the mp_int to standard output */
+ void s_print(char *tag, mp_int z);
+ void s_print_buf(char *tag, mp_digit *buf, mp_size num);
+ #endif
+
+ /* {{{ get_default_precision() */
+
+ mp_size mp_get_default_precision(void)
+ {
+ return default_precision;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_set_default_precision(s) */
+
+ void mp_set_default_precision(mp_size s)
+ {
+ NRCHECK(s > 0);
+
+ default_precision = (mp_size) ROUND_PREC(s);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_get_multiply_threshold() */
+
+ mp_size mp_get_multiply_threshold(void)
+ {
+ return multiply_threshold;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_set_multiply_threshold(s) */
+
+ void mp_set_multiply_threshold(mp_size s)
+ {
+ multiply_threshold = s;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_init(z) */
+
+ mp_result mp_int_init(mp_int z)
+ {
+ return mp_int_init_size(z, default_precision);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_alloc() */
+
+ mp_int mp_int_alloc(void)
+ {
+ mp_int out = px_alloc(sizeof(mpz_t));
+
+ assert(out != NULL);
+ out->digits = NULL;
+ out->used = 0;
+ out->alloc = 0;
+ out->sign = 0;
+
+ return out;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_init_size(z, prec) */
+
+ mp_result mp_int_init_size(mp_int z, mp_size prec)
+ {
+ CHECK(z != NULL);
+
+ prec = (mp_size) ROUND_PREC(prec);
+ prec = MAX(prec, default_precision);
+
+ if((MP_DIGITS(z) = s_alloc(prec)) == NULL)
+ return MP_MEMORY;
+
+ z->digits[0] = 0;
+ MP_USED(z) = 1;
+ MP_ALLOC(z) = prec;
+ MP_SIGN(z) = MP_ZPOS;
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_init_copy(z, old) */
+
+ mp_result mp_int_init_copy(mp_int z, mp_int old)
+ {
+ mp_result res;
+ mp_size uold, target;
+
+ CHECK(z != NULL && old != NULL);
+
+ uold = MP_USED(old);
+ target = MAX(uold, default_precision);
+
+ if((res = mp_int_init_size(z, target)) != MP_OK)
+ return res;
+
+ MP_USED(z) = uold;
+ MP_SIGN(z) = MP_SIGN(old);
+ COPY(MP_DIGITS(old), MP_DIGITS(z), uold);
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_init_value(z, value) */
+
+ mp_result mp_int_init_value(mp_int z, int value)
+ {
+ mp_result res;
+
+ CHECK(z != NULL);
+
+ if((res = mp_int_init(z)) != MP_OK)
+ return res;
+
+ return mp_int_set_value(z, value);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_set_value(z, value) */
+
+ mp_result mp_int_set_value(mp_int z, int value)
+ {
+ mp_size ndig;
+
+ CHECK(z != NULL);
+
+ /* How many digits to copy */
+ ndig = (mp_size) MP_VALUE_DIGITS(value);
+
+ if(!s_pad(z, ndig))
+ return MP_MEMORY;
+
+ MP_USED(z) = (mp_size)s_vpack(value, MP_DIGITS(z));
+ MP_SIGN(z) = (value < 0) ? MP_NEG : MP_ZPOS;
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_clear(z) */
+
+ void mp_int_clear(mp_int z)
+ {
+ if(z == NULL)
+ return;
+
+ if(MP_DIGITS(z) != NULL) {
+ s_free(MP_DIGITS(z));
+ MP_DIGITS(z) = NULL;
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_free(z) */
+
+ void mp_int_free(mp_int z)
+ {
+ NRCHECK(z != NULL);
+
+ if(z->digits != NULL)
+ mp_int_clear(z);
+
+ px_free(z);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_copy(a, c) */
+
+ mp_result mp_int_copy(mp_int a, mp_int c)
+ {
+ CHECK(a != NULL && c != NULL);
+
+ if(a != c) {
+ mp_size ua = MP_USED(a);
+ mp_digit *da, *dc;
+
+ if(!s_pad(c, ua))
+ return MP_MEMORY;
+
+ da = MP_DIGITS(a); dc = MP_DIGITS(c);
+ COPY(da, dc, ua);
+
+ MP_USED(c) = ua;
+ MP_SIGN(c) = MP_SIGN(a);
+ }
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_swap(a, c) */
+
+ void mp_int_swap(mp_int a, mp_int c)
+ {
+ if(a != c) {
+ mpz_t tmp = *a;
+
+ *a = *c;
+ *c = tmp;
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_zero(z) */
+
+ void mp_int_zero(mp_int z)
+ {
+ NRCHECK(z != NULL);
+
+ z->digits[0] = 0;
+ MP_USED(z) = 1;
+ MP_SIGN(z) = MP_ZPOS;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_abs(a, c) */
+
+ mp_result mp_int_abs(mp_int a, mp_int c)
+ {
+ mp_result res;
+
+ CHECK(a != NULL && c != NULL);
+
+ if((res = mp_int_copy(a, c)) != MP_OK)
+ return res;
+
+ MP_SIGN(c) = MP_ZPOS;
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_neg(a, c) */
+
+ mp_result mp_int_neg(mp_int a, mp_int c)
+ {
+ mp_result res;
+
+ CHECK(a != NULL && c != NULL);
+
+ if((res = mp_int_copy(a, c)) != MP_OK)
+ return res;
+
+ if(CMPZ(c) != 0)
+ MP_SIGN(c) = 1 - MP_SIGN(a);
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_add(a, b, c) */
+
+ mp_result mp_int_add(mp_int a, mp_int b, mp_int c)
+ {
+ mp_size ua, ub, uc, max;
+
+ CHECK(a != NULL && b != NULL && c != NULL);
+
+ ua = MP_USED(a); ub = MP_USED(b); uc = MP_USED(c);
+ max = MAX(ua, ub);
+
+ if(MP_SIGN(a) == MP_SIGN(b)) {
+ /* Same sign -- add magnitudes, preserve sign of addends */
+ mp_digit carry;
+
+ if(!s_pad(c, max))
+ return MP_MEMORY;
+
+ carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub);
+ uc = max;
+
+ if(carry) {
+ if(!s_pad(c, max + 1))
+ return MP_MEMORY;
+
+ c->digits[max] = carry;
+ ++uc;
+ }
+
+ MP_USED(c) = uc;
+ MP_SIGN(c) = MP_SIGN(a);
+
+ }
+ else {
+ /* Different signs -- subtract magnitudes, preserve sign of greater */
+ mp_int x, y;
+ int cmp = s_ucmp(a, b); /* magnitude comparision, sign ignored */
+
+ /* Set x to max(a, b), y to min(a, b) to simplify later code */
+ if(cmp >= 0) {
+ x = a; y = b;
+ }
+ else {
+ x = b; y = a;
+ }
+
+ if(!s_pad(c, MP_USED(x)))
+ return MP_MEMORY;
+
+ /* Subtract smaller from larger */
+ s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y));
+ MP_USED(c) = MP_USED(x);
+ CLAMP(c);
+
+ /* Give result the sign of the larger */
+ MP_SIGN(c) = MP_SIGN(x);
+ }
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_add_value(a, value, c) */
+
+ mp_result mp_int_add_value(mp_int a, int value, mp_int c)
+ {
+ mpz_t vtmp;
+ mp_digit vbuf[MP_VALUE_DIGITS(value)];
+
+ s_fake(&vtmp, value, vbuf);
+
+ return mp_int_add(a, &vtmp, c);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_sub(a, b, c) */
+
+ mp_result mp_int_sub(mp_int a, mp_int b, mp_int c)
+ {
+ mp_size ua, ub, uc, max;
+
+ CHECK(a != NULL && b != NULL && c != NULL);
+
+ ua = MP_USED(a); ub = MP_USED(b); uc = MP_USED(c);
+ max = MAX(ua, ub);
+
+ if(MP_SIGN(a) != MP_SIGN(b)) {
+ /* Different signs -- add magnitudes and keep sign of a */
+ mp_digit carry;
+
+ if(!s_pad(c, max))
+ return MP_MEMORY;
+
+ carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub);
+ uc = max;
+
+ if(carry) {
+ if(!s_pad(c, max + 1))
+ return MP_MEMORY;
+
+ c->digits[max] = carry;
+ ++uc;
+ }
+
+ MP_USED(c) = uc;
+ MP_SIGN(c) = MP_SIGN(a);
+
+ }
+ else {
+ /* Same signs -- subtract magnitudes */
+ mp_int x, y;
+ mp_sign osign;
+ int cmp = s_ucmp(a, b);
+
+ if(!s_pad(c, max))
+ return MP_MEMORY;
+
+ if(cmp >= 0) {
+ x = a; y = b; osign = MP_ZPOS;
+ }
+ else {
+ x = b; y = a; osign = MP_NEG;
+ }
+
+ if(MP_SIGN(a) == MP_NEG && cmp != 0)
+ osign = 1 - osign;
+
+ s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y));
+ MP_USED(c) = MP_USED(x);
+ CLAMP(c);
+
+ MP_SIGN(c) = osign;
+ }
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_sub_value(a, value, c) */
+
+ mp_result mp_int_sub_value(mp_int a, int value, mp_int c)
+ {
+ mpz_t vtmp;
+ mp_digit vbuf[MP_VALUE_DIGITS(value)];
+
+ s_fake(&vtmp, value, vbuf);
+
+ return mp_int_sub(a, &vtmp, c);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_mul(a, b, c) */
+
+ mp_result mp_int_mul(mp_int a, mp_int b, mp_int c)
+ {
+ mp_digit *out;
+ mp_size osize, ua, ub, p = 0;
+ mp_sign osign;
+
+ CHECK(a != NULL && b != NULL && c != NULL);
+
+ /* If either input is zero, we can shortcut multiplication */
+ if(mp_int_compare_zero(a) == 0 || mp_int_compare_zero(b) == 0) {
+ mp_int_zero(c);
+ return MP_OK;
+ }
+
+ /* Output is positive if inputs have same sign, otherwise negative */
+ osign = (MP_SIGN(a) == MP_SIGN(b)) ? MP_ZPOS : MP_NEG;
+
+ /* If the output is not equal to any of the inputs, we'll write the
+ results there directly; otherwise, allocate a temporary space. */
+ ua = MP_USED(a); ub = MP_USED(b);
+ osize = ua + ub;
+
+ if(c == a || c == b) {
+ p = ROUND_PREC(osize);
+ p = MAX(p, default_precision);
+
+ if((out = s_alloc(p)) == NULL)
+ return MP_MEMORY;
+ }
+ else {
+ if(!s_pad(c, osize))
+ return MP_MEMORY;
+
+ out = MP_DIGITS(c);
+ }
+ ZERO(out, osize);
+
+ if(!s_kmul(MP_DIGITS(a), MP_DIGITS(b), out, ua, ub))
+ return MP_MEMORY;
+
+ /* If we allocated a new buffer, get rid of whatever memory c was
+ already using, and fix up its fields to reflect that.
+ */
+ if(out != MP_DIGITS(c)) {
+ s_free(MP_DIGITS(c));
+ MP_DIGITS(c) = out;
+ MP_ALLOC(c) = p;
+ }
+
+ MP_USED(c) = osize; /* might not be true, but we'll fix it ... */
+ CLAMP(c); /* ... right here */
+ MP_SIGN(c) = osign;
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_mul_value(a, value, c) */
+
+ mp_result mp_int_mul_value(mp_int a, int value, mp_int c)
+ {
+ mpz_t vtmp;
+ mp_digit vbuf[MP_VALUE_DIGITS(value)];
+
+ s_fake(&vtmp, value, vbuf);
+
+ return mp_int_mul(a, &vtmp, c);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_mul_pow2(a, p2, c) */
+
+ mp_result mp_int_mul_pow2(mp_int a, int p2, mp_int c)
+ {
+ mp_result res;
+ CHECK(a != NULL && c != NULL && p2 >= 0);
+
+ if((res = mp_int_copy(a, c)) != MP_OK)
+ return res;
+
+ if(s_qmul(c, (mp_size) p2))
+ return MP_OK;
+ else
+ return MP_MEMORY;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_sqr(a, c) */
+
+ mp_result mp_int_sqr(mp_int a, mp_int c)
+ {
+ mp_digit *out;
+ mp_size osize, p = 0;
+
+ CHECK(a != NULL && c != NULL);
+
+ /* Get a temporary buffer big enough to hold the result */
+ osize = (mp_size) 2 * MP_USED(a);
+ if(a == c) {
+ p = ROUND_PREC(osize);
+ p = MAX(p, default_precision);
+
+ if((out = s_alloc(p)) == NULL)
+ return MP_MEMORY;
+ }
+ else {
+ if(!s_pad(c, osize))
+ return MP_MEMORY;
+
+ out = MP_DIGITS(c);
+ }
+ ZERO(out, osize);
+
+ s_ksqr(MP_DIGITS(a), out, MP_USED(a));
+
+ /* Get rid of whatever memory c was already using, and fix up its
+ fields to reflect the new digit array it's using
+ */
+ if(out != MP_DIGITS(c)) {
+ s_free(MP_DIGITS(c));
+ MP_DIGITS(c) = out;
+ MP_ALLOC(c) = p;
+ }
+
+ MP_USED(c) = osize; /* might not be true, but we'll fix it ... */
+ CLAMP(c); /* ... right here */
+ MP_SIGN(c) = MP_ZPOS;
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_div(a, b, q, r) */
+
+ mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r)
+ {
+ int cmp, last = 0, lg;
+ mp_result res = MP_OK;
+ mpz_t temp[2];
+ mp_int qout, rout;
+ mp_sign sa = MP_SIGN(a), sb = MP_SIGN(b);
+
+ CHECK(a != NULL && b != NULL && q != r);
+
+ if(CMPZ(b) == 0)
+ return MP_UNDEF;
+ else if((cmp = s_ucmp(a, b)) < 0) {
+ /* If |a| < |b|, no division is required:
+ q = 0, r = a
+ */
+ if(r && (res = mp_int_copy(a, r)) != MP_OK)
+ return res;
+
+ if(q)
+ mp_int_zero(q);
+
+ return MP_OK;
+ }
+ else if(cmp == 0) {
+ /* If |a| = |b|, no division is required:
+ q = 1 or -1, r = 0
+ */
+ if(r)
+ mp_int_zero(r);
+
+ if(q) {
+ mp_int_zero(q);
+ q->digits[0] = 1;
+
+ if(sa != sb)
+ MP_SIGN(q) = MP_NEG;
+ }
+
+ return MP_OK;
+ }
+
+ /* When |a| > |b|, real division is required. We need someplace to
+ store quotient and remainder, but q and r are allowed to be NULL
+ or to overlap with the inputs.
+ */
+ if((lg = s_isp2(b)) < 0) {
+ if(q && b != q && (res = mp_int_copy(a, q)) == MP_OK) {
+ qout = q;
+ }
+ else {
+ qout = TEMP(last);
+ SETUP(mp_int_init_copy(TEMP(last), a), last);
+ }
+
+ if(r && a != r && (res = mp_int_copy(b, r)) == MP_OK) {
+ rout = r;
+ }
+ else {
+ rout = TEMP(last);
+ SETUP(mp_int_init_copy(TEMP(last), b), last);
+ }
+
+ if((res = s_udiv(qout, rout)) != MP_OK) goto CLEANUP;
+ }
+ else {
+ if(q && (res = mp_int_copy(a, q)) != MP_OK) goto CLEANUP;
+ if(r && (res = mp_int_copy(a, r)) != MP_OK) goto CLEANUP;
+
+ if(q) s_qdiv(q, (mp_size) lg); qout = q;
+ if(r) s_qmod(r, (mp_size) lg); rout = r;
+ }
+
+ /* Recompute signs for output */
+ if(rout) {
+ MP_SIGN(rout) = sa;
+ if(CMPZ(rout) == 0)
+ MP_SIGN(rout) = MP_ZPOS;
+ }
+ if(qout) {
+ MP_SIGN(qout) = (sa == sb) ? MP_ZPOS : MP_NEG;
+ if(CMPZ(qout) == 0)
+ MP_SIGN(qout) = MP_ZPOS;
+ }
+
+ if(q && (res = mp_int_copy(qout, q)) != MP_OK) goto CLEANUP;
+ if(r && (res = mp_int_copy(rout, r)) != MP_OK) goto CLEANUP;
+
+ CLEANUP:
+ while(--last >= 0)
+ mp_int_clear(TEMP(last));
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_mod(a, m, c) */
+
+ mp_result mp_int_mod(mp_int a, mp_int m, mp_int c)
+ {
+ mp_result res;
+ mpz_t tmp;
+ mp_int out;
+
+ if(m == c) {
+ if((res = mp_int_init(&tmp)) != MP_OK)
+ return res;
+
+ out = &tmp;
+ }
+ else {
+ out = c;
+ }
+
+ if((res = mp_int_div(a, m, NULL, out)) != MP_OK)
+ goto CLEANUP;
+
+ if(CMPZ(out) < 0)
+ res = mp_int_add(out, m, c);
+ else
+ res = mp_int_copy(out, c);
+
+ CLEANUP:
+ if(out != c)
+ mp_int_clear(&tmp);
+
+ return res;
+ }
+
+ /* }}} */
+
+
+ /* {{{ mp_int_div_value(a, value, q, r) */
+
+ mp_result mp_int_div_value(mp_int a, int value, mp_int q, int *r)
+ {
+ mpz_t vtmp, rtmp;
+ mp_digit vbuf[MP_VALUE_DIGITS(value)];
+ mp_result res;
+
+ if((res = mp_int_init(&rtmp)) != MP_OK) return res;
+ s_fake(&vtmp, value, vbuf);
+
+ if((res = mp_int_div(a, &vtmp, q, &rtmp)) != MP_OK)
+ goto CLEANUP;
+
+ if(r)
+ (void) mp_int_to_int(&rtmp, r); /* can't fail */
+
+ CLEANUP:
+ mp_int_clear(&rtmp);
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_div_pow2(a, p2, q, r) */
+
+ mp_result mp_int_div_pow2(mp_int a, int p2, mp_int q, mp_int r)
+ {
+ mp_result res = MP_OK;
+
+ CHECK(a != NULL && p2 >= 0 && q != r);
+
+ if(q != NULL && (res = mp_int_copy(a, q)) == MP_OK)
+ s_qdiv(q, (mp_size) p2);
+
+ if(res == MP_OK && r != NULL && (res = mp_int_copy(a, r)) == MP_OK)
+ s_qmod(r, (mp_size) p2);
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_expt(a, b, c) */
+
+ mp_result mp_int_expt(mp_int a, int b, mp_int c)
+ {
+ mpz_t t;
+ mp_result res;
+ unsigned int v = abs(b);
+
+ CHECK(b >= 0 && c != NULL);
+
+ if((res = mp_int_init_copy(&t, a)) != MP_OK)
+ return res;
+
+ (void) mp_int_set_value(c, 1);
+ while(v != 0) {
+ if(v & 1) {
+ if((res = mp_int_mul(c, &t, c)) != MP_OK)
+ goto CLEANUP;
+ }
+
+ v >>= 1;
+ if(v == 0) break;
+
+ if((res = mp_int_sqr(&t, &t)) != MP_OK)
+ goto CLEANUP;
+ }
+
+ CLEANUP:
+ mp_int_clear(&t);
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_expt_value(a, b, c) */
+
+ mp_result mp_int_expt_value(int a, int b, mp_int c)
+ {
+ mpz_t t;
+ mp_result res;
+ unsigned int v = abs(b);
+
+ CHECK(b >= 0 && c != NULL);
+
+ if((res = mp_int_init_value(&t, a)) != MP_OK)
+ return res;
+
+ (void) mp_int_set_value(c, 1);
+ while(v != 0) {
+ if(v & 1) {
+ if((res = mp_int_mul(c, &t, c)) != MP_OK)
+ goto CLEANUP;
+ }
+
+ v >>= 1;
+ if(v == 0) break;
+
+ if((res = mp_int_sqr(&t, &t)) != MP_OK)
+ goto CLEANUP;
+ }
+
+ CLEANUP:
+ mp_int_clear(&t);
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_compare(a, b) */
+
+ int mp_int_compare(mp_int a, mp_int b)
+ {
+ mp_sign sa;
+
+ CHECK(a != NULL && b != NULL);
+
+ sa = MP_SIGN(a);
+ if(sa == MP_SIGN(b)) {
+ int cmp = s_ucmp(a, b);
+
+ /* If they're both zero or positive, the normal comparison
+ applies; if both negative, the sense is reversed. */
+ if(sa == MP_ZPOS)
+ return cmp;
+ else
+ return -cmp;
+
+ }
+ else {
+ if(sa == MP_ZPOS)
+ return 1;
+ else
+ return -1;
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_compare_unsigned(a, b) */
+
+ int mp_int_compare_unsigned(mp_int a, mp_int b)
+ {
+ NRCHECK(a != NULL && b != NULL);
+
+ return s_ucmp(a, b);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_compare_zero(z) */
+
+ int mp_int_compare_zero(mp_int z)
+ {
+ NRCHECK(z != NULL);
+
+ if(MP_USED(z) == 1 && z->digits[0] == 0)
+ return 0;
+ else if(MP_SIGN(z) == MP_ZPOS)
+ return 1;
+ else
+ return -1;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_compare_value(z, value) */
+
+ int mp_int_compare_value(mp_int z, int value)
+ {
+ mp_sign vsign = (value < 0) ? MP_NEG : MP_ZPOS;
+ int cmp;
+
+ CHECK(z != NULL);
+
+ if(vsign == MP_SIGN(z)) {
+ cmp = s_vcmp(z, value);
+
+ if(vsign == MP_ZPOS)
+ return cmp;
+ else
+ return -cmp;
+ }
+ else {
+ if(value < 0)
+ return 1;
+ else
+ return -1;
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_exptmod(a, b, m, c) */
+
+ mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c)
+ {
+ mp_result res;
+ mp_size um;
+ mpz_t temp[3];
+ mp_int s;
+ int last = 0;
+
+ CHECK(a != NULL && b != NULL && c != NULL && m != NULL);
+
+ /* Zero moduli and negative exponents are not considered. */
+ if(CMPZ(m) == 0)
+ return MP_UNDEF;
+ if(CMPZ(b) < 0)
+ return MP_RANGE;
+
+ um = MP_USED(m);
+ SETUP(mp_int_init_size(TEMP(0), 2 * um), last);
+ SETUP(mp_int_init_size(TEMP(1), 2 * um), last);
+
+ if(c == b || c == m) {
+ SETUP(mp_int_init_size(TEMP(2), 2 * um), last);
+ s = TEMP(2);
+ }
+ else {
+ s = c;
+ }
+
+ if((res = mp_int_mod(a, m, TEMP(0))) != MP_OK) goto CLEANUP;
+
+ if((res = s_brmu(TEMP(1), m)) != MP_OK) goto CLEANUP;
+
+ if((res = s_embar(TEMP(0), b, m, TEMP(1), s)) != MP_OK)
+ goto CLEANUP;
+
+ res = mp_int_copy(s, c);
+
+ CLEANUP:
+ while(--last >= 0)
+ mp_int_clear(TEMP(last));
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_exptmod_evalue(a, value, m, c) */
+
+ mp_result mp_int_exptmod_evalue(mp_int a, int value, mp_int m, mp_int c)
+ {
+ mpz_t vtmp;
+ mp_digit vbuf[MP_VALUE_DIGITS(value)];
+
+ s_fake(&vtmp, value, vbuf);
+
+ return mp_int_exptmod(a, &vtmp, m, c);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_exptmod_bvalue(v, b, m, c) */
+
+ mp_result mp_int_exptmod_bvalue(int value, mp_int b,
+ mp_int m, mp_int c)
+ {
+ mpz_t vtmp;
+ mp_digit vbuf[MP_VALUE_DIGITS(value)];
+
+ s_fake(&vtmp, value, vbuf);
+
+ return mp_int_exptmod(&vtmp, b, m, c);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_exptmod_known(a, b, m, mu, c) */
+
+ mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
+ {
+ mp_result res;
+ mp_size um;
+ mpz_t temp[2];
+ mp_int s;
+ int last = 0;
+
+ CHECK(a && b && m && c);
+
+ /* Zero moduli and negative exponents are not considered. */
+ if(CMPZ(m) == 0)
+ return MP_UNDEF;
+ if(CMPZ(b) < 0)
+ return MP_RANGE;
+
+ um = MP_USED(m);
+ SETUP(mp_int_init_size(TEMP(0), 2 * um), last);
+
+ if(c == b || c == m) {
+ SETUP(mp_int_init_size(TEMP(1), 2 * um), last);
+ s = TEMP(1);
+ }
+ else {
+ s = c;
+ }
+
+ if((res = mp_int_mod(a, m, TEMP(0))) != MP_OK) goto CLEANUP;
+
+ if((res = s_embar(TEMP(0), b, m, mu, s)) != MP_OK)
+ goto CLEANUP;
+
+ res = mp_int_copy(s, c);
+
+ CLEANUP:
+ while(--last >= 0)
+ mp_int_clear(TEMP(last));
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_redux_const(m, c) */
+
+ mp_result mp_int_redux_const(mp_int m, mp_int c)
+ {
+ CHECK(m != NULL && c != NULL && m != c);
+
+ return s_brmu(c, m);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_invmod(a, m, c) */
+
+ mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c)
+ {
+ mp_result res;
+ mp_sign sa;
+ int last = 0;
+ mpz_t temp[2];
+
+ CHECK(a != NULL && m != NULL && c != NULL);
+
+ if(CMPZ(a) == 0 || CMPZ(m) <= 0)
+ return MP_RANGE;
+
+ sa = MP_SIGN(a); /* need this for the result later */
+
+ for(last = 0; last < 2; ++last)
+ if((res = mp_int_init(TEMP(last))) != MP_OK)
+ goto CLEANUP;
+
+ if((res = mp_int_egcd(a, m, TEMP(0), TEMP(1), NULL)) != MP_OK)
+ goto CLEANUP;
+
+ if(mp_int_compare_value(TEMP(0), 1) != 0) {
+ res = MP_UNDEF;
+ goto CLEANUP;
+ }
+
+ /* It is first necessary to constrain the value to the proper range */
+ if((res = mp_int_mod(TEMP(1), m, TEMP(1))) != MP_OK)
+ goto CLEANUP;
+
+ /* Now, if 'a' was originally negative, the value we have is
+ actually the magnitude of the negative representative; to get the
+ positive value we have to subtract from the modulus. Otherwise,
+ the value is okay as it stands.
+ */
+ if(sa == MP_NEG)
+ res = mp_int_sub(m, TEMP(1), c);
+ else
+ res = mp_int_copy(TEMP(1), c);
+
+ CLEANUP:
+ while(--last >= 0)
+ mp_int_clear(TEMP(last));
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_gcd(a, b, c) */
+
+ /* Binary GCD algorithm due to Josef Stein, 1961 */
+ mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c)
+ {
+ int ca, cb, k = 0;
+ mpz_t u, v, t;
+ mp_result res;
+
+ CHECK(a != NULL && b != NULL && c != NULL);
+
+ ca = CMPZ(a);
+ cb = CMPZ(b);
+ if(ca == 0 && cb == 0)
+ return MP_UNDEF;
+ else if(ca == 0)
+ return mp_int_abs(b, c);
+ else if(cb == 0)
+ return mp_int_abs(a, c);
+
+ if((res = mp_int_init(&t)) != MP_OK)
+ return res;
+ if((res = mp_int_init_copy(&u, a)) != MP_OK)
+ goto U;
+ if((res = mp_int_init_copy(&v, b)) != MP_OK)
+ goto V;
+
+ MP_SIGN(&u) = MP_ZPOS; MP_SIGN(&v) = MP_ZPOS;
+
+ { /* Divide out common factors of 2 from u and v */
+ int div2_u = s_dp2k(&u), div2_v = s_dp2k(&v);
+
+ k = MIN(div2_u, div2_v);
+ s_qdiv(&u, (mp_size) k);
+ s_qdiv(&v, (mp_size) k);
+ }
+
+ if(mp_int_is_odd(&u)) {
+ if((res = mp_int_neg(&v, &t)) != MP_OK)
+ goto CLEANUP;
+ }
+ else {
+ if((res = mp_int_copy(&u, &t)) != MP_OK)
+ goto CLEANUP;
+ }
+
+ for(;;) {
+ s_qdiv(&t, s_dp2k(&t));
+
+ if(CMPZ(&t) > 0) {
+ if((res = mp_int_copy(&t, &u)) != MP_OK)
+ goto CLEANUP;
+ }
+ else {
+ if((res = mp_int_neg(&t, &v)) != MP_OK)
+ goto CLEANUP;
+ }
+
+ if((res = mp_int_sub(&u, &v, &t)) != MP_OK)
+ goto CLEANUP;
+
+ if(CMPZ(&t) == 0)
+ break;
+ }
+
+ if((res = mp_int_abs(&u, c)) != MP_OK)
+ goto CLEANUP;
+ if(!s_qmul(c, (mp_size) k))
+ res = MP_MEMORY;
+
+ CLEANUP:
+ mp_int_clear(&v);
+ V: mp_int_clear(&u);
+ U: mp_int_clear(&t);
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_egcd(a, b, c, x, y) */
+
+ /* This is the binary GCD algorithm again, but this time we keep track
+ of the elementary matrix operations as we go, so we can get values
+ x and y satisfying c = ax + by.
+ */
+ mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c,
+ mp_int x, mp_int y)
+ {
+ int k, last = 0, ca, cb;
+ mpz_t temp[8];
+ mp_result res;
+
+ CHECK(a != NULL && b != NULL && c != NULL &&
+ (x != NULL || y != NULL));
+
+ ca = CMPZ(a);
+ cb = CMPZ(b);
+ if(ca == 0 && cb == 0)
+ return MP_UNDEF;
+ else if(ca == 0) {
+ if((res = mp_int_abs(b, c)) != MP_OK) return res;
+ mp_int_zero(x); (void) mp_int_set_value(y, 1); return MP_OK;
+ }
+ else if(cb == 0) {
+ if((res = mp_int_abs(a, c)) != MP_OK) return res;
+ (void) mp_int_set_value(x, 1); mp_int_zero(y); return MP_OK;
+ }
+
+ /* Initialize temporaries:
+ A:0, B:1, C:2, D:3, u:4, v:5, ou:6, ov:7 */
+ for(last = 0; last < 4; ++last) {
+ if((res = mp_int_init(TEMP(last))) != MP_OK)
+ goto CLEANUP;
+ }
+ TEMP(0)->digits[0] = 1;
+ TEMP(3)->digits[0] = 1;
+
+ SETUP(mp_int_init_copy(TEMP(4), a), last);
+ SETUP(mp_int_init_copy(TEMP(5), b), last);
+
+ /* We will work with absolute values here */
+ MP_SIGN(TEMP(4)) = MP_ZPOS;
+ MP_SIGN(TEMP(5)) = MP_ZPOS;
+
+ { /* Divide out common factors of 2 from u and v */
+ int div2_u = s_dp2k(TEMP(4)), div2_v = s_dp2k(TEMP(5));
+
+ k = MIN(div2_u, div2_v);
+ s_qdiv(TEMP(4), k);
+ s_qdiv(TEMP(5), k);
+ }
+
+ SETUP(mp_int_init_copy(TEMP(6), TEMP(4)), last);
+ SETUP(mp_int_init_copy(TEMP(7), TEMP(5)), last);
+
+ for(;;) {
+ while(mp_int_is_even(TEMP(4))) {
+ s_qdiv(TEMP(4), 1);
+
+ if(mp_int_is_odd(TEMP(0)) || mp_int_is_odd(TEMP(1))) {
+ if((res = mp_int_add(TEMP(0), TEMP(7), TEMP(0))) != MP_OK)
+ goto CLEANUP;
+ if((res = mp_int_sub(TEMP(1), TEMP(6), TEMP(1))) != MP_OK)
+ goto CLEANUP;
+ }
+
+ s_qdiv(TEMP(0), 1);
+ s_qdiv(TEMP(1), 1);
+ }
+
+ while(mp_int_is_even(TEMP(5))) {
+ s_qdiv(TEMP(5), 1);
+
+ if(mp_int_is_odd(TEMP(2)) || mp_int_is_odd(TEMP(3))) {
+ if((res = mp_int_add(TEMP(2), TEMP(7), TEMP(2))) != MP_OK)
+ goto CLEANUP;
+ if((res = mp_int_sub(TEMP(3), TEMP(6), TEMP(3))) != MP_OK)
+ goto CLEANUP;
+ }
+
+ s_qdiv(TEMP(2), 1);
+ s_qdiv(TEMP(3), 1);
+ }
+
+ if(mp_int_compare(TEMP(4), TEMP(5)) >= 0) {
+ if((res = mp_int_sub(TEMP(4), TEMP(5), TEMP(4))) != MP_OK) goto CLEANUP;
+ if((res = mp_int_sub(TEMP(0), TEMP(2), TEMP(0))) != MP_OK) goto CLEANUP;
+ if((res = mp_int_sub(TEMP(1), TEMP(3), TEMP(1))) != MP_OK) goto CLEANUP;
+ }
+ else {
+ if((res = mp_int_sub(TEMP(5), TEMP(4), TEMP(5))) != MP_OK) goto CLEANUP;
+ if((res = mp_int_sub(TEMP(2), TEMP(0), TEMP(2))) != MP_OK) goto CLEANUP;
+ if((res = mp_int_sub(TEMP(3), TEMP(1), TEMP(3))) != MP_OK) goto CLEANUP;
+ }
+
+ if(CMPZ(TEMP(4)) == 0) {
+ if(x && (res = mp_int_copy(TEMP(2), x)) != MP_OK) goto CLEANUP;
+ if(y && (res = mp_int_copy(TEMP(3), y)) != MP_OK) goto CLEANUP;
+ if(c) {
+ if(!s_qmul(TEMP(5), k)) {
+ res = MP_MEMORY;
+ goto CLEANUP;
+ }
+
+ res = mp_int_copy(TEMP(5), c);
+ }
+
+ break;
+ }
+ }
+
+ CLEANUP:
+ while(--last >= 0)
+ mp_int_clear(TEMP(last));
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_divisible_value(a, v) */
+
+ int mp_int_divisible_value(mp_int a, int v)
+ {
+ int rem = 0;
+
+ if(mp_int_div_value(a, v, NULL, &rem) != MP_OK)
+ return 0;
+
+ return rem == 0;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_is_pow2(z) */
+
+ int mp_int_is_pow2(mp_int z)
+ {
+ CHECK(z != NULL);
+
+ return s_isp2(z);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_sqrt(a, c) */
+
+ mp_result mp_int_sqrt(mp_int a, mp_int c)
+ {
+ mp_result res = MP_OK;
+ mpz_t temp[2];
+ int last = 0;
+
+ CHECK(a != NULL && c != NULL);
+
+ /* The square root of a negative value does not exist in the integers. */
+ if(MP_SIGN(a) == MP_NEG)
+ return MP_UNDEF;
+
+ SETUP(mp_int_init_copy(TEMP(last), a), last);
+ SETUP(mp_int_init(TEMP(last)), last);
+
+ for(;;) {
+ if((res = mp_int_sqr(TEMP(0), TEMP(1))) != MP_OK)
+ goto CLEANUP;
+
+ if(mp_int_compare_unsigned(a, TEMP(1)) == 0) break;
+
+ if((res = mp_int_copy(a, TEMP(1))) != MP_OK)
+ goto CLEANUP;
+ if((res = mp_int_div(TEMP(1), TEMP(0), TEMP(1), NULL)) != MP_OK)
+ goto CLEANUP;
+ if((res = mp_int_add(TEMP(0), TEMP(1), TEMP(1))) != MP_OK)
+ goto CLEANUP;
+ if((res = mp_int_div_pow2(TEMP(1), 1, TEMP(1), NULL)) != MP_OK)
+ goto CLEANUP;
+
+ if(mp_int_compare_unsigned(TEMP(0), TEMP(1)) == 0) break;
+ if((res = mp_int_sub_value(TEMP(0), 1, TEMP(0))) != MP_OK) goto CLEANUP;
+ if(mp_int_compare_unsigned(TEMP(0), TEMP(1)) == 0) break;
+
+ if((res = mp_int_copy(TEMP(1), TEMP(0))) != MP_OK) goto CLEANUP;
+ }
+
+ res = mp_int_copy(TEMP(0), c);
+
+ CLEANUP:
+ while(--last >= 0)
+ mp_int_clear(TEMP(last));
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_to_int(z, out) */
+
+ mp_result mp_int_to_int(mp_int z, int *out)
+ {
+ unsigned int uv = 0;
+ mp_size uz;
+ mp_digit *dz;
+ mp_sign sz;
+
+ CHECK(z != NULL);
+
+ /* Make sure the value is representable as an int */
+ sz = MP_SIGN(z);
+ if((sz == MP_ZPOS && mp_int_compare_value(z, INT_MAX) > 0) ||
+ mp_int_compare_value(z, INT_MIN) < 0)
+ return MP_RANGE;
+
+ uz = MP_USED(z);
+ dz = MP_DIGITS(z) + uz - 1;
+
+ while(uz > 0) {
+ uv <<= MP_DIGIT_BIT/2;
+ uv = (uv << (MP_DIGIT_BIT/2)) | *dz--;
+ --uz;
+ }
+
+ if(out)
+ *out = (sz == MP_NEG) ? -(int)uv : (int)uv;
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_to_string(z, radix, str, limit) */
+
+ mp_result mp_int_to_string(mp_int z, mp_size radix,
+ char *str, int limit)
+ {
+ mp_result res;
+ int cmp = 0;
+
+ CHECK(z != NULL && str != NULL && limit >= 2);
+
+ if(radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
+ return MP_RANGE;
+
+ if(CMPZ(z) == 0) {
+ *str++ = s_val2ch(0, mp_flags & MP_CAP_DIGITS);
+ }
+ else {
+ mpz_t tmp;
+ char *h, *t;
+
+ if((res = mp_int_init_copy(&tmp, z)) != MP_OK)
+ return res;
+
+ if(MP_SIGN(z) == MP_NEG) {
+ *str++ = '-';
+ --limit;
+ }
+ h = str;
+
+ /* Generate digits in reverse order until finished or limit reached */
+ for(/* */; limit > 0; --limit) {
+ mp_digit d;
+
+ if((cmp = CMPZ(&tmp)) == 0)
+ break;
+
+ d = s_ddiv(&tmp, (mp_digit)radix);
+ *str++ = s_val2ch(d, mp_flags & MP_CAP_DIGITS);
+ }
+ t = str - 1;
+
+ /* Put digits back in correct output order */
+ while(h < t) {
+ char tc = *h;
+ *h++ = *t;
+ *t-- = tc;
+ }
+
+ mp_int_clear(&tmp);
+ }
+
+ *str = '\0';
+ if(cmp == 0)
+ return MP_OK;
+ else
+ return MP_TRUNC;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_string_len(z, radix) */
+
+ mp_result mp_int_string_len(mp_int z, mp_size radix)
+ {
+ int len;
+
+ CHECK(z != NULL);
+
+ if(radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
+ return MP_RANGE;
+
+ len = s_outlen(z, radix) + 1; /* for terminator */
+
+ /* Allow for sign marker on negatives */
+ if(MP_SIGN(z) == MP_NEG)
+ len += 1;
+
+ return len;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_read_string(z, radix, *str) */
+
+ /* Read zero-terminated string into z */
+ mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str)
+ {
+ return mp_int_read_cstring(z, radix, str, NULL);
+
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_read_cstring(z, radix, *str, **end) */
+
+ mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end)
+ {
+ int ch;
+
+ CHECK(z != NULL && str != NULL);
+
+ if(radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
+ return MP_RANGE;
+
+ /* Skip leading whitespace */
+ while(isspace((int)*str))
+ ++str;
+
+ /* Handle leading sign tag (+/-, positive default) */
+ switch(*str) {
+ case '-':
+ MP_SIGN(z) = MP_NEG;
+ ++str;
+ break;
+ case '+':
+ ++str; /* fallthrough */
+ default:
+ MP_SIGN(z) = MP_ZPOS;
+ break;
+ }
+
+ /* Skip leading zeroes */
+ while((ch = s_ch2val(*str, radix)) == 0)
+ ++str;
+
+ /* Make sure there is enough space for the value */
+ if(!s_pad(z, s_inlen(strlen(str), radix)))
+ return MP_MEMORY;
+
+ MP_USED(z) = 1; z->digits[0] = 0;
+
+ while(*str != '\0' && ((ch = s_ch2val(*str, radix)) >= 0)) {
+ s_dmul(z, (mp_digit)radix);
+ s_dadd(z, (mp_digit)ch);
+ ++str;
+ }
+
+ CLAMP(z);
+
+ /* Override sign for zero, even if negative specified. */
+ if(CMPZ(z) == 0)
+ MP_SIGN(z) = MP_ZPOS;
+
+ if(end != NULL)
+ *end = (char *)str;
+
+ /* Return a truncation error if the string has unprocessed
+ characters remaining, so the caller can tell if the whole string
+ was done */
+ if(*str != '\0')
+ return MP_TRUNC;
+ else
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_count_bits(z) */
+
+ mp_result mp_int_count_bits(mp_int z)
+ {
+ mp_size nbits = 0, uz;
+ mp_digit d;
+
+ CHECK(z != NULL);
+
+ uz = MP_USED(z);
+ if(uz == 1 && z->digits[0] == 0)
+ return 1;
+
+ --uz;
+ nbits = uz * MP_DIGIT_BIT;
+ d = z->digits[uz];
+
+ while(d != 0) {
+ d >>= 1;
+ ++nbits;
+ }
+
+ return nbits;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_to_binary(z, buf, limit) */
+
+ mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit)
+ {
+ static const int PAD_FOR_2C = 1;
+
+ mp_result res;
+ int limpos = limit;
+
+ CHECK(z != NULL && buf != NULL);
+
+ res = s_tobin(z, buf, &limpos, PAD_FOR_2C);
+
+ if(MP_SIGN(z) == MP_NEG)
+ s_2comp(buf, limpos);
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_read_binary(z, buf, len) */
+
+ mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len)
+ {
+ mp_size need, i;
+ unsigned char *tmp;
+ mp_digit *dz;
+
+ CHECK(z != NULL && buf != NULL && len > 0);
+
+ /* Figure out how many digits are needed to represent this value */
+ need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT;
+ if(!s_pad(z, need))
+ return MP_MEMORY;
+
+ mp_int_zero(z);
+
+ /* If the high-order bit is set, take the 2's complement before
+ reading the value (it will be restored afterward) */
+ if(buf[0] >> (CHAR_BIT - 1)) {
+ MP_SIGN(z) = MP_NEG;
+ s_2comp(buf, len);
+ }
+
+ dz = MP_DIGITS(z);
+ for(tmp = buf, i = len; i > 0; --i, ++tmp) {
+ s_qmul(z, (mp_size) CHAR_BIT);
+ *dz |= *tmp;
+ }
+
+ /* Restore 2's complement if we took it before */
+ if(MP_SIGN(z) == MP_NEG)
+ s_2comp(buf, len);
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_binary_len(z) */
+
+ mp_result mp_int_binary_len(mp_int z)
+ {
+ mp_result res = mp_int_count_bits(z);
+ int bytes = mp_int_unsigned_len(z);
+
+ if(res <= 0)
+ return res;
+
+ bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT;
+
+ /* If the highest-order bit falls exactly on a byte boundary, we
+ need to pad with an extra byte so that the sign will be read
+ correctly when reading it back in. */
+ if(bytes * CHAR_BIT == res)
+ ++bytes;
+
+ return bytes;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_to_unsigned(z, buf, limit) */
+
+ mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit)
+ {
+ static const int NO_PADDING = 0;
+
+ CHECK(z != NULL && buf != NULL);
+
+ return s_tobin(z, buf, &limit, NO_PADDING);
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_read_unsigned(z, buf, len) */
+
+ mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len)
+ {
+ mp_size need, i;
+ unsigned char *tmp;
+ mp_digit *dz;
+
+ CHECK(z != NULL && buf != NULL && len > 0);
+
+ /* Figure out how many digits are needed to represent this value */
+ need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT;
+ if(!s_pad(z, need))
+ return MP_MEMORY;
+
+ mp_int_zero(z);
+
+ dz = MP_DIGITS(z);
+ for(tmp = buf, i = len; i > 0; --i, ++tmp) {
+ (void) s_qmul(z, CHAR_BIT);
+ *dz |= *tmp;
+ }
+
+ return MP_OK;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_int_unsigned_len(z) */
+
+ mp_result mp_int_unsigned_len(mp_int z)
+ {
+ mp_result res = mp_int_count_bits(z);
+ int bytes;
+
+ if(res <= 0)
+ return res;
+
+ bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT;
+
+ return bytes;
+ }
+
+ /* }}} */
+
+ /* {{{ mp_error_string(res) */
+
+ const char *mp_error_string(mp_result res)
+ {
+ int ix;
+ if(res > 0)
+ return s_unknown_err;
+
+ res = -res;
+ for(ix = 0; ix < res && s_error_msg[ix] != NULL; ++ix)
+ ;
+
+ if(s_error_msg[ix] != NULL)
+ return s_error_msg[ix];
+ else
+ return s_unknown_err;
+ }
+
+ /* }}} */
+
+ /*------------------------------------------------------------------------*/
+ /* Private functions for internal use. These make assumptions. */
+
+ /* {{{ s_alloc(num) */
+
+ static mp_digit *s_alloc(mp_size num)
+ {
+ mp_digit *out = px_alloc(num * sizeof(mp_digit));
+
+ assert(out != NULL); /* for debugging */
+
+ return out;
+ }
+
+ /* }}} */
+
+ /* {{{ s_realloc(old, num) */
+
+ static mp_digit *s_realloc(mp_digit *old, mp_size num)
+ {
+ mp_digit *new = px_realloc(old, num * sizeof(mp_digit));
+
+ assert(new != NULL); /* for debugging */
+
+ return new;
+ }
+
+ /* }}} */
+
+ /* {{{ s_free(ptr) */
+
+ #if TRACEABLE_FREE
+ static void s_free(void *ptr)
+ {
+ px_free(ptr);
+ }
+ #endif
+
+ /* }}} */
+
+ /* {{{ s_pad(z, min) */
+
+ static int s_pad(mp_int z, mp_size min)
+ {
+ if(MP_ALLOC(z) < min) {
+ mp_size nsize = ROUND_PREC(min);
+ mp_digit *tmp = s_realloc(MP_DIGITS(z), nsize);
+
+ if(tmp == NULL)
+ return 0;
+
+ MP_DIGITS(z) = tmp;
+ MP_ALLOC(z) = nsize;
+ }
+
+ return 1;
+ }
+
+ /* }}} */
+
+ /* {{{ s_clamp(z) */
+
+ #if TRACEABLE_CLAMP
+ static void s_clamp(mp_int z)
+ {
+ mp_size uz = MP_USED(z);
+ mp_digit *zd = MP_DIGITS(z) + uz - 1;
+
+ while(uz > 1 && (*zd-- == 0))
+ --uz;
+
+ MP_USED(z) = uz;
+ }
+ #endif
+
+ /* }}} */
+
+ /* {{{ s_fake(z, value, vbuf) */
+
+ static void s_fake(mp_int z, int value, mp_digit vbuf[])
+ {
+ mp_size uv = (mp_size)s_vpack(value, vbuf);
+
+ z->used = uv;
+ z->alloc = MP_VALUE_DIGITS(value);
+ z->sign = (value < 0) ? MP_NEG : MP_ZPOS;
+ z->digits = vbuf;
+ }
+
+ /* }}} */
+
+ /* {{{ s_cdig(da, db, len) */
+
+ static int s_cdig(mp_digit *da, mp_digit *db, mp_size len)
+ {
+ mp_digit *dat = da + len - 1, *dbt = db + len - 1;
+
+ for(/* */; len != 0; --len, --dat, --dbt) {
+ if(*dat > *dbt)
+ return 1;
+ else if(*dat < *dbt)
+ return -1;
+ }
+
+ return 0;
+ }
+
+ /* }}} */
+
+ /* {{{ s_vpack(v, t[]) */
+
+ static int s_vpack(int v, mp_digit t[])
+ {
+ unsigned int uv = (unsigned int)((v < 0) ? -v : v);
+ int ndig = 0;
+
+ if(uv == 0)
+ t[ndig++] = 0;
+ else {
+ while(uv != 0) {
+ t[ndig++] = (mp_digit) uv;
+ uv >>= MP_DIGIT_BIT/2;
+ uv >>= MP_DIGIT_BIT/2;
+ }
+ }
+
+ return ndig;
+ }
+
+ /* }}} */
+
+ /* {{{ s_ucmp(a, b) */
+
+ static int s_ucmp(mp_int a, mp_int b)
+ {
+ mp_size ua = MP_USED(a), ub = MP_USED(b);
+
+ if(ua > ub)
+ return 1;
+ else if(ub > ua)
+ return -1;
+ else
+ return s_cdig(MP_DIGITS(a), MP_DIGITS(b), ua);
+ }
+
+ /* }}} */
+
+ /* {{{ s_vcmp(a, v) */
+
+ static int s_vcmp(mp_int a, int v)
+ {
+ mp_digit vdig[MP_VALUE_DIGITS(v)];
+ int ndig = 0;
+ mp_size ua = MP_USED(a);
+
+ ndig = s_vpack(v, vdig);
+
+ if(ua > ndig)
+ return 1;
+ else if(ua < ndig)
+ return -1;
+ else
+ return s_cdig(MP_DIGITS(a), vdig, ndig);
+ }
+
+ /* }}} */
+
+ /* {{{ s_uadd(da, db, dc, size_a, size_b) */
+
+ static mp_digit s_uadd(mp_digit *da, mp_digit *db, mp_digit *dc,
+ mp_size size_a, mp_size size_b)
+ {
+ mp_size pos;
+ mp_word w = 0;
+
+ /* Insure that da is the longer of the two to simplify later code */
+ if(size_b > size_a) {
+ SWAP(mp_digit *, da, db);
+ SWAP(mp_size, size_a, size_b);
+ }
+
+ /* Add corresponding digits until the shorter number runs out */
+ for(pos = 0; pos < size_b; ++pos, ++da, ++db, ++dc) {
+ w = w + (mp_word)*da + (mp_word)*db;
+ *dc = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+ }
+
+ /* Propagate carries as far as necessary */
+ for(/* */; pos < size_a; ++pos, ++da, ++dc) {
+ w = w + *da;
+
+ *dc = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+ }
+
+ /* Return carry out */
+ return (mp_digit)w;
+ }
+
+ /* }}} */
+
+ /* {{{ s_usub(da, db, dc, size_a, size_b) */
+
+ static void s_usub(mp_digit *da, mp_digit *db, mp_digit *dc,
+ mp_size size_a, mp_size size_b)
+ {
+ mp_size pos;
+ mp_word w = 0;
+
+ /* We assume that |a| >= |b| so this should definitely hold */
+ assert(size_a >= size_b);
+
+ /* Subtract corresponding digits and propagate borrow */
+ for(pos = 0; pos < size_b; ++pos, ++da, ++db, ++dc) {
+ w = ((mp_word)MP_DIGIT_MAX + 1 + /* MP_RADIX */
+ (mp_word)*da) - w - (mp_word)*db;
+
+ *dc = LOWER_HALF(w);
+ w = (UPPER_HALF(w) == 0);
+ }
+
+ /* Finish the subtraction for remaining upper digits of da */
+ for(/* */; pos < size_a; ++pos, ++da, ++dc) {
+ w = ((mp_word)MP_DIGIT_MAX + 1 + /* MP_RADIX */
+ (mp_word)*da) - w;
+
+ *dc = LOWER_HALF(w);
+ w = (UPPER_HALF(w) == 0);
+ }
+
+ /* If there is a borrow out at the end, it violates the precondition */
+ assert(w == 0);
+ }
+
+ /* }}} */
+
+ /* {{{ s_kmul(da, db, dc, size_a, size_b) */
+
+ static int s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc,
+ mp_size size_a, mp_size size_b)
+ {
+ mp_size bot_size;
+
+ /* Make sure b is the smaller of the two input values */
+ if(size_b > size_a) {
+ SWAP(mp_digit *, da, db);
+ SWAP(mp_size, size_a, size_b);
+ }
+
+ /* Insure that the bottom is the larger half in an odd-length split;
+ the code below relies on this being true.
+ */
+ bot_size = (size_a + 1) / 2;
+
+ /* If the values are big enough to bother with recursion, use the
+ Karatsuba algorithm to compute the product; otherwise use the
+ normal multiplication algorithm
+ */
+ if(multiply_threshold &&
+ size_a >= multiply_threshold &&
+ size_b > bot_size) {
+
+ mp_digit *t1, *t2, *t3, carry;
+
+ mp_digit *a_top = da + bot_size;
+ mp_digit *b_top = db + bot_size;
+
+ mp_size at_size = size_a - bot_size;
+ mp_size bt_size = size_b - bot_size;
+ mp_size buf_size = 2 * bot_size;
+
+ /* Do a single allocation for all three temporary buffers needed;
+ each buffer must be big enough to hold the product of two
+ bottom halves, and one buffer needs space for the completed
+ product; twice the space is plenty.
+ */
+ if((t1 = s_alloc(4 * buf_size)) == NULL) return 0;
+ t2 = t1 + buf_size;
+ t3 = t2 + buf_size;
+ ZERO(t1, 4 * buf_size);
+
+ /* t1 and t2 are initially used as temporaries to compute the inner product
+ (a1 + a0)(b1 + b0) = a1b1 + a1b0 + a0b1 + a0b0
+ */
+ carry = s_uadd(da, a_top, t1, bot_size, at_size); /* t1 = a1 + a0 */
+ t1[bot_size] = carry;
+
+ carry = s_uadd(db, b_top, t2, bot_size, bt_size); /* t2 = b1 + b0 */
+ t2[bot_size] = carry;
+
+ (void) s_kmul(t1, t2, t3, bot_size + 1, bot_size + 1); /* t3 = t1 * t2 */
+
+ /* Now we'll get t1 = a0b0 and t2 = a1b1, and subtract them out so that
+ we're left with only the pieces we want: t3 = a1b0 + a0b1
+ */
+ ZERO(t1, bot_size + 1);
+ ZERO(t2, bot_size + 1);
+ (void) s_kmul(da, db, t1, bot_size, bot_size); /* t1 = a0 * b0 */
+ (void) s_kmul(a_top, b_top, t2, at_size, bt_size); /* t2 = a1 * b1 */
+
+ /* Subtract out t1 and t2 to get the inner product */
+ s_usub(t3, t1, t3, buf_size + 2, buf_size);
+ s_usub(t3, t2, t3, buf_size + 2, buf_size);
+
+ /* Assemble the output value */
+ COPY(t1, dc, buf_size);
+ (void) s_uadd(t3, dc + bot_size, dc + bot_size,
+ buf_size + 1, buf_size + 1);
+
+ (void) s_uadd(t2, dc + 2*bot_size, dc + 2*bot_size,
+ buf_size, buf_size);
+
+ s_free(t1); /* note t2 and t3 are just internal pointers to t1 */
+ }
+ else {
+ s_umul(da, db, dc, size_a, size_b);
+ }
+
+ return 1;
+ }
+
+ /* }}} */
+
+ /* {{{ s_umul(da, db, dc, size_a, size_b) */
+
+ static void s_umul(mp_digit *da, mp_digit *db, mp_digit *dc,
+ mp_size size_a, mp_size size_b)
+ {
+ mp_size a, b;
+ mp_word w;
+
+ for(a = 0; a < size_a; ++a, ++dc, ++da) {
+ mp_digit *dct = dc;
+ mp_digit *dbt = db;
+
+ if(*da == 0)
+ continue;
+
+ w = 0;
+ for(b = 0; b < size_b; ++b, ++dbt, ++dct) {
+ w = (mp_word)*da * (mp_word)*dbt + w + (mp_word)*dct;
+
+ *dct = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+ }
+
+ *dct = (mp_digit)w;
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ s_ksqr(da, dc, size_a) */
+
+ static int s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a)
+ {
+ if(multiply_threshold && size_a > multiply_threshold) {
+ mp_size bot_size = (size_a + 1) / 2;
+ mp_digit *a_top = da + bot_size;
+ mp_digit *t1, *t2, *t3;
+ mp_size at_size = size_a - bot_size;
+ mp_size buf_size = 2 * bot_size;
+
+ if((t1 = s_alloc(4 * buf_size)) == NULL) return 0;
+ t2 = t1 + buf_size;
+ t3 = t2 + buf_size;
+ ZERO(t1, 4 * buf_size);
+
+ (void) s_ksqr(da, t1, bot_size); /* t1 = a0 ^ 2 */
+ (void) s_ksqr(a_top, t2, at_size); /* t2 = a1 ^ 2 */
+
+ (void) s_kmul(da, a_top, t3, bot_size, at_size); /* t3 = a0 * a1 */
+
+ /* Quick multiply t3 by 2, shifting left (can't overflow) */
+ {
+ int i, top = bot_size + at_size;
+ mp_word w, save = 0;
+
+ for(i = 0; i < top; ++i) {
+ w = t3[i];
+ w = (w << 1) | save;
+ t3[i] = LOWER_HALF(w);
+ save = UPPER_HALF(w);
+ }
+ t3[i] = LOWER_HALF(save);
+ }
+
+ /* Assemble the output value */
+ COPY(t1, dc, 2 * bot_size);
+ (void) s_uadd(t3, dc + bot_size, dc + bot_size,
+ buf_size + 1, buf_size + 1);
+
+ (void) s_uadd(t2, dc + 2*bot_size, dc + 2*bot_size,
+ buf_size, buf_size);
+
+ px_free(t1); /* note that t2 and t2 are internal pointers only */
+
+ }
+ else {
+ s_usqr(da, dc, size_a);
+ }
+
+ return 1;
+ }
+
+ /* }}} */
+
+ /* {{{ s_usqr(da, dc, size_a) */
+
+ static void s_usqr(mp_digit *da, mp_digit *dc, mp_size size_a)
+ {
+ mp_size i, j;
+ mp_word w;
+
+ for(i = 0; i < size_a; ++i, dc += 2, ++da) {
+ mp_digit *dct = dc, *dat = da;
+
+ if(*da == 0)
+ continue;
+
+ /* Take care of the first digit, no rollover */
+ w = (mp_word)*dat * (mp_word)*dat + (mp_word)*dct;
+ *dct = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+ ++dat; ++dct;
+
+ for(j = i + 1; j < size_a; ++j, ++dat, ++dct) {
+ mp_word t = (mp_word)*da * (mp_word)*dat;
+ mp_word u = w + (mp_word)*dct, ov = 0;
+
+ /* Check if doubling t will overflow a word */
+ if(HIGH_BIT_SET(t))
+ ov = 1;
+
+ w = t + t;
+
+ /* Check if adding u to w will overflow a word */
+ if(ADD_WILL_OVERFLOW(w, u))
+ ov = 1;
+
+ w += u;
+
+ *dct = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+ if(ov) {
+ w += MP_DIGIT_MAX; /* MP_RADIX */
+ ++w;
+ }
+ }
+
+ w = w + *dct;
+ *dct = (mp_digit)w;
+ while((w = UPPER_HALF(w)) != 0) {
+ ++dct; w = w + *dct;
+ *dct = LOWER_HALF(w);
+ }
+
+ assert(w == 0);
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ s_dadd(a, b) */
+
+ static void s_dadd(mp_int a, mp_digit b)
+ {
+ mp_word w = 0;
+ mp_digit *da = MP_DIGITS(a);
+ mp_size ua = MP_USED(a);
+
+ w = (mp_word)*da + b;
+ *da++ = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+
+ for(ua -= 1; ua > 0; --ua, ++da) {
+ w = (mp_word)*da + w;
+
+ *da = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+ }
+
+ if(w) {
+ *da = (mp_digit)w;
+ MP_USED(a) += 1;
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ s_dmul(a, b) */
+
+ static void s_dmul(mp_int a, mp_digit b)
+ {
+ mp_word w = 0;
+ mp_digit *da = MP_DIGITS(a);
+ mp_size ua = MP_USED(a);
+
+ while(ua > 0) {
+ w = (mp_word)*da * b + w;
+ *da++ = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+ --ua;
+ }
+
+ if(w) {
+ *da = (mp_digit)w;
+ MP_USED(a) += 1;
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ s_dbmul(da, b, dc, size_a) */
+
+ static void s_dbmul(mp_digit *da, mp_digit b, mp_digit *dc, mp_size size_a)
+ {
+ mp_word w = 0;
+
+ while(size_a > 0) {
+ w = (mp_word)*da++ * (mp_word)b + w;
+
+ *dc++ = LOWER_HALF(w);
+ w = UPPER_HALF(w);
+ --size_a;
+ }
+
+ if(w)
+ *dc = LOWER_HALF(w);
+ }
+
+ /* }}} */
+
+ /* {{{ s_ddiv(da, d, dc, size_a) */
+
+ static mp_digit s_ddiv(mp_int a, mp_digit b)
+ {
+ mp_word w = 0, qdigit;
+ mp_size ua = MP_USED(a);
+ mp_digit *da = MP_DIGITS(a) + ua - 1;
+
+ for(/* */; ua > 0; --ua, --da) {
+ w = (w << MP_DIGIT_BIT) | *da;
+
+ if(w >= b) {
+ qdigit = w / b;
+ w = w % b;
+ }
+ else {
+ qdigit = 0;
+ }
+
+ *da = (mp_digit)qdigit;
+ }
+
+ CLAMP(a);
+ return (mp_digit)w;
+ }
+
+ /* }}} */
+
+ /* {{{ s_qdiv(z, p2) */
+
+ static void s_qdiv(mp_int z, mp_size p2)
+ {
+ mp_size ndig = p2 / MP_DIGIT_BIT, nbits = p2 % MP_DIGIT_BIT;
+ mp_size uz = MP_USED(z);
+
+ if(ndig) {
+ mp_size mark;
+ mp_digit *to, *from;
+
+ if(ndig >= uz) {
+ mp_int_zero(z);
+ return;
+ }
+
+ to = MP_DIGITS(z); from = to + ndig;
+
+ for(mark = ndig; mark < uz; ++mark)
+ *to++ = *from++;
+
+ MP_USED(z) = uz - ndig;
+ }
+
+ if(nbits) {
+ mp_digit d = 0, *dz, save;
+ mp_size up = MP_DIGIT_BIT - nbits;
+
+ uz = MP_USED(z);
+ dz = MP_DIGITS(z) + uz - 1;
+
+ for(/* */; uz > 0; --uz, --dz) {
+ save = *dz;
+
+ *dz = (*dz >> nbits) | (d << up);
+ d = save;
+ }
+
+ CLAMP(z);
+ }
+
+ if(MP_USED(z) == 1 && z->digits[0] == 0)
+ MP_SIGN(z) = MP_ZPOS;
+ }
+
+ /* }}} */
+
+ /* {{{ s_qmod(z, p2) */
+
+ static void s_qmod(mp_int z, mp_size p2)
+ {
+ mp_size start = p2 / MP_DIGIT_BIT + 1, rest = p2 % MP_DIGIT_BIT;
+ mp_size uz = MP_USED(z);
+ mp_digit mask = (1 << rest) - 1;
+
+ if(start <= uz) {
+ MP_USED(z) = start;
+ z->digits[start - 1] &= mask;
+ CLAMP(z);
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ s_qmul(z, p2) */
+
+ static int s_qmul(mp_int z, mp_size p2)
+ {
+ mp_size uz, need, rest, extra, i;
+ mp_digit *from, *to, d;
+
+ if(p2 == 0)
+ return 1;
+
+ uz = MP_USED(z);
+ need = p2 / MP_DIGIT_BIT; rest = p2 % MP_DIGIT_BIT;
+
+ /* Figure out if we need an extra digit at the top end; this occurs
+ if the topmost `rest' bits of the high-order digit of z are not
+ zero, meaning they will be shifted off the end if not preserved */
+ extra = 0;
+ if(rest != 0) {
+ mp_digit *dz = MP_DIGITS(z) + uz - 1;
+
+ if((*dz >> (MP_DIGIT_BIT - rest)) != 0)
+ extra = 1;
+ }
+
+ if(!s_pad(z, uz + need + extra))
+ return 0;
+
+ /* If we need to shift by whole digits, do that in one pass, then
+ to back and shift by partial digits.
+ */
+ if(need > 0) {
+ from = MP_DIGITS(z) + uz - 1;
+ to = from + need;
+
+ for(i = 0; i < uz; ++i)
+ *to-- = *from--;
+
+ ZERO(MP_DIGITS(z), need);
+ uz += need;
+ }
+
+ if(rest) {
+ d = 0;
+ for(i = need, from = MP_DIGITS(z) + need; i < uz; ++i, ++from) {
+ mp_digit save = *from;
+
+ *from = (*from << rest) | (d >> (MP_DIGIT_BIT - rest));
+ d = save;
+ }
+
+ d >>= (MP_DIGIT_BIT - rest);
+ if(d != 0) {
+ *from = d;
+ uz += extra;
+ }
+ }
+
+ MP_USED(z) = uz;
+ CLAMP(z);
+
+ return 1;
+ }
+
+ /* }}} */
+
+ /* {{{ s_qsub(z, p2) */
+
+ /* Subtract |z| from 2^p2, assuming 2^p2 > |z|, and set z to be positive */
+ static int s_qsub(mp_int z, mp_size p2)
+ {
+ mp_digit hi = (1 << (p2 % MP_DIGIT_BIT)), *zp;
+ mp_size tdig = (p2 / MP_DIGIT_BIT), pos;
+ mp_word w = 0;
+
+ if(!s_pad(z, tdig + 1))
+ return 0;
+
+ for(pos = 0, zp = MP_DIGITS(z); pos < tdig; ++pos, ++zp) {
+ w = ((mp_word) MP_DIGIT_MAX + 1) - w - (mp_word)*zp;
+
+ *zp = LOWER_HALF(w);
+ w = UPPER_HALF(w) ? 0 : 1;
+ }
+
+ w = ((mp_word) MP_DIGIT_MAX + 1 + hi) - w - (mp_word)*zp;
+ *zp = LOWER_HALF(w);
+
+ assert(UPPER_HALF(w) != 0); /* no borrow out should be possible */
+
+ MP_SIGN(z) = MP_ZPOS;
+ CLAMP(z);
+
+ return 1;
+ }
+
+ /* }}} */
+
+ /* {{{ s_dp2k(z) */
+
+ static int s_dp2k(mp_int z)
+ {
+ int k = 0;
+ mp_digit *dp = MP_DIGITS(z), d;
+
+ if(MP_USED(z) == 1 && *dp == 0)
+ return 1;
+
+ while(*dp == 0) {
+ k += MP_DIGIT_BIT;
+ ++dp;
+ }
+
+ d = *dp;
+ while((d & 1) == 0) {
+ d >>= 1;
+ ++k;
+ }
+
+ return k;
+ }
+
+ /* }}} */
+
+ /* {{{ s_isp2(z) */
+
+ static int s_isp2(mp_int z)
+ {
+ mp_size uz = MP_USED(z), k = 0;
+ mp_digit *dz = MP_DIGITS(z), d;
+
+ while(uz > 1) {
+ if(*dz++ != 0)
+ return -1;
+ k += MP_DIGIT_BIT;
+ --uz;
+ }
+
+ d = *dz;
+ while(d > 1) {
+ if(d & 1)
+ return -1;
+ ++k; d >>= 1;
+ }
+
+ return (int) k;
+ }
+
+ /* }}} */
+
+ /* {{{ s_2expt(z, k) */
+
+ static int s_2expt(mp_int z, int k)
+ {
+ mp_size ndig, rest;
+ mp_digit *dz;
+
+ ndig = (k + MP_DIGIT_BIT) / MP_DIGIT_BIT;
+ rest = k % MP_DIGIT_BIT;
+
+ if(!s_pad(z, ndig))
+ return 0;
+
+ dz = MP_DIGITS(z);
+ ZERO(dz, ndig);
+ *(dz + ndig - 1) = (1 << rest);
+ MP_USED(z) = ndig;
+
+ return 1;
+ }
+
+ /* }}} */
+
+ /* {{{ s_norm(a, b) */
+
+ static int s_norm(mp_int a, mp_int b)
+ {
+ mp_digit d = b->digits[MP_USED(b) - 1];
+ int k = 0;
+
+ while(d < (mp_digit) (1 << (MP_DIGIT_BIT - 1))) { /* d < (MP_RADIX / 2) */
+ d <<= 1;
+ ++k;
+ }
+
+ /* These multiplications can't fail */
+ if(k != 0) {
+ (void) s_qmul(a, (mp_size) k);
+ (void) s_qmul(b, (mp_size) k);
+ }
+
+ return k;
+ }
+
+ /* }}} */
+
+ /* {{{ s_brmu(z, m) */
+
+ static mp_result s_brmu(mp_int z, mp_int m)
+ {
+ mp_size um = MP_USED(m) * 2;
+
+ if(!s_pad(z, um))
+ return MP_MEMORY;
+
+ s_2expt(z, MP_DIGIT_BIT * um);
+ return mp_int_div(z, m, z, NULL);
+ }
+
+ /* }}} */
+
+ /* {{{ s_reduce(x, m, mu, q1, q2) */
+
+ static int s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2)
+ {
+ mp_size um = MP_USED(m), umb_p1, umb_m1;
+
+ umb_p1 = (um + 1) * MP_DIGIT_BIT;
+ umb_m1 = (um - 1) * MP_DIGIT_BIT;
+
+ if(mp_int_copy(x, q1) != MP_OK)
+ return 0;
+
+ /* Compute q2 = floor((floor(x / b^(k-1)) * mu) / b^(k+1)) */
+ s_qdiv(q1, umb_m1);
+ UMUL(q1, mu, q2);
+ s_qdiv(q2, umb_p1);
+
+ /* Set x = x mod b^(k+1) */
+ s_qmod(x, umb_p1);
+
+ /* Now, q is a guess for the quotient a / m.
+ Compute x - q * m mod b^(k+1), replacing x. This may be off
+ by a factor of 2m, but no more than that.
+ */
+ UMUL(q2, m, q1);
+ s_qmod(q1, umb_p1);
+ (void) mp_int_sub(x, q1, x); /* can't fail */
+
+ /* The result may be < 0; if it is, add b^(k+1) to pin it in the
+ proper range. */
+ if((CMPZ(x) < 0) && !s_qsub(x, umb_p1))
+ return 0;
+
+ /* If x > m, we need to back it off until it is in range.
+ This will be required at most twice. */
+ if(mp_int_compare(x, m) >= 0)
+ (void) mp_int_sub(x, m, x);
+ if(mp_int_compare(x, m) >= 0)
+ (void) mp_int_sub(x, m, x);
+
+ /* At this point, x has been properly reduced. */
+ return 1;
+ }
+
+ /* }}} */
+
+ /* {{{ s_embar(a, b, m, mu, c) */
+
+ /* Perform modular exponentiation using Barrett's method, where mu is
+ the reduction constant for m. Assumes a < m, b > 0. */
+ static mp_result s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
+ {
+ mp_digit *db, *dbt, umu, d;
+ mpz_t temp[3];
+ mp_result res;
+ int last = 0;
+
+ umu = MP_USED(mu); db = MP_DIGITS(b); dbt = db + MP_USED(b) - 1;
+
+ while(last < 3)
+ SETUP(mp_int_init_size(TEMP(last), 2 * umu), last);
+
+ (void) mp_int_set_value(c, 1);
+
+ /* Take care of low-order digits */
+ while(db < dbt) {
+ int i;
+
+ for(d = *db, i = MP_DIGIT_BIT; i > 0; --i, d >>= 1) {
+ if(d & 1) {
+ /* The use of a second temporary avoids allocation */
+ UMUL(c, a, TEMP(0));
+ if(!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) {
+ res = MP_MEMORY; goto CLEANUP;
+ }
+ mp_int_copy(TEMP(0), c);
+ }
+
+
+ USQR(a, TEMP(0));
+ assert(MP_SIGN(TEMP(0)) == MP_ZPOS);
+ if(!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) {
+ res = MP_MEMORY; goto CLEANUP;
+ }
+ assert(MP_SIGN(TEMP(0)) == MP_ZPOS);
+ mp_int_copy(TEMP(0), a);
+
+
+ }
+
+ ++db;
+ }
+
+ /* Take care of highest-order digit */
+ d = *dbt;
+ for(;;) {
+ if(d & 1) {
+ UMUL(c, a, TEMP(0));
+ if(!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) {
+ res = MP_MEMORY; goto CLEANUP;
+ }
+ mp_int_copy(TEMP(0), c);
+ }
+
+ d >>= 1;
+ if(!d) break;
+
+ USQR(a, TEMP(0));
+ if(!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) {
+ res = MP_MEMORY; goto CLEANUP;
+ }
+ (void) mp_int_copy(TEMP(0), a);
+ }
+
+ CLEANUP:
+ while(--last >= 0)
+ mp_int_clear(TEMP(last));
+
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ s_udiv(a, b) */
+
+ /* Precondition: a >= b and b > 0
+ Postcondition: a' = a / b, b' = a % b
+ */
+ static mp_result s_udiv(mp_int a, mp_int b)
+ {
+ mpz_t q, r, t;
+ mp_size ua, ub, qpos = 0;
+ mp_digit *da, btop;
+ mp_result res = MP_OK;
+ int k, skip = 0;
+
+ /* Force signs to positive */
+ MP_SIGN(a) = MP_ZPOS;
+ MP_SIGN(b) = MP_ZPOS;
+
+ /* Normalize, per Knuth */
+ k = s_norm(a, b);
+
+ ua = MP_USED(a); ub = MP_USED(b); btop = b->digits[ub - 1];
+ if((res = mp_int_init_size(&q, ua)) != MP_OK) return res;
+ if((res = mp_int_init_size(&t, ua + 1)) != MP_OK) goto CLEANUP;
+
+ da = MP_DIGITS(a);
+ r.digits = da + ua - 1; /* The contents of r are shared with a */
+ r.used = 1;
+ r.sign = MP_ZPOS;
+ r.alloc = MP_ALLOC(a);
+ ZERO(t.digits, t.alloc);
+
+ /* Solve for quotient digits, store in q.digits in reverse order */
+ while(r.digits >= da) {
+ assert(qpos <= q.alloc);
+
+ if(s_ucmp(b, &r) > 0) {
+ r.digits -= 1;
+ r.used += 1;
+
+ if(++skip > 1)
+ q.digits[qpos++] = 0;
+
+ CLAMP(&r);
+ }
+ else {
+ mp_word pfx = r.digits[r.used - 1];
+ mp_word qdigit;
+
+ if(r.used > 1 && (pfx < btop || r.digits[r.used - 2] == 0)) {
+ pfx <<= MP_DIGIT_BIT / 2;
+ pfx <<= MP_DIGIT_BIT / 2;
+ pfx |= r.digits[r.used - 2];
+ }
+
+ qdigit = pfx / btop;
+ if(qdigit > MP_DIGIT_MAX)
+ qdigit = 1;
+
+ s_dbmul(MP_DIGITS(b), (mp_digit) qdigit, t.digits, ub);
+ t.used = ub + 1; CLAMP(&t);
+ while(s_ucmp(&t, &r) > 0) {
+ --qdigit;
+ (void) mp_int_sub(&t, b, &t); /* cannot fail */
+ }
+
+ s_usub(r.digits, t.digits, r.digits, r.used, t.used);
+ CLAMP(&r);
+
+ q.digits[qpos++] = (mp_digit) qdigit;
+ ZERO(t.digits, t.used);
+ skip = 0;
+ }
+ }
+
+ /* Put quotient digits in the correct order, and discard extra zeroes */
+ q.used = qpos;
+ REV(mp_digit, q.digits, qpos);
+ CLAMP(&q);
+
+ /* Denormalize the remainder */
+ CLAMP(a);
+ if(k != 0)
+ s_qdiv(a, k);
+
+ mp_int_copy(a, b); /* ok: 0 <= r < b */
+ mp_int_copy(&q, a); /* ok: q <= a */
+
+ mp_int_clear(&t);
+ CLEANUP:
+ mp_int_clear(&q);
+ return res;
+ }
+
+ /* }}} */
+
+ /* {{{ s_outlen(z, r) */
+
+ /* Precondition: 2 <= r < 64 */
+ static int s_outlen(mp_int z, mp_size r)
+ {
+ mp_result bits;
+ double raw;
+
+ bits = mp_int_count_bits(z);
+ raw = (double)bits * s_log2[r];
+
+ return (int)(raw + 0.999999);
+ }
+
+ /* }}} */
+
+ /* {{{ s_inlen(len, r) */
+
+ static mp_size s_inlen(int len, mp_size r)
+ {
+ double raw = (double)len / s_log2[r];
+ mp_size bits = (mp_size)(raw + 0.5);
+
+ return (mp_size)((bits + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT);
+ }
+
+ /* }}} */
+
+ /* {{{ s_ch2val(c, r) */
+
+ static int s_ch2val(char c, int r)
+ {
+ int out;
+
+ if(isdigit((int)c))
+ out = c - '0';
+ else if(r > 10 && isalpha((int)c))
+ out = toupper(c) - 'A' + 10;
+ else
+ return -1;
+
+ return (out >= r) ? -1 : out;
+ }
+
+ /* }}} */
+
+ /* {{{ s_val2ch(v, caps) */
+
+ static char s_val2ch(int v, int caps)
+ {
+ assert(v >= 0);
+
+ if(v < 10)
+ return v + '0';
+ else {
+ char out = (v - 10) + 'a';
+
+ if(caps)
+ return toupper(out);
+ else
+ return out;
+ }
+ }
+
+ /* }}} */
+
+ /* {{{ s_2comp(buf, len) */
+
+ static void s_2comp(unsigned char *buf, int len)
+ {
+ int i;
+ unsigned short s = 1;
+
+ for(i = len - 1; i >= 0; --i) {
+ unsigned char c = ~buf[i];
+
+ s = c + s;
+ c = s & UCHAR_MAX;
+ s >>= CHAR_BIT;
+
+ buf[i] = c;
+ }
+
+ /* last carry out is ignored */
+ }
+
+ /* }}} */
+
+ /* {{{ s_tobin(z, buf, *limpos) */
+
+ static mp_result s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad)
+ {
+ mp_size uz;
+ mp_digit *dz;
+ int pos = 0, limit = *limpos;
+
+ uz = MP_USED(z); dz = MP_DIGITS(z);
+ while(uz > 0 && pos < limit) {
+ mp_digit d = *dz++;
+ int i;
+
+ for(i = sizeof(mp_digit); i > 0 && pos < limit; --i) {
+ buf[pos++] = (unsigned char)d;
+ d >>= CHAR_BIT;
+
+ /* Don't write leading zeroes */
+ if(d == 0 && uz == 1)
+ i = 0; /* exit loop without signaling truncation */
+ }
+
+ /* Detect truncation (loop exited with pos >= limit) */
+ if(i > 0) break;
+
+ --uz;
+ }
+
+ if(pad != 0 && (buf[pos - 1] >> (CHAR_BIT - 1))) {
+ if(pos < limit)
+ buf[pos++] = 0;
+ else
+ uz = 1;
+ }
+
+ /* Digits are in reverse order, fix that */
+ REV(unsigned char, buf, pos);
+
+ /* Return the number of bytes actually written */
+ *limpos = pos;
+
+ return (uz == 0) ? MP_OK : MP_TRUNC;
+ }
+
+ /* }}} */
+
+ /* {{{ s_print(tag, z) */
+
+ #if 0
+ void s_print(char *tag, mp_int z)
+ {
+ int i;
+
+ fprintf(stderr, "%s: %c ", tag,
+ (MP_SIGN(z) == MP_NEG) ? '-' : '+');
+
+ for(i = MP_USED(z) - 1; i >= 0; --i)
+ fprintf(stderr, "%0*X", (int)(MP_DIGIT_BIT / 4), z->digits[i]);
+
+ fputc('\n', stderr);
+
+ }
+
+ void s_print_buf(char *tag, mp_digit *buf, mp_size num)
+ {
+ int i;
+
+ fprintf(stderr, "%s: ", tag);
+
+ for(i = num - 1; i >= 0; --i)
+ fprintf(stderr, "%0*X", (int)(MP_DIGIT_BIT / 4), buf[i]);
+
+ fputc('\n', stderr);
+ }
+ #endif
+
+ /* }}} */
+
+ /* HERE THERE BE DRAGONS */
Index: pgsql/contrib/pgcrypto/imath.h
===================================================================
*** /dev/null
--- pgsql/contrib/pgcrypto/imath.h
***************
*** 0 ****
--- 1,212 ----
+ /*
+ Name: imath.h
+ Purpose: Arbitrary precision integer arithmetic routines.
+ Author: M. J. Fromberger <http://www.dartmouth.edu/~sting/>
+ Info: $Id: imath.h 21 2006-04-02 18:58:36Z sting $
+
+ Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved.
+
+ Permission is hereby granted, free of charge, to any person
+ obtaining a copy of this software and associated documentation files
+ (the "Software"), to deal in the Software without restriction,
+ including without limitation the rights to use, copy, modify, merge,
+ publish, distribute, sublicense, and/or sell copies of the Software,
+ and to permit persons to whom the Software is furnished to do so,
+ subject to the following conditions:
+
+ The above copyright notice and this permission notice shall be
+ included in all copies or substantial portions of the Software.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ SOFTWARE.
+ */
+
+ #ifndef IMATH_H_
+ #define IMATH_H_
+
+ /* use always 32bit digits - should some arch use 16bit digits? */
+ #define USE_LONG_LONG
+
+ #include <limits.h>
+
+ typedef unsigned char mp_sign;
+ typedef unsigned int mp_size;
+ typedef int mp_result;
+ #ifdef USE_LONG_LONG
+ typedef unsigned int mp_digit;
+ typedef unsigned long long mp_word;
+ #else
+ typedef unsigned short mp_digit;
+ typedef unsigned int mp_word;
+ #endif
+
+ typedef struct mpz {
+ mp_digit *digits;
+ mp_size alloc;
+ mp_size used;
+ mp_sign sign;
+ } mpz_t, *mp_int;
+
+ #define MP_DIGITS(Z) ((Z)->digits)
+ #define MP_ALLOC(Z) ((Z)->alloc)
+ #define MP_USED(Z) ((Z)->used)
+ #define MP_SIGN(Z) ((Z)->sign)
+
+ extern const mp_result MP_OK;
+ extern const mp_result MP_FALSE;
+ extern const mp_result MP_TRUE;
+ extern const mp_result MP_MEMORY;
+ extern const mp_result MP_RANGE;
+ extern const mp_result MP_UNDEF;
+ extern const mp_result MP_TRUNC;
+ extern const mp_result MP_BADARG;
+
+ #define MP_DIGIT_BIT (sizeof(mp_digit) * CHAR_BIT)
+ #define MP_WORD_BIT (sizeof(mp_word) * CHAR_BIT)
+
+ #ifdef USE_LONG_LONG
+ # ifndef ULONG_LONG_MAX
+ # ifdef ULLONG_MAX
+ # define ULONG_LONG_MAX ULLONG_MAX
+ # else
+ # error "Maximum value of unsigned long long not defined!"
+ # endif
+ # endif
+ # define MP_DIGIT_MAX (ULONG_MAX * 1ULL)
+ # define MP_WORD_MAX ULONG_LONG_MAX
+ #else
+ # define MP_DIGIT_MAX (USHRT_MAX * 1UL)
+ # define MP_WORD_MAX (UINT_MAX * 1UL)
+ #endif
+
+ #define MP_MIN_RADIX 2
+ #define MP_MAX_RADIX 36
+
+ extern const mp_sign MP_NEG;
+ extern const mp_sign MP_ZPOS;
+
+ #define mp_int_is_odd(Z) ((Z)->digits[0] & 1)
+ #define mp_int_is_even(Z) !((Z)->digits[0] & 1)
+
+ mp_size mp_get_default_precision(void);
+ void mp_set_default_precision(mp_size s);
+ mp_size mp_get_multiply_threshold(void);
+ void mp_set_multiply_threshold(mp_size s);
+
+ mp_result mp_int_init(mp_int z);
+ mp_int mp_int_alloc(void);
+ mp_result mp_int_init_size(mp_int z, mp_size prec);
+ mp_result mp_int_init_copy(mp_int z, mp_int old);
+ mp_result mp_int_init_value(mp_int z, int value);
+ mp_result mp_int_set_value(mp_int z, int value);
+ void mp_int_clear(mp_int z);
+ void mp_int_free(mp_int z);
+
+ mp_result mp_int_copy(mp_int a, mp_int c); /* c = a */
+ void mp_int_swap(mp_int a, mp_int c); /* swap a, c */
+ void mp_int_zero(mp_int z); /* z = 0 */
+ mp_result mp_int_abs(mp_int a, mp_int c); /* c = |a| */
+ mp_result mp_int_neg(mp_int a, mp_int c); /* c = -a */
+ mp_result mp_int_add(mp_int a, mp_int b, mp_int c); /* c = a + b */
+ mp_result mp_int_add_value(mp_int a, int value, mp_int c);
+ mp_result mp_int_sub(mp_int a, mp_int b, mp_int c); /* c = a - b */
+ mp_result mp_int_sub_value(mp_int a, int value, mp_int c);
+ mp_result mp_int_mul(mp_int a, mp_int b, mp_int c); /* c = a * b */
+ mp_result mp_int_mul_value(mp_int a, int value, mp_int c);
+ mp_result mp_int_mul_pow2(mp_int a, int p2, mp_int c);
+ mp_result mp_int_sqr(mp_int a, mp_int c); /* c = a * a */
+ mp_result mp_int_div(mp_int a, mp_int b, /* q = a / b */
+ mp_int q, mp_int r); /* r = a % b */
+ mp_result mp_int_div_value(mp_int a, int value, /* q = a / value */
+ mp_int q, int *r); /* r = a % value */
+ mp_result mp_int_div_pow2(mp_int a, int p2, /* q = a / 2^p2 */
+ mp_int q, mp_int r); /* r = q % 2^p2 */
+ mp_result mp_int_mod(mp_int a, mp_int m, mp_int c); /* c = a % m */
+ #define mp_int_mod_value(A, V, R) mp_int_div_value((A), (V), 0, (R))
+ mp_result mp_int_expt(mp_int a, int b, mp_int c); /* c = a^b */
+ mp_result mp_int_expt_value(int a, int b, mp_int c); /* c = a^b */
+
+ int mp_int_compare(mp_int a, mp_int b); /* a <=> b */
+ int mp_int_compare_unsigned(mp_int a, mp_int b); /* |a| <=> |b| */
+ int mp_int_compare_zero(mp_int z); /* a <=> 0 */
+ int mp_int_compare_value(mp_int z, int value); /* a <=> v */
+
+ /* Returns true if v|a, false otherwise (including errors) */
+ int mp_int_divisible_value(mp_int a, int v);
+
+ /* Returns k >= 0 such that z = 2^k, if one exists; otherwise < 0 */
+ int mp_int_is_pow2(mp_int z);
+
+ mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m,
+ mp_int c); /* c = a^b (mod m) */
+ mp_result mp_int_exptmod_evalue(mp_int a, int value,
+ mp_int m, mp_int c); /* c = a^v (mod m) */
+ mp_result mp_int_exptmod_bvalue(int value, mp_int b,
+ mp_int m, mp_int c); /* c = v^b (mod m) */
+ mp_result mp_int_exptmod_known(mp_int a, mp_int b,
+ mp_int m, mp_int mu,
+ mp_int c); /* c = a^b (mod m) */
+ mp_result mp_int_redux_const(mp_int m, mp_int c);
+
+ mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c); /* c = 1/a (mod m) */
+
+ mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c); /* c = gcd(a, b) */
+
+ mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, /* c = gcd(a, b) */
+ mp_int x, mp_int y); /* c = ax + by */
+
+ mp_result mp_int_sqrt(mp_int a, mp_int c); /* c = floor(sqrt(q)) */
+
+ /* Convert to an int, if representable (returns MP_RANGE if not). */
+ mp_result mp_int_to_int(mp_int z, int *out);
+
+ /* Convert to nul-terminated string with the specified radix, writing at
+ most limit characters including the nul terminator */
+ mp_result mp_int_to_string(mp_int z, mp_size radix,
+ char *str, int limit);
+
+ /* Return the number of characters required to represent
+ z in the given radix. May over-estimate. */
+ mp_result mp_int_string_len(mp_int z, mp_size radix);
+
+ /* Read zero-terminated string into z */
+ mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str);
+ mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str,
+ char **end);
+
+ /* Return the number of significant bits in z */
+ mp_result mp_int_count_bits(mp_int z);
+
+ /* Convert z to two's complement binary, writing at most limit bytes */
+ mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit);
+
+ /* Read a two's complement binary value into z from the given buffer */
+ mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len);
+
+ /* Return the number of bytes required to represent z in binary. */
+ mp_result mp_int_binary_len(mp_int z);
+
+ /* Convert z to unsigned binary, writing at most limit bytes */
+ mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit);
+
+ /* Read an unsigned binary value into z from the given buffer */
+ mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len);
+
+ /* Return the number of bytes required to represent z as unsigned output */
+ mp_result mp_int_unsigned_len(mp_int z);
+
+ /* Return a statically allocated string describing error code res */
+ const char *mp_error_string(mp_result res);
+
+ #if 0
+ void s_print(char *tag, mp_int z);
+ void s_print_buf(char *tag, mp_digit *buf, mp_size num);
+ #endif
+
+ #endif /* end IMATH_H_ */

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