/*-
* SPDX-License-Identifier: BSD-2-Clause
*
* Copyright (c) 2001 Dima Dorfman.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
/*
* This is the traditional Berkeley MP library implemented in terms of
* the OpenSSL BIGNUM library. It was written to replace libgmp, and
* is meant to be as compatible with the latter as feasible.
*
* There seems to be a lack of documentation for the Berkeley MP
* interface. All I could find was libgmp documentation (which didn't
* talk about the semantics of the functions) and an old SunOS 4.1
* manual page from 1989. The latter wasn't very detailed, either,
* but at least described what the function's arguments were. In
* general the interface seems to be archaic, somewhat poorly
* designed, and poorly, if at all, documented. It is considered
* harmful.
*
* Miscellaneous notes on this implementation:
*
* - The SunOS manual page mentioned above indicates that if an error
* occurs, the library should "produce messages and core images."
* Given that most of the functions don't have return values (and
* thus no sane way of alerting the caller to an error), this seems
* reasonable. The MPERR and MPERRX macros call warn and warnx,
* respectively, then abort().
*
* - All the functions which take an argument to be "filled in"
* assume that the argument has been initialized by one of the *tom()
* routines before being passed to it. I never saw this documented
* anywhere, but this seems to be consistent with the way this
* library is used.
*
* - msqrt() is the only routine which had to be implemented which
* doesn't have a close counterpart in the OpenSSL BIGNUM library.
* It was implemented by hand using Newton's recursive formula.
* Doing it this way, although more error-prone, has the positive
* sideaffect of testing a lot of other functions; if msqrt()
* produces the correct results, most of the other routines will as
* well.
*
* - Internal-use-only routines (i.e., those defined here statically
* and not in mp.h) have an underscore prepended to their name (this
* is more for aesthetical reasons than technical). All such
* routines take an extra argument, 'msg', that denotes what they
* should call themselves in an error message. This is so a user
* doesn't get an error message from a function they didn't call.
*/
#include <sys/cdefs.h>
#include <ctype.h>
#include <err.h>
#include <errno.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <openssl/crypto.h>
#include <openssl/err.h>
#include "mp.h"
#define MPERR(s) do { warn s; abort(); } while (0)
#define MPERRX(s) do { warnx s; abort(); } while (0)
#define BN_ERRCHECK(msg, expr) do { \
if (!(expr)) _bnerr(msg); \
} while (0)
static void _bnerr(const char *);
static MINT *_dtom(const char *, const char *);
static MINT *_itom(const char *, short);
static void _madd(const char *, const MINT *, const MINT *, MINT *);
static int _mcmpa(const char *, const MINT *, const MINT *);
static void _mdiv(const char *, const MINT *, const MINT *, MINT *, MINT *,
BN_CTX *);
static void _mfree(const char *, MINT *);
static void _moveb(const char *, const BIGNUM *, MINT *);
static void _movem(const char *, const MINT *, MINT *);
static void _msub(const char *, const MINT *, const MINT *, MINT *);
static char *_mtod(const char *, const MINT *);
static char *_mtox(const char *, const MINT *);
static void _mult(const char *, const MINT *, const MINT *, MINT *, BN_CTX *);
static void _sdiv(const char *, const MINT *, short, MINT *, short *, BN_CTX *);
static MINT *_xtom(const char *, const char *);
/*
* Report an error from one of the BN_* functions using MPERRX.
*/
static void
_bnerr(const char *msg)
{
ERR_load_crypto_strings();
MPERRX(("%s: %s", msg, ERR_reason_error_string(ERR_get_error())));
}
/*
* Convert a decimal string to an MINT.
*/
static MINT *
_dtom(const char *msg, const char *s)
{
MINT *mp;
mp = malloc(sizeof(*mp));
if (mp == NULL)
MPERR(("%s", msg));
mp->bn = BN_new();
if (mp->bn == NULL)
_bnerr(msg);
BN_ERRCHECK(msg, BN_dec2bn(&mp->bn, s));
return (mp);
}
/*
* Compute the greatest common divisor of mp1 and mp2; result goes in rmp.
*/
void
mp_gcd(const MINT *mp1, const MINT *mp2, MINT *rmp)
{
BIGNUM *b;
BN_CTX *c;
b = NULL;
c = BN_CTX_new();
if (c != NULL)
b = BN_new();
if (c == NULL || b == NULL)
_bnerr("gcd");
BN_ERRCHECK("gcd", BN_gcd(b, mp1->bn, mp2->bn, c));
_moveb("gcd", b, rmp);
BN_free(b);
BN_CTX_free(c);
}
/*
* Make an MINT out of a short integer. Return value must be mfree()'d.
*/
static MINT *
_itom(const char *msg, short n)
{
MINT *mp;
char *s;
asprintf(&s, "%x", n);
if (s == NULL)
MPERR(("%s", msg));
mp = _xtom(msg, s);
free(s);
return (mp);
}
MINT *
mp_itom(short n)
{
return (_itom("itom", n));
}
/*
* Compute rmp=mp1+mp2.
*/
static void
_madd(const char *msg, const MINT *mp1, const MINT *mp2, MINT *rmp)
{
BIGNUM *b;
b = BN_new();
if (b == NULL)
_bnerr(msg);
BN_ERRCHECK(msg, BN_add(b, mp1->bn, mp2->bn));
_moveb(msg, b, rmp);
BN_free(b);
}
void
mp_madd(const MINT *mp1, const MINT *mp2, MINT *rmp)
{
_madd("madd", mp1, mp2, rmp);
}
/*
* Return -1, 0, or 1 if mp1<mp2, mp1==mp2, or mp1>mp2, respectivley.
*/
int
mp_mcmp(const MINT *mp1, const MINT *mp2)
{
return (BN_cmp(mp1->bn, mp2->bn));
}
/*
* Same as mcmp but compares absolute values.
*/
static int
_mcmpa(const char *msg __unused, const MINT *mp1, const MINT *mp2)
{
return (BN_ucmp(mp1->bn, mp2->bn));
}
/*
* Compute qmp=nmp/dmp and rmp=nmp%dmp.
*/
static void
_mdiv(const char *msg, const MINT *nmp, const MINT *dmp, MINT *qmp, MINT *rmp,
BN_CTX *c)
{
BIGNUM *q, *r;
q = NULL;
r = BN_new();
if (r != NULL)
q = BN_new();
if (r == NULL || q == NULL)
_bnerr(msg);
BN_ERRCHECK(msg, BN_div(q, r, nmp->bn, dmp->bn, c));
_moveb(msg, q, qmp);
_moveb(msg, r, rmp);
BN_free(q);
BN_free(r);
}
void
mp_mdiv(const MINT *nmp, const MINT *dmp, MINT *qmp, MINT *rmp)
{
BN_CTX *c;
c = BN_CTX_new();
if (c == NULL)
_bnerr("mdiv");
_mdiv("mdiv", nmp, dmp, qmp, rmp, c);
BN_CTX_free(c);
}
/*
* Free memory associated with an MINT.
*/
static void
_mfree(const char *msg __unused, MINT *mp)
{
BN_clear(mp->bn);
BN_free(mp->bn);
free(mp);
}
void
mp_mfree(MINT *mp)
{
_mfree("mfree", mp);
}
/*
* Read an integer from standard input and stick the result in mp.
* The input is treated to be in base 10. This must be the silliest
* API in existence; why can't the program read in a string and call
* xtom()? (Or if base 10 is desires, perhaps dtom() could be
* exported.)
*/
void
mp_min(MINT *mp)
{
MINT *rmp;
char *line, *nline;
size_t linelen;
line = fgetln(stdin, &linelen);
if (line == NULL)
MPERR(("min"));
nline = malloc(linelen + 1);
if (nline == NULL)
MPERR(("min"));
memcpy(nline, line, linelen);
nline[linelen] = '\0';
rmp = _dtom("min", nline);
_movem("min", rmp, mp);
_mfree("min", rmp);
free(nline);
}
/*
* Print the value of mp to standard output in base 10. See blurb
* above min() for why this is so useless.
*/
void
mp_mout(const MINT *mp)
{
char *s;
s = _mtod("mout", mp);
printf("%s", s);
free(s);
}
/*
* Set the value of tmp to the value of smp (i.e., tmp=smp).
*/
void
mp_move(const MINT *smp, MINT *tmp)
{
_movem("move", smp, tmp);
}
/*
* Internal routine to set the value of tmp to that of sbp.
*/
static void
_moveb(const char *msg, const BIGNUM *sbp, MINT *tmp)
{
BN_ERRCHECK(msg, BN_copy(tmp->bn, sbp));
}
/*
* Internal routine to set the value of tmp to that of smp.
*/
static void
_movem(const char *msg, const MINT *smp, MINT *tmp)
{
BN_ERRCHECK(msg, BN_copy(tmp->bn, smp->bn));
}
/*
* Compute the square root of nmp and put the result in xmp. The
* remainder goes in rmp. Should satisfy: rmp=nmp-(xmp*xmp).
*
* Note that the OpenSSL BIGNUM library does not have a square root
* function, so this had to be implemented by hand using Newton's
* recursive formula:
*
* x = (x + (n / x)) / 2
*
* where x is the square root of the positive number n. In the
* beginning, x should be a reasonable guess, but the value 1,
* although suboptimal, works, too; this is that is used below.
*/
void
mp_msqrt(const MINT *nmp, MINT *xmp, MINT *rmp)
{
BN_CTX *c;
MINT *tolerance;
MINT *ox, *x;
MINT *z1, *z2, *z3;
short i;
c = BN_CTX_new();
if (c == NULL)
_bnerr("msqrt");
tolerance = _itom("msqrt", 1);
x = _itom("msqrt", 1);
ox = _itom("msqrt", 0);
z1 = _itom("msqrt", 0);
z2 = _itom("msqrt", 0);
z3 = _itom("msqrt", 0);
do {
_movem("msqrt", x, ox);
_mdiv("msqrt", nmp, x, z1, z2, c);
_madd("msqrt", x, z1, z2);
_sdiv("msqrt", z2, 2, x, &i, c);
_msub("msqrt", ox, x, z3);
} while (_mcmpa("msqrt", z3, tolerance) == 1);
_movem("msqrt", x, xmp);
_mult("msqrt", x, x, z1, c);
_msub("msqrt", nmp, z1, z2);
_movem("msqrt", z2, rmp);
_mfree("msqrt", tolerance);
_mfree("msqrt", ox);
_mfree("msqrt", x);
_mfree("msqrt", z1);
_mfree("msqrt", z2);
_mfree("msqrt", z3);
BN_CTX_free(c);
}
/*
* Compute rmp=mp1-mp2.
*/
static void
_msub(const char *msg, const MINT *mp1, const MINT *mp2, MINT *rmp)
{
BIGNUM *b;
b = BN_new();
if (b == NULL)
_bnerr(msg);
BN_ERRCHECK(msg, BN_sub(b, mp1->bn, mp2->bn));
_moveb(msg, b, rmp);
BN_free(b);
}
void
mp_msub(const MINT *mp1, const MINT *mp2, MINT *rmp)
{
_msub("msub", mp1, mp2, rmp);
}
/*
* Return a decimal representation of mp. Return value must be
* free()'d.
*/
static char *
_mtod(const char *msg, const MINT *mp)
{
char *s, *s2;
s = BN_bn2dec(mp->bn);
if (s == NULL)
_bnerr(msg);
asprintf(&s2, "%s", s);
if (s2 == NULL)
MPERR(("%s", msg));
OPENSSL_free(s);
return (s2);
}
/*
* Return a hexadecimal representation of mp. Return value must be
* free()'d.
*/
static char *
_mtox(const char *msg, const MINT *mp)
{
char *p, *s, *s2;
int len;
s = BN_bn2hex(mp->bn);
if (s == NULL)
_bnerr(msg);
asprintf(&s2, "%s", s);
if (s2 == NULL)
MPERR(("%s", msg));
OPENSSL_free(s);
/*
* This is a kludge for libgmp compatibility. The latter's
* implementation of this function returns lower-case letters,
* but BN_bn2hex returns upper-case. Some programs (e.g.,
* newkey(1)) are sensitive to this. Although it's probably
* their fault, it's nice to be compatible.
*/
len = strlen(s2);
for (p = s2; p < s2 + len; p++)
*p = tolower(*p);
return (s2);
}
char *
mp_mtox(const MINT *mp)
{
return (_mtox("mtox", mp));
}
/*
* Compute rmp=mp1*mp2.
*/
static void
_mult(const char *msg, const MINT *mp1, const MINT *mp2, MINT *rmp, BN_CTX *c)
{
BIGNUM *b;
b = BN_new();
if (b == NULL)
_bnerr(msg);
BN_ERRCHECK(msg, BN_mul(b, mp1->bn, mp2->bn, c));
_moveb(msg, b, rmp);
BN_free(b);
}
void
mp_mult(const MINT *mp1, const MINT *mp2, MINT *rmp)
{
BN_CTX *c;
c = BN_CTX_new();
if (c == NULL)
_bnerr("mult");
_mult("mult", mp1, mp2, rmp, c);
BN_CTX_free(c);
}
/*
* Compute rmp=(bmp^emp)mod mmp. (Note that here and above rpow() '^'
* means 'raise to power', not 'bitwise XOR'.)
*/
void
mp_pow(const MINT *bmp, const MINT *emp, const MINT *mmp, MINT *rmp)
{
BIGNUM *b;
BN_CTX *c;
b = NULL;
c = BN_CTX_new();
if (c != NULL)
b = BN_new();
if (c == NULL || b == NULL)
_bnerr("pow");
BN_ERRCHECK("pow", BN_mod_exp(b, bmp->bn, emp->bn, mmp->bn, c));
_moveb("pow", b, rmp);
BN_free(b);
BN_CTX_free(c);
}
/*
* Compute rmp=bmp^e. (See note above pow().)
*/
void
mp_rpow(const MINT *bmp, short e, MINT *rmp)
{
MINT *emp;
BIGNUM *b;
BN_CTX *c;
b = NULL;
c = BN_CTX_new();
if (c != NULL)
b = BN_new();
if (c == NULL || b == NULL)
_bnerr("rpow");
emp = _itom("rpow", e);
BN_ERRCHECK("rpow", BN_exp(b, bmp->bn, emp->bn, c));
_moveb("rpow", b, rmp);
_mfree("rpow", emp);
BN_free(b);
BN_CTX_free(c);
}
/*
* Compute qmp=nmp/d and ro=nmp%d.
*/
static void
_sdiv(const char *msg, const MINT *nmp, short d, MINT *qmp, short *ro,
BN_CTX *c)
{
MINT *dmp, *rmp;
BIGNUM *q, *r;
char *s;
r = NULL;
q = BN_new();
if (q != NULL)
r = BN_new();
if (q == NULL || r == NULL)
_bnerr(msg);
dmp = _itom(msg, d);
rmp = _itom(msg, 0);
BN_ERRCHECK(msg, BN_div(q, r, nmp->bn, dmp->bn, c));
_moveb(msg, q, qmp);
_moveb(msg, r, rmp);
s = _mtox(msg, rmp);
errno = 0;
*ro = strtol(s, NULL, 16);
if (errno != 0)
MPERR(("%s underflow or overflow", msg));
free(s);
_mfree(msg, dmp);
_mfree(msg, rmp);
BN_free(r);
BN_free(q);
}
void
mp_sdiv(const MINT *nmp, short d, MINT *qmp, short *ro)
{
BN_CTX *c;
c = BN_CTX_new();
if (c == NULL)
_bnerr("sdiv");
_sdiv("sdiv", nmp, d, qmp, ro, c);
BN_CTX_free(c);
}
/*
* Convert a hexadecimal string to an MINT.
*/
static MINT *
_xtom(const char *msg, const char *s)
{
MINT *mp;
mp = malloc(sizeof(*mp));
if (mp == NULL)
MPERR(("%s", msg));
mp->bn = BN_new();
if (mp->bn == NULL)
_bnerr(msg);
BN_ERRCHECK(msg, BN_hex2bn(&mp->bn, s));
return (mp);
}
MINT *
mp_xtom(const char *s)
{
return (_xtom("xtom", s));
}
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