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/* crypto/bn/bn.h */ /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * 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 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. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``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. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ /* ==================================================================== * Copyright (c) 1998-2018 The OpenSSL Project. 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. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED 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 OpenSSL PROJECT OR * ITS 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 product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * * Portions of the attached software ("Contribution") are developed by * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. * * The Contribution is licensed pursuant to the Eric Young open source * license provided above. * * The binary polynomial arithmetic software is originally written by * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. * */ #ifndef HEADER_BN_H # define HEADER_BN_H # include <limits.h> # include <openssl/e_os2.h> # ifndef OPENSSL_NO_FP_API # include <stdio.h> /* FILE */ # endif # include <openssl/ossl_typ.h> # include <openssl/crypto.h> #ifdef __cplusplus extern "C" { #endif /* * These preprocessor symbols control various aspects of the bignum headers * and library code. They're not defined by any "normal" configuration, as * they are intended for development and testing purposes. NB: defining all * three can be useful for debugging application code as well as openssl * itself. BN_DEBUG - turn on various debugging alterations to the bignum * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up * mismanagement of bignum internals. You must also define BN_DEBUG. */ /* #define BN_DEBUG */ /* #define BN_DEBUG_RAND */ # ifndef OPENSSL_SMALL_FOOTPRINT # define BN_MUL_COMBA # define BN_SQR_COMBA # define BN_RECURSION # endif /* * This next option uses the C libraries (2 word)/(1 word) function. If it is * not defined, I use my C version (which is slower). The reason for this * flag is that when the particular C compiler library routine is used, and * the library is linked with a different compiler, the library is missing. * This mostly happens when the library is built with gcc and then linked * using normal cc. This would be a common occurrence because gcc normally * produces code that is 2 times faster than system compilers for the big * number stuff. For machines with only one compiler (or shared libraries), * this should be on. Again this in only really a problem on machines using * "long long's", are 32bit, and are not using my assembler code. */ # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \ defined(OPENSSL_SYS_WIN32) || defined(linux) # ifndef BN_DIV2W # define BN_DIV2W # endif # endif /* * assuming long is 64bit - this is the DEC Alpha unsigned long long is only * 64 bits :-(, don't define BN_LLONG for the DEC Alpha */ # ifdef SIXTY_FOUR_BIT_LONG # define BN_ULLONG unsigned long long # define BN_ULONG unsigned long # define BN_LONG long # define BN_BITS 128 # define BN_BYTES 8 # define BN_BITS2 64 # define BN_BITS4 32 # define BN_MASK (0xffffffffffffffffffffffffffffffffLL) # define BN_MASK2 (0xffffffffffffffffL) # define BN_MASK2l (0xffffffffL) # define BN_MASK2h (0xffffffff00000000L) # define BN_MASK2h1 (0xffffffff80000000L) # define BN_TBIT (0x8000000000000000L) # define BN_DEC_CONV (10000000000000000000UL) # define BN_DEC_FMT1 "%lu" # define BN_DEC_FMT2 "%019lu" # define BN_DEC_NUM 19 # define BN_HEX_FMT1 "%lX" # define BN_HEX_FMT2 "%016lX" # endif /* * This is where the long long data type is 64 bits, but long is 32. For * machines where there are 64bit registers, this is the mode to use. IRIX, * on R4000 and above should use this mode, along with the relevant assembler * code :-). Do NOT define BN_LLONG. */ # ifdef SIXTY_FOUR_BIT # undef BN_LLONG # undef BN_ULLONG # define BN_ULONG unsigned long long # define BN_LONG long long # define BN_BITS 128 # define BN_BYTES 8 # define BN_BITS2 64 # define BN_BITS4 32 # define BN_MASK2 (0xffffffffffffffffLL) # define BN_MASK2l (0xffffffffL) # define BN_MASK2h (0xffffffff00000000LL) # define BN_MASK2h1 (0xffffffff80000000LL) # define BN_TBIT (0x8000000000000000LL) # define BN_DEC_CONV (10000000000000000000ULL) # define BN_DEC_FMT1 "%llu" # define BN_DEC_FMT2 "%019llu" # define BN_DEC_NUM 19 # define BN_HEX_FMT1 "%llX" # define BN_HEX_FMT2 "%016llX" # endif # ifdef THIRTY_TWO_BIT # ifdef BN_LLONG # if defined(_WIN32) && !defined(__GNUC__) # define BN_ULLONG unsigned __int64 # define BN_MASK (0xffffffffffffffffI64) # else # define BN_ULLONG unsigned long long # define BN_MASK (0xffffffffffffffffLL) # endif # endif # define BN_ULONG unsigned int # define BN_LONG int # define BN_BITS 64 # define BN_BYTES 4 # define BN_BITS2 32 # define BN_BITS4 16 # define BN_MASK2 (0xffffffffL) # define BN_MASK2l (0xffff) # define BN_MASK2h1 (0xffff8000L) # define BN_MASK2h (0xffff0000L) # define BN_TBIT (0x80000000L) # define BN_DEC_CONV (1000000000L) # define BN_DEC_FMT1 "%u" # define BN_DEC_FMT2 "%09u" # define BN_DEC_NUM 9 # define BN_HEX_FMT1 "%X" # define BN_HEX_FMT2 "%08X" # endif # define BN_DEFAULT_BITS 1280 # define BN_FLG_MALLOCED 0x01 # define BN_FLG_STATIC_DATA 0x02 /* * avoid leaking exponent information through timing, * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime, * BN_div() will call BN_div_no_branch, * BN_mod_inverse() will call BN_mod_inverse_no_branch. */ # define BN_FLG_CONSTTIME 0x04 # ifdef OPENSSL_NO_DEPRECATED /* deprecated name for the flag */ # define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME /* * avoid leaking exponent information through timings * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */ # endif # ifndef OPENSSL_NO_DEPRECATED # define BN_FLG_FREE 0x8000 /* used for debuging */ # endif # define BN_set_flags(b,n) ((b)->flags|=(n)) # define BN_get_flags(b,n) ((b)->flags&(n)) /* * get a clone of a BIGNUM with changed flags, for *temporary* use only (the * two BIGNUMs cannot not be used in parallel!) */ # define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \ (dest)->top=(b)->top, \ (dest)->dmax=(b)->dmax, \ (dest)->neg=(b)->neg, \ (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \ | ((b)->flags & ~BN_FLG_MALLOCED) \ | BN_FLG_STATIC_DATA \ | (n))) /* Already declared in ossl_typ.h */ # if 0 typedef struct bignum_st BIGNUM; /* Used for temp variables (declaration hidden in bn_lcl.h) */ typedef struct bignum_ctx BN_CTX; typedef struct bn_blinding_st BN_BLINDING; typedef struct bn_mont_ctx_st BN_MONT_CTX; typedef struct bn_recp_ctx_st BN_RECP_CTX; typedef struct bn_gencb_st BN_GENCB; # endif struct bignum_st { BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit * chunks. */ int top; /* Index of last used d +1. */ /* The next are internal book keeping for bn_expand. */ int dmax; /* Size of the d array. */ int neg; /* one if the number is negative */ int flags; }; /* Used for montgomery multiplication */ struct bn_mont_ctx_st { int ri; /* number of bits in R */ BIGNUM RR; /* used to convert to montgomery form */ BIGNUM N; /* The modulus */ BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only * stored for bignum algorithm) */ BN_ULONG n0[2]; /* least significant word(s) of Ni; (type * changed with 0.9.9, was "BN_ULONG n0;" * before) */ int flags; }; /* * Used for reciprocal division/mod functions It cannot be shared between * threads */ struct bn_recp_ctx_st { BIGNUM N; /* the divisor */ BIGNUM Nr; /* the reciprocal */ int num_bits; int shift; int flags; }; /* Used for slow "generation" functions. */ struct bn_gencb_st { unsigned int ver; /* To handle binary (in)compatibility */ void *arg; /* callback-specific data */ union { /* if(ver==1) - handles old style callbacks */ void (*cb_1) (int, int, void *); /* if(ver==2) - new callback style */ int (*cb_2) (int, int, BN_GENCB *); } cb; }; /* Wrapper function to make using BN_GENCB easier, */ int BN_GENCB_call(BN_GENCB *cb, int a, int b); /* Macro to populate a BN_GENCB structure with an "old"-style callback */ # define BN_GENCB_set_old(gencb, callback, cb_arg) { \ BN_GENCB *tmp_gencb = (gencb); \ tmp_gencb->ver = 1; \ tmp_gencb->arg = (cb_arg); \ tmp_gencb->cb.cb_1 = (callback); } /* Macro to populate a BN_GENCB structure with a "new"-style callback */ # define BN_GENCB_set(gencb, callback, cb_arg) { \ BN_GENCB *tmp_gencb = (gencb); \ tmp_gencb->ver = 2; \ tmp_gencb->arg = (cb_arg); \ tmp_gencb->cb.cb_2 = (callback); } # define BN_prime_checks 0 /* default: select number of iterations based * on the size of the number */ /* * BN_prime_checks_for_size() returns the number of Miller-Rabin iterations * that will be done for checking that a random number is probably prime. The * error rate for accepting a composite number as prime depends on the size of * the prime |b|. The error rates used are for calculating an RSA key with 2 primes, * and so the level is what you would expect for a key of double the size of the * prime. * * This table is generated using the algorithm of FIPS PUB 186-4 * Digital Signature Standard (DSS), section F.1, page 117. * (https://dx.doi.org/10.6028/NIST.FIPS.186-4) * * The following magma script was used to generate the output: * securitybits:=125; * k:=1024; * for t:=1 to 65 do * for M:=3 to Floor(2*Sqrt(k-1)-1) do * S:=0; * // Sum over m * for m:=3 to M do * s:=0; * // Sum over j * for j:=2 to m do * s+:=(RealField(32)!2)^-(j+(k-1)/j); * end for; * S+:=2^(m-(m-1)*t)*s; * end for; * A:=2^(k-2-M*t); * B:=8*(Pi(RealField(32))^2-6)/3*2^(k-2)*S; * pkt:=2.00743*Log(2)*k*2^-k*(A+B); * seclevel:=Floor(-Log(2,pkt)); * if seclevel ge securitybits then * printf "k: %5o, security: %o bits (t: %o, M: %o)\n",k,seclevel,t,M; * break; * end if; * end for; * if seclevel ge securitybits then break; end if; * end for; * * It can be run online at: * http://magma.maths.usyd.edu.au/calc * * And will output: * k: 1024, security: 129 bits (t: 6, M: 23) * * k is the number of bits of the prime, securitybits is the level we want to * reach. * * prime length | RSA key size | # MR tests | security level * -------------+--------------|------------+--------------- * (b) >= 6394 | >= 12788 | 3 | 256 bit * (b) >= 3747 | >= 7494 | 3 | 192 bit * (b) >= 1345 | >= 2690 | 4 | 128 bit * (b) >= 1080 | >= 2160 | 5 | 128 bit * (b) >= 852 | >= 1704 | 5 | 112 bit * (b) >= 476 | >= 952 | 5 | 80 bit * (b) >= 400 | >= 800 | 6 | 80 bit * (b) >= 347 | >= 694 | 7 | 80 bit * (b) >= 308 | >= 616 | 8 | 80 bit * (b) >= 55 | >= 110 | 27 | 64 bit * (b) >= 6 | >= 12 | 34 | 64 bit */ # define BN_prime_checks_for_size(b) ((b) >= 3747 ? 3 : \ (b) >= 1345 ? 4 : \ (b) >= 476 ? 5 : \ (b) >= 400 ? 6 : \ (b) >= 347 ? 7 : \ (b) >= 308 ? 8 : \ (b) >= 55 ? 27 : \ /* b >= 6 */ 34) # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8) /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */ # define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \ (((w) == 0) && ((a)->top == 0))) # define BN_is_zero(a) ((a)->top == 0) # define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg) # define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg)) # define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1)) # define BN_one(a) (BN_set_word((a),1)) # define BN_zero_ex(a) \ do { \ BIGNUM *_tmp_bn = (a); \ _tmp_bn->top = 0; \ _tmp_bn->neg = 0; \ } while(0) # ifdef OPENSSL_NO_DEPRECATED # define BN_zero(a) BN_zero_ex(a) # else # define BN_zero(a) (BN_set_word((a),0)) # endif const BIGNUM *BN_value_one(void); char *BN_options(void); BN_CTX *BN_CTX_new(void); # ifndef OPENSSL_NO_DEPRECATED void BN_CTX_init(BN_CTX *c); # endif void BN_CTX_free(BN_CTX *c); void BN_CTX_start(BN_CTX *ctx); BIGNUM *BN_CTX_get(BN_CTX *ctx); void BN_CTX_end(BN_CTX *ctx); int BN_rand(BIGNUM *rnd, int bits, int top, int bottom); int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom); int BN_rand_range(BIGNUM *rnd, const BIGNUM *range); int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range); int BN_num_bits(const BIGNUM *a); int BN_num_bits_word(BN_ULONG); BIGNUM *BN_new(void); void BN_init(BIGNUM *); void BN_clear_free(BIGNUM *a); BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b); void BN_swap(BIGNUM *a, BIGNUM *b); BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret); int BN_bn2bin(const BIGNUM *a, unsigned char *to); BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret); int BN_bn2mpi(const BIGNUM *a, unsigned char *to); int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); /** BN_set_negative sets sign of a BIGNUM * \param b pointer to the BIGNUM object * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise */ void BN_set_negative(BIGNUM *b, int n); /** BN_is_negative returns 1 if the BIGNUM is negative * \param a pointer to the BIGNUM object * \return 1 if a < 0 and 0 otherwise */ # define BN_is_negative(a) ((a)->neg != 0) int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx); # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx)) int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx); int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx); int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m); int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx); int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m); int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx); int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m); int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx); int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m); BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w); BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w); int BN_mul_word(BIGNUM *a, BN_ULONG w); int BN_add_word(BIGNUM *a, BN_ULONG w); int BN_sub_word(BIGNUM *a, BN_ULONG w); int BN_set_word(BIGNUM *a, BN_ULONG w); BN_ULONG BN_get_word(const BIGNUM *a); int BN_cmp(const BIGNUM *a, const BIGNUM *b); void BN_free(BIGNUM *a); int BN_is_bit_set(const BIGNUM *a, int n); int BN_lshift(BIGNUM *r, const BIGNUM *a, int n); int BN_lshift1(BIGNUM *r, const BIGNUM *a); int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx); int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx); int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont); int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx); int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1, const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx); int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx); int BN_mask_bits(BIGNUM *a, int n); # ifndef OPENSSL_NO_FP_API int BN_print_fp(FILE *fp, const BIGNUM *a); # endif # ifdef HEADER_BIO_H int BN_print(BIO *fp, const BIGNUM *a); # else int BN_print(void *fp, const BIGNUM *a); # endif int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx); int BN_rshift(BIGNUM *r, const BIGNUM *a, int n); int BN_rshift1(BIGNUM *r, const BIGNUM *a); void BN_clear(BIGNUM *a); BIGNUM *BN_dup(const BIGNUM *a); int BN_ucmp(const BIGNUM *a, const BIGNUM *b); int BN_set_bit(BIGNUM *a, int n); int BN_clear_bit(BIGNUM *a, int n); char *BN_bn2hex(const BIGNUM *a); char *BN_bn2dec(const BIGNUM *a); int BN_hex2bn(BIGNUM **a, const char *str); int BN_dec2bn(BIGNUM **a, const char *str); int BN_asc2bn(BIGNUM **a, const char *str); int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns * -2 for * error */ BIGNUM *BN_mod_inverse(BIGNUM *ret, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx); BIGNUM *BN_mod_sqrt(BIGNUM *ret, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx); void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords); /* Deprecated versions */ # ifndef OPENSSL_NO_DEPRECATED BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, void (*callback) (int, int, void *), void *cb_arg); int BN_is_prime(const BIGNUM *p, int nchecks, void (*callback) (int, int, void *), BN_CTX *ctx, void *cb_arg); int BN_is_prime_fasttest(const BIGNUM *p, int nchecks, void (*callback) (int, int, void *), BN_CTX *ctx, void *cb_arg, int do_trial_division); # endif /* !defined(OPENSSL_NO_DEPRECATED) */ /* Newer versions */ int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb); int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb); int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, int do_trial_division, BN_GENCB *cb); int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx); int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb); int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1, BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb); BN_MONT_CTX *BN_MONT_CTX_new(void); void BN_MONT_CTX_init(BN_MONT_CTX *ctx); int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_MONT_CTX *mont, BN_CTX *ctx); # define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\ (r),(a),&((mont)->RR),(mont),(ctx)) int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx); void BN_MONT_CTX_free(BN_MONT_CTX *mont); int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx); BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from); BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, const BIGNUM *mod, BN_CTX *ctx); /* BN_BLINDING flags */ # define BN_BLINDING_NO_UPDATE 0x00000001 # define BN_BLINDING_NO_RECREATE 0x00000002 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod); void BN_BLINDING_free(BN_BLINDING *b); int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx); int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx); int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx); int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *); int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *); # ifndef OPENSSL_NO_DEPRECATED unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *); void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long); # endif CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *); unsigned long BN_BLINDING_get_flags(const BN_BLINDING *); void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long); BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b, const BIGNUM *e, BIGNUM *m, BN_CTX *ctx, int (*bn_mod_exp) (BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx), BN_MONT_CTX *m_ctx); # ifndef OPENSSL_NO_DEPRECATED void BN_set_params(int mul, int high, int low, int mont); int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */ # endif void BN_RECP_CTX_init(BN_RECP_CTX *recp); BN_RECP_CTX *BN_RECP_CTX_new(void); void BN_RECP_CTX_free(BN_RECP_CTX *recp); int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx); int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, BN_RECP_CTX *recp, BN_CTX *ctx); int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx); int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, BN_RECP_CTX *recp, BN_CTX *ctx); # ifndef OPENSSL_NO_EC2M /* * Functions for arithmetic over binary polynomials represented by BIGNUMs. * The BIGNUM::neg property of BIGNUMs representing binary polynomials is * ignored. Note that input arguments are not const so that their bit arrays * can be expanded to the appropriate size if needed. */ /* * r = a + b */ int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); # define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b) /* * r=a mod p */ int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /* r = (a * b) mod p */ int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a * a) mod p */ int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = (1 / b) mod p */ int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */ int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */ int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = sqrt(a) mod p */ int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r^2 + r = a mod p */ int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); # define BN_GF2m_cmp(a, b) BN_ucmp((a), (b)) /*- * Some functions allow for representation of the irreducible polynomials * as an unsigned int[], say p. The irreducible f(t) is then of the form: * t^p[0] + t^p[1] + ... + t^p[k] * where m = p[0] > p[1] > ... > p[k] = 0. */ /* r = a mod p */ int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]); /* r = (a * b) mod p */ int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx); /* r = (a * a) mod p */ int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx); /* r = (1 / b) mod p */ int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[], BN_CTX *ctx); /* r = (a / b) mod p */ int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */ int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */ int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx); /* r^2 + r = a mod p */ int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx); int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max); int BN_GF2m_arr2poly(const int p[], BIGNUM *a); # endif /* * faster mod functions for the 'NIST primes' 0 <= a < p^2 */ int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); const BIGNUM *BN_get0_nist_prime_192(void); const BIGNUM *BN_get0_nist_prime_224(void); const BIGNUM *BN_get0_nist_prime_256(void); const BIGNUM *BN_get0_nist_prime_384(void); const BIGNUM *BN_get0_nist_prime_521(void); /* library internal functions */ # define bn_expand(a,bits) \ ( \ bits > (INT_MAX - BN_BITS2 + 1) ? \ NULL \ : \ (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax) ? \ (a) \ : \ bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2) \ ) # define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words))) BIGNUM *bn_expand2(BIGNUM *a, int words); # ifndef OPENSSL_NO_DEPRECATED BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */ # endif /*- * Bignum consistency macros * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from * bignum data after direct manipulations on the data. There is also an * "internal" macro, bn_check_top(), for verifying that there are no leading * zeroes. Unfortunately, some auditing is required due to the fact that * bn_fix_top() has become an overabused duct-tape because bignum data is * occasionally passed around in an inconsistent state. So the following * changes have been made to sort this out; * - bn_fix_top()s implementation has been moved to bn_correct_top() * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and * bn_check_top() is as before. * - if BN_DEBUG *is* defined; * - bn_check_top() tries to pollute unused words even if the bignum 'top' is * consistent. (ed: only if BN_DEBUG_RAND is defined) * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything. * The idea is to have debug builds flag up inconsistent bignums when they * occur. If that occurs in a bn_fix_top(), we examine the code in question; if * the use of bn_fix_top() was appropriate (ie. it follows directly after code * that manipulates the bignum) it is converted to bn_correct_top(), and if it * was not appropriate, we convert it permanently to bn_check_top() and track * down the cause of the bug. Eventually, no internal code should be using the * bn_fix_top() macro. External applications and libraries should try this with * their own code too, both in terms of building against the openssl headers * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it * defined. This not only improves external code, it provides more test * coverage for openssl's own code. */ # ifdef BN_DEBUG /* We only need assert() when debugging */ # include <assert.h> /* * The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with * bn_correct_top, in other words such vectors are permitted to have zeros * in most significant limbs. Such vectors are used internally to achieve * execution time invariance for critical operations with private keys. * It's BN_DEBUG-only flag, because user application is not supposed to * observe it anyway. Moreover, optimizing compiler would actually remove * all operations manipulating the bit in question in non-BN_DEBUG build. */ # define BN_FLG_FIXED_TOP 0x10000 # ifdef BN_DEBUG_RAND /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */ # ifndef RAND_pseudo_bytes int RAND_pseudo_bytes(unsigned char *buf, int num); # define BN_DEBUG_TRIX # endif # define bn_pollute(a) \ do { \ const BIGNUM *_bnum1 = (a); \ if(_bnum1->top < _bnum1->dmax) { \ unsigned char _tmp_char; \ /* We cast away const without the compiler knowing, any \ * *genuinely* constant variables that aren't mutable \ * wouldn't be constructed with top!=dmax. */ \ BN_ULONG *_not_const; \ memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \ /* Debug only - safe to ignore error return */ \ RAND_pseudo_bytes(&_tmp_char, 1); \ memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \ (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \ } \ } while(0) # ifdef BN_DEBUG_TRIX # undef RAND_pseudo_bytes # endif # else # define bn_pollute(a) # endif # define bn_check_top(a) \ do { \ const BIGNUM *_bnum2 = (a); \ if (_bnum2 != NULL) { \ int _top = _bnum2->top; \ assert((_top == 0) || \ (_bnum2->flags & BN_FLG_FIXED_TOP) || \ (_bnum2->d[_top - 1] != 0)); \ bn_pollute(_bnum2); \ } \ } while(0) # define bn_fix_top(a) bn_check_top(a) # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2) # define bn_wcheck_size(bn, words) \ do { \ const BIGNUM *_bnum2 = (bn); \ assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \ /* avoid unused variable warning with NDEBUG */ \ (void)(_bnum2); \ } while(0) # else /* !BN_DEBUG */ # define BN_FLG_FIXED_TOP 0 # define bn_pollute(a) # define bn_check_top(a) # define bn_fix_top(a) bn_correct_top(a) # define bn_check_size(bn, bits) # define bn_wcheck_size(bn, words) # endif # define bn_correct_top(a) \ { \ BN_ULONG *ftl; \ int tmp_top = (a)->top; \ if (tmp_top > 0) \ { \ for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \ if (*(ftl--)) break; \ (a)->top = tmp_top; \ } \ if ((a)->top == 0) \ (a)->neg = 0; \ bn_pollute(a); \ } BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w); BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w); void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num); BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, int num); BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, int num); /* Primes from RFC 2409 */ BIGNUM *get_rfc2409_prime_768(BIGNUM *bn); BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn); /* Primes from RFC 3526 */ BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn); BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn); BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn); BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn); BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn); BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn); int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom); /* BEGIN ERROR CODES */ /* * The following lines are auto generated by the script mkerr.pl. Any changes * made after this point may be overwritten when the script is next run. */ void ERR_load_BN_strings(void); /* Error codes for the BN functions. */ /* Function codes. */ # define BN_F_BNRAND 127 # define BN_F_BN_BLINDING_CONVERT_EX 100 # define BN_F_BN_BLINDING_CREATE_PARAM 128 # define BN_F_BN_BLINDING_INVERT_EX 101 # define BN_F_BN_BLINDING_NEW 102 # define BN_F_BN_BLINDING_UPDATE 103 # define BN_F_BN_BN2DEC 104 # define BN_F_BN_BN2HEX 105 # define BN_F_BN_CTX_GET 116 # define BN_F_BN_CTX_NEW 106 # define BN_F_BN_CTX_START 129 # define BN_F_BN_DIV 107 # define BN_F_BN_DIV_NO_BRANCH 138 # define BN_F_BN_DIV_RECP 130 # define BN_F_BN_EXP 123 # define BN_F_BN_EXPAND2 108 # define BN_F_BN_EXPAND_INTERNAL 120 # define BN_F_BN_GF2M_MOD 131 # define BN_F_BN_GF2M_MOD_EXP 132 # define BN_F_BN_GF2M_MOD_MUL 133 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135 # define BN_F_BN_GF2M_MOD_SQR 136 # define BN_F_BN_GF2M_MOD_SQRT 137 # define BN_F_BN_LSHIFT 145 # define BN_F_BN_MOD_EXP2_MONT 118 # define BN_F_BN_MOD_EXP_MONT 109 # define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124 # define BN_F_BN_MOD_EXP_MONT_WORD 117 # define BN_F_BN_MOD_EXP_RECP 125 # define BN_F_BN_MOD_EXP_SIMPLE 126 # define BN_F_BN_MOD_INVERSE 110 # define BN_F_BN_MOD_INVERSE_NO_BRANCH 139 # define BN_F_BN_MOD_LSHIFT_QUICK 119 # define BN_F_BN_MOD_MUL_RECIPROCAL 111 # define BN_F_BN_MOD_SQRT 121 # define BN_F_BN_MPI2BN 112 # define BN_F_BN_NEW 113 # define BN_F_BN_RAND 114 # define BN_F_BN_RAND_RANGE 122 # define BN_F_BN_RSHIFT 146 # define BN_F_BN_USUB 115 /* Reason codes. */ # define BN_R_ARG2_LT_ARG3 100 # define BN_R_BAD_RECIPROCAL 101 # define BN_R_BIGNUM_TOO_LONG 114 # define BN_R_BITS_TOO_SMALL 118 # define BN_R_CALLED_WITH_EVEN_MODULUS 102 # define BN_R_DIV_BY_ZERO 103 # define BN_R_ENCODING_ERROR 104 # define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105 # define BN_R_INPUT_NOT_REDUCED 110 # define BN_R_INVALID_LENGTH 106 # define BN_R_INVALID_RANGE 115 # define BN_R_INVALID_SHIFT 119 # define BN_R_NOT_A_SQUARE 111 # define BN_R_NOT_INITIALIZED 107 # define BN_R_NO_INVERSE 108 # define BN_R_NO_SOLUTION 116 # define BN_R_P_IS_NOT_PRIME 112 # define BN_R_TOO_MANY_ITERATIONS 113 # define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109 #ifdef __cplusplus } #endif #endif