| /* 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) 1998-2006 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 OPENSSL_HEADER_BN_INTERNAL_H |
| #define OPENSSL_HEADER_BN_INTERNAL_H |
| |
| #include <openssl/base.h> |
| |
| #if defined(OPENSSL_X86_64) && defined(_MSC_VER) |
| OPENSSL_MSVC_PRAGMA(warning(push, 3)) |
| #include <intrin.h> |
| OPENSSL_MSVC_PRAGMA(warning(pop)) |
| #pragma intrinsic(__umulh, _umul128) |
| #endif |
| |
| #include "../../internal.h" |
| |
| #if defined(__cplusplus) |
| extern "C" { |
| #endif |
| |
| #if defined(OPENSSL_64_BIT) |
| |
| #if !defined(_MSC_VER) |
| // MSVC doesn't support two-word integers on 64-bit. |
| #define BN_ULLONG uint128_t |
| #endif |
| |
| #define BN_BITS2 64 |
| #define BN_BYTES 8 |
| #define BN_BITS4 32 |
| #define BN_MASK2 (0xffffffffffffffffUL) |
| #define BN_MASK2l (0xffffffffUL) |
| #define BN_MASK2h (0xffffffff00000000UL) |
| #define BN_MASK2h1 (0xffffffff80000000UL) |
| #define BN_MONT_CTX_N0_LIMBS 1 |
| #define BN_DEC_CONV (10000000000000000000UL) |
| #define BN_DEC_NUM 19 |
| #define TOBN(hi, lo) ((BN_ULONG)(hi) << 32 | (lo)) |
| |
| #elif defined(OPENSSL_32_BIT) |
| |
| #define BN_ULLONG uint64_t |
| #define BN_BITS2 32 |
| #define BN_BYTES 4 |
| #define BN_BITS4 16 |
| #define BN_MASK2 (0xffffffffUL) |
| #define BN_MASK2l (0xffffUL) |
| #define BN_MASK2h1 (0xffff8000UL) |
| #define BN_MASK2h (0xffff0000UL) |
| // On some 32-bit platforms, Montgomery multiplication is done using 64-bit |
| // arithmetic with SIMD instructions. On such platforms, |BN_MONT_CTX::n0| |
| // needs to be two words long. Only certain 32-bit platforms actually make use |
| // of n0[1] and shorter R value would suffice for the others. However, |
| // currently only the assembly files know which is which. |
| #define BN_MONT_CTX_N0_LIMBS 2 |
| #define BN_DEC_CONV (1000000000UL) |
| #define BN_DEC_NUM 9 |
| #define TOBN(hi, lo) (lo), (hi) |
| |
| #else |
| #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT" |
| #endif |
| |
| |
| #define STATIC_BIGNUM(x) \ |
| { \ |
| (BN_ULONG *)(x), sizeof(x) / sizeof(BN_ULONG), \ |
| sizeof(x) / sizeof(BN_ULONG), 0, BN_FLG_STATIC_DATA \ |
| } |
| |
| #if defined(BN_ULLONG) |
| #define Lw(t) ((BN_ULONG)(t)) |
| #define Hw(t) ((BN_ULONG)((t) >> BN_BITS2)) |
| #endif |
| |
| // bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or |
| // until |top| is zero. If |bn| is zero, |bn->neg| is set to zero. |
| void bn_correct_top(BIGNUM *bn); |
| |
| // bn_wexpand ensures that |bn| has at least |words| works of space without |
| // altering its value. It returns one on success or zero on allocation |
| // failure. |
| int bn_wexpand(BIGNUM *bn, size_t words); |
| |
| // bn_expand acts the same as |bn_wexpand|, but takes a number of bits rather |
| // than a number of words. |
| int bn_expand(BIGNUM *bn, size_t bits); |
| |
| // bn_set_words sets |bn| to the value encoded in the |num| words in |words|, |
| // least significant word first. |
| int bn_set_words(BIGNUM *bn, const BN_ULONG *words, size_t num); |
| |
| // bn_mul_add_words multiples |ap| by |w|, adds the result to |rp|, and places |
| // the result in |rp|. |ap| and |rp| must both be |num| words long. It returns |
| // the carry word of the operation. |ap| and |rp| may be equal but otherwise may |
| // not alias. |
| BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, |
| BN_ULONG w); |
| |
| // bn_mul_words multiples |ap| by |w| and places the result in |rp|. |ap| and |
| // |rp| must both be |num| words long. It returns the carry word of the |
| // operation. |ap| and |rp| may be equal but otherwise may not alias. |
| BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, BN_ULONG w); |
| |
| // bn_sqr_words sets |rp[2*i]| and |rp[2*i+1]| to |ap[i]|'s square, for all |i| |
| // up to |num|. |ap| is an array of |num| words and |rp| an array of |2*num| |
| // words. |ap| and |rp| may not alias. |
| // |
| // This gives the contribution of the |ap[i]*ap[i]| terms when squaring |ap|. |
| void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num); |
| |
| // bn_add_words adds |ap| to |bp| and places the result in |rp|, each of which |
| // are |num| words long. It returns the carry bit, which is one if the operation |
| // overflowed and zero otherwise. Any pair of |ap|, |bp|, and |rp| may be equal |
| // to each other but otherwise may not alias. |
| BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| size_t num); |
| |
| // bn_sub_words subtracts |bp| from |ap| and places the result in |rp|. It |
| // returns the borrow bit, which is one if the computation underflowed and zero |
| // otherwise. Any pair of |ap|, |bp|, and |rp| may be equal to each other but |
| // otherwise may not alias. |
| BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| size_t num); |
| |
| // bn_mul_comba4 sets |r| to the product of |a| and |b|. |
| void bn_mul_comba4(BN_ULONG r[8], const BN_ULONG a[4], const BN_ULONG b[4]); |
| |
| // bn_mul_comba8 sets |r| to the product of |a| and |b|. |
| void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]); |
| |
| // bn_sqr_comba8 sets |r| to |a|^2. |
| void bn_sqr_comba8(BN_ULONG r[16], const BN_ULONG a[4]); |
| |
| // bn_sqr_comba4 sets |r| to |a|^2. |
| void bn_sqr_comba4(BN_ULONG r[8], const BN_ULONG a[4]); |
| |
| // bn_cmp_words returns a value less than, equal to or greater than zero if |
| // the, length |n|, array |a| is less than, equal to or greater than |b|. |
| int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n); |
| |
| // bn_cmp_words returns a value less than, equal to or greater than zero if the |
| // array |a| is less than, equal to or greater than |b|. The arrays can be of |
| // different lengths: |cl| gives the minimum of the two lengths and |dl| gives |
| // the length of |a| minus the length of |b|. |
| int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl); |
| |
| // bn_less_than_words returns one if |a| < |b| and zero otherwise, where |a| |
| // and |b| both are |len| words long. It runs in constant time. |
| int bn_less_than_words(const BN_ULONG *a, const BN_ULONG *b, size_t len); |
| |
| // bn_in_range_words returns one if |min_inclusive| <= |a| < |max_exclusive|, |
| // where |a| and |max_exclusive| both are |len| words long. This function leaks |
| // which of [0, min_inclusive), [min_inclusive, max_exclusive), and |
| // [max_exclusive, 2^(BN_BITS2*len)) contains |a|, but otherwise the value of |
| // |a| is secret. |
| int bn_in_range_words(const BN_ULONG *a, BN_ULONG min_inclusive, |
| const BN_ULONG *max_exclusive, size_t len); |
| |
| // bn_rand_range_words sets |out| to a uniformly distributed random number from |
| // |min_inclusive| to |max_exclusive|. Both |out| and |max_exclusive| are |len| |
| // words long. |
| // |
| // This function runs in time independent of the result, but |min_inclusive| and |
| // |max_exclusive| are public data. (Information about the range is unavoidably |
| // leaked by how many iterations it took to select a number.) |
| int bn_rand_range_words(BN_ULONG *out, BN_ULONG min_inclusive, |
| const BN_ULONG *max_exclusive, size_t len, |
| const uint8_t additional_data[32]); |
| |
| int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| const BN_ULONG *np, const BN_ULONG *n0, int num); |
| |
| uint64_t bn_mont_n0(const BIGNUM *n); |
| int bn_mod_exp_base_2_vartime(BIGNUM *r, unsigned p, const BIGNUM *n); |
| |
| #if defined(OPENSSL_X86_64) && defined(_MSC_VER) |
| #define BN_UMULT_LOHI(low, high, a, b) ((low) = _umul128((a), (b), &(high))) |
| #endif |
| |
| #if !defined(BN_ULLONG) && !defined(BN_UMULT_LOHI) |
| #error "Either BN_ULLONG or BN_UMULT_LOHI must be defined on every platform." |
| #endif |
| |
| // bn_mod_inverse_prime sets |out| to the modular inverse of |a| modulo |p|, |
| // computed with Fermat's Little Theorem. It returns one on success and zero on |
| // error. If |mont_p| is NULL, one will be computed temporarily. |
| int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p, |
| BN_CTX *ctx, const BN_MONT_CTX *mont_p); |
| |
| // bn_mod_inverse_secret_prime behaves like |bn_mod_inverse_prime| but uses |
| // |BN_mod_exp_mont_consttime| instead of |BN_mod_exp_mont| in hopes of |
| // protecting the exponent. |
| int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p, |
| BN_CTX *ctx, const BN_MONT_CTX *mont_p); |
| |
| // bn_jacobi returns the Jacobi symbol of |a| and |b| (which is -1, 0 or 1), or |
| // -2 on error. |
| int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); |
| |
| // bn_is_bit_set_words returns one if bit |bit| is set in |a| and zero |
| // otherwise. |
| int bn_is_bit_set_words(const BN_ULONG *a, size_t num, unsigned bit); |
| |
| |
| // Low-level operations for small numbers. |
| // |
| // The following functions implement algorithms suitable for use with scalars |
| // and field elements in elliptic curves. They rely on the number being small |
| // both to stack-allocate various temporaries and because they do not implement |
| // optimizations useful for the larger values used in RSA. |
| |
| // BN_SMALL_MAX_WORDS is the largest size input these functions handle. This |
| // limit allows temporaries to be more easily stack-allocated. This limit is set |
| // to accommodate P-521. |
| #if defined(OPENSSL_32_BIT) |
| #define BN_SMALL_MAX_WORDS 17 |
| #else |
| #define BN_SMALL_MAX_WORDS 9 |
| #endif |
| |
| // bn_mul_small sets |r| to |a|*|b|. |num_r| must be |num_a| + |num_b|. |r| may |
| // not alias with |a| or |b|. This function returns one on success and zero if |
| // lengths are inconsistent. |
| int bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a, |
| const BN_ULONG *b, size_t num_b); |
| |
| // bn_sqr_small sets |r| to |a|^2. |num_a| must be at most |BN_SMALL_MAX_WORDS|. |
| // |num_r| must be |num_a|*2. |r| and |a| may not alias. This function returns |
| // one on success and zero on programmer error. |
| int bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a); |
| |
| // In the following functions, the modulus must be at most |BN_SMALL_MAX_WORDS| |
| // words long. |
| |
| // bn_to_montgomery_small sets |r| to |a| translated to the Montgomery domain. |
| // |num_a| and |num_r| must be the length of the modulus, which is |
| // |mont->N.top|. |a| must be fully reduced. This function returns one on |
| // success and zero if lengths are inconsistent. |r| and |a| may alias. |
| int bn_to_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, |
| size_t num_a, const BN_MONT_CTX *mont); |
| |
| // bn_from_montgomery_small sets |r| to |a| translated out of the Montgomery |
| // domain. |num_r| must be the length of the modulus, which is |mont->N.top|. |
| // |a| must be at most |mont->N.top| * R and |num_a| must be at most 2 * |
| // |mont->N.top|. This function returns one on success and zero if lengths are |
| // inconsistent. |r| and |a| may alias. |
| int bn_from_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, |
| size_t num_a, const BN_MONT_CTX *mont); |
| |
| // bn_mod_mul_montgomery_small sets |r| to |a| * |b| mod |mont->N|. Both inputs |
| // and outputs are in the Montgomery domain. |num_r| must be the length of the |
| // modulus, which is |mont->N.top|. This function returns one on success and |
| // zero on internal error or inconsistent lengths. Any two of |r|, |a|, and |b| |
| // may alias. |
| // |
| // This function requires |a| * |b| < N * R, where N is the modulus and R is the |
| // Montgomery divisor, 2^(N.top * BN_BITS2). This should generally be satisfied |
| // by ensuring |a| and |b| are fully reduced, however ECDSA has one computation |
| // which requires the more general bound. |
| int bn_mod_mul_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, |
| size_t num_a, const BN_ULONG *b, size_t num_b, |
| const BN_MONT_CTX *mont); |
| |
| // bn_mod_exp_mont_small sets |r| to |a|^|p| mod |mont->N|. It returns one on |
| // success and zero on programmer or internal error. Both inputs and outputs are |
| // in the Montgomery domain. |num_r| and |num_a| must be |mont->N.top|, which |
| // must be at most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. This |
| // function runs in time independent of |a|, but |p| and |mont->N| are public |
| // values. |
| // |
| // Note this function differs from |BN_mod_exp_mont| which uses Montgomery |
| // reduction but takes input and output outside the Montgomery domain. Combine |
| // this function with |bn_from_montgomery_small| and |bn_to_montgomery_small| |
| // if necessary. |
| int bn_mod_exp_mont_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, |
| size_t num_a, const BN_ULONG *p, size_t num_p, |
| const BN_MONT_CTX *mont); |
| |
| // bn_mod_inverse_prime_mont_small sets |r| to |a|^-1 mod |mont->N|. |mont->N| |
| // must be a prime. |num_r| and |num_a| must be |mont->N.top|, which must be at |
| // most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. This function runs in |
| // time independent of |a|, but |mont->N| is a public value. |
| int bn_mod_inverse_prime_mont_small(BN_ULONG *r, size_t num_r, |
| const BN_ULONG *a, size_t num_a, |
| const BN_MONT_CTX *mont); |
| |
| |
| #if defined(__cplusplus) |
| } // extern C |
| #endif |
| |
| #endif // OPENSSL_HEADER_BN_INTERNAL_H |