| /* 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(BORINGSSL_HAS_UINT128) |
| // MSVC doesn't support two-word integers on 64-bit. |
| #define BN_ULLONG uint128_t |
| #if defined(BORINGSSL_CAN_DIVIDE_UINT128) |
| #define BN_CAN_DIVIDE_ULLONG |
| #endif |
| #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_CAN_DIVIDE_ULLONG |
| #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 |
| |
| #if !defined(OPENSSL_NO_ASM) && (defined(__GNUC__) || defined(__clang__)) |
| #define BN_CAN_USE_INLINE_ASM |
| #endif |
| |
| // |BN_mod_exp_mont_consttime| is based on the assumption that the L1 data |
| // cache line width of the target processor is at least the following value. |
| #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH 64 |
| |
| // The number of |BN_ULONG|s needed for the |BN_mod_exp_mont_consttime| stack- |
| // allocated storage buffer. The buffer is just the right size for the RSAZ |
| // and is about ~1KB larger than what's necessary (4480 bytes) for 1024-bit |
| // inputs. |
| #define MOD_EXP_CTIME_STORAGE_LEN \ |
| (((320u * 3u) + (32u * 9u * 16u)) / sizeof(BN_ULONG)) |
| |
| #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_minimal_width returns the minimal value of |bn->top| which fits the |
| // value of |bn|. |
| int bn_minimal_width(const BIGNUM *bn); |
| |
| // bn_set_minimal_width sets |bn->width| to |bn_minimal_width(bn)|. If |bn| is |
| // zero, |bn->neg| is set to zero. |
| void bn_set_minimal_width(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_resize_words adjusts |bn->top| to be |words|. It returns one on success |
| // and zero on allocation error or if |bn|'s value is too large. |
| OPENSSL_EXPORT int bn_resize_words(BIGNUM *bn, size_t words); |
| |
| // bn_select_words sets |r| to |a| if |mask| is all ones or |b| if |mask| is |
| // all zeros. |
| void bn_select_words(BN_ULONG *r, BN_ULONG mask, const BN_ULONG *a, |
| const BN_ULONG *b, size_t num); |
| |
| // 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_fits_in_words returns one if |bn| may be represented in |num| words, plus |
| // a sign bit, and zero otherwise. |
| int bn_fits_in_words(const BIGNUM *bn, size_t num); |
| |
| // bn_copy_words copies the value of |bn| to |out| and returns one if the value |
| // is representable in |num| words. Otherwise, it returns zero. |
| int bn_copy_words(BN_ULONG *out, size_t num, const BIGNUM *bn); |
| |
| // 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_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. |a| and |
| // |max_exclusive| are treated as 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]); |
| |
| // bn_range_secret_range behaves like |BN_rand_range_ex|, but treats |
| // |max_exclusive| as secret. Because of this constraint, the distribution of |
| // values returned is more complex. |
| // |
| // Rather than repeatedly generating values until one is in range, which would |
| // leak information, it generates one value. If the value is in range, it sets |
| // |*out_is_uniform| to one. Otherwise, it sets |*out_is_uniform| to zero, |
| // fixing up the value to force it in range. |
| // |
| // The subset of calls to |bn_rand_secret_range| which set |*out_is_uniform| to |
| // one are uniformly distributed in the target range. Calls overall are not. |
| // This function is intended for use in situations where the extra values are |
| // still usable and where the number of iterations needed to reach the target |
| // number of uniform outputs may be blinded for negligible probabilities of |
| // timing leaks. |
| // |
| // Although this function treats |max_exclusive| as secret, it treats the number |
| // of bits in |max_exclusive| as public. |
| int bn_rand_secret_range(BIGNUM *r, int *out_is_uniform, BN_ULONG min_inclusive, |
| const BIGNUM *max_exclusive); |
| |
| #if !defined(OPENSSL_NO_ASM) && \ |
| (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \ |
| defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64)) |
| #define OPENSSL_BN_ASM_MONT |
| // bn_mul_mont writes |ap| * |bp| mod |np| to |rp|, each |num| words |
| // long. Inputs and outputs are in Montgomery form. |n0| is a pointer to the |
| // corresponding field in |BN_MONT_CTX|. It returns one if |bn_mul_mont| handles |
| // inputs of this size and zero otherwise. |
| // |
| // TODO(davidben): The x86_64 implementation expects a 32-bit input and masks |
| // off upper bits. The aarch64 implementation expects a 64-bit input and does |
| // not. |size_t| is the safer option but not strictly correct for x86_64. But |
| // this function implicitly already has a bound on the size of |num| because it |
| // internally creates |num|-sized stack allocation. |
| // |
| // See also discussion in |ToWord| in abi_test.h for notes on smaller-than-word |
| // inputs. |
| int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| const BN_ULONG *np, const BN_ULONG *n0, size_t num); |
| #endif |
| |
| #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) |
| #define OPENSSL_BN_ASM_MONT5 |
| |
| // bn_mul_mont_gather5 multiples loads index |power| of |table|, multiplies it |
| // by |ap| modulo |np|, and stores the result in |rp|. The values are |num| |
| // words long and represented in Montgomery form. |n0| is a pointer to the |
| // corresponding field in |BN_MONT_CTX|. |
| void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, |
| const BN_ULONG *table, const BN_ULONG *np, |
| const BN_ULONG *n0, int num, int power); |
| |
| // bn_scatter5 stores |inp| to index |power| of |table|. |inp| and each entry of |
| // |table| are |num| words long. |power| must be less than 32. |table| must be |
| // 32*|num| words long. |
| void bn_scatter5(const BN_ULONG *inp, size_t num, BN_ULONG *table, |
| size_t power); |
| |
| // bn_gather5 loads index |power| of |table| and stores it in |out|. |out| and |
| // each entry of |table| are |num| words long. |power| must be less than 32. |
| void bn_gather5(BN_ULONG *out, size_t num, BN_ULONG *table, size_t power); |
| |
| // bn_power5 squares |ap| five times and multiplies it by the value stored at |
| // index |power| of |table|, modulo |np|. It stores the result in |rp|. The |
| // values are |num| words long and represented in Montgomery form. |n0| is a |
| // pointer to the corresponding field in |BN_MONT_CTX|. |num| must be divisible |
| // by 8. |
| void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *table, |
| const BN_ULONG *np, const BN_ULONG *n0, int num, int power); |
| |
| // bn_from_montgomery converts |ap| from Montgomery form modulo |np| and writes |
| // the result in |rp|, each of which is |num| words long. It returns one on |
| // success and zero if it cannot handle inputs of length |num|. |n0| is a |
| // pointer to the corresponding field in |BN_MONT_CTX|. |
| int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, |
| const BN_ULONG *not_used, const BN_ULONG *np, |
| const BN_ULONG *n0, int num); |
| #endif // !OPENSSL_NO_ASM && OPENSSL_X86_64 |
| |
| uint64_t bn_mont_n0(const BIGNUM *n); |
| |
| // bn_mod_exp_base_2_consttime calculates r = 2**p (mod n). |p| must be larger |
| // than log_2(n); i.e. 2**p must be larger than |n|. |n| must be positive and |
| // odd. |p| and the bit width of |n| are assumed public, but |n| is otherwise |
| // treated as secret. |
| int bn_mod_exp_base_2_consttime(BIGNUM *r, unsigned p, const BIGNUM *n, |
| BN_CTX *ctx); |
| |
| #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_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); |
| |
| // bn_one_to_montgomery sets |r| to one in Montgomery form. It returns one on |
| // success and zero on error. This function treats the bit width of the modulus |
| // as public. |
| int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx); |
| |
| // bn_less_than_montgomery_R returns one if |bn| is less than the Montgomery R |
| // value for |mont| and zero otherwise. |
| int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont); |
| |
| // bn_mod_u16_consttime returns |bn| mod |d|, ignoring |bn|'s sign bit. It runs |
| // in time independent of the value of |bn|, but it treats |d| as public. |
| OPENSSL_EXPORT uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d); |
| |
| // bn_odd_number_is_obviously_composite returns one if |bn| is divisible by one |
| // of the first several odd primes and zero otherwise. |
| int bn_odd_number_is_obviously_composite(const BIGNUM *bn); |
| |
| // A BN_MILLER_RABIN stores state common to each Miller-Rabin iteration. It is |
| // initialized within an existing |BN_CTX| scope and may not be used after |
| // that scope is released with |BN_CTX_end|. Field names match those in FIPS |
| // 186-4, section C.3.1. |
| typedef struct { |
| // w1 is w-1. |
| BIGNUM *w1; |
| // m is (w-1)/2^a. |
| BIGNUM *m; |
| // one_mont is 1 (mod w) in Montgomery form. |
| BIGNUM *one_mont; |
| // w1_mont is w-1 (mod w) in Montgomery form. |
| BIGNUM *w1_mont; |
| // w_bits is BN_num_bits(w). |
| int w_bits; |
| // a is the largest integer such that 2^a divides w-1. |
| int a; |
| } BN_MILLER_RABIN; |
| |
| // bn_miller_rabin_init initializes |miller_rabin| for testing if |mont->N| is |
| // prime. It returns one on success and zero on error. |
| OPENSSL_EXPORT int bn_miller_rabin_init(BN_MILLER_RABIN *miller_rabin, |
| const BN_MONT_CTX *mont, BN_CTX *ctx); |
| |
| // bn_miller_rabin_iteration performs one Miller-Rabin iteration, checking if |
| // |b| is a composite witness for |mont->N|. |miller_rabin| must have been |
| // initialized with |bn_miller_rabin_setup|. On success, it returns one and sets |
| // |*out_is_possibly_prime| to one if |mont->N| may still be prime or zero if |
| // |b| shows it is composite. On allocation or internal failure, it returns |
| // zero. |
| OPENSSL_EXPORT int bn_miller_rabin_iteration( |
| const BN_MILLER_RABIN *miller_rabin, int *out_is_possibly_prime, |
| const BIGNUM *b, const BN_MONT_CTX *mont, BN_CTX *ctx); |
| |
| // bn_rshift1_words sets |r| to |a| >> 1, where both arrays are |num| bits wide. |
| void bn_rshift1_words(BN_ULONG *r, const BN_ULONG *a, size_t num); |
| |
| // bn_rshift_words sets |r| to |a| >> |shift|, where both arrays are |num| bits |
| // wide. |
| void bn_rshift_words(BN_ULONG *r, const BN_ULONG *a, unsigned shift, |
| size_t num); |
| |
| // bn_rshift_secret_shift behaves like |BN_rshift| but runs in time independent |
| // of both |a| and |n|. |
| OPENSSL_EXPORT int bn_rshift_secret_shift(BIGNUM *r, const BIGNUM *a, |
| unsigned n, BN_CTX *ctx); |
| |
| // bn_reduce_once sets |r| to |a| mod |m| where 0 <= |a| < 2*|m|. It returns |
| // zero if |a| < |m| and a mask of all ones if |a| >= |m|. Each array is |num| |
| // words long, but |a| has an additional word specified by |carry|. |carry| must |
| // be zero or one, as implied by the bounds on |a|. |
| // |
| // |r|, |a|, and |m| may not alias. Use |bn_reduce_once_in_place| if |r| and |a| |
| // must alias. |
| BN_ULONG bn_reduce_once(BN_ULONG *r, const BN_ULONG *a, BN_ULONG carry, |
| const BN_ULONG *m, size_t num); |
| |
| // bn_reduce_once_in_place behaves like |bn_reduce_once| but acts in-place on |
| // |r|, using |tmp| as scratch space. |r|, |tmp|, and |m| may not alias. |
| BN_ULONG bn_reduce_once_in_place(BN_ULONG *r, BN_ULONG carry, const BN_ULONG *m, |
| BN_ULONG *tmp, size_t num); |
| |
| |
| // Constant-time non-modular arithmetic. |
| // |
| // The following functions implement non-modular arithmetic in constant-time |
| // and pessimally set |r->width| to the largest possible word size. |
| // |
| // Note this means that, e.g., repeatedly multiplying by one will cause widths |
| // to increase without bound. The corresponding public API functions minimize |
| // their outputs to avoid regressing calculator consumers. |
| |
| // bn_uadd_consttime behaves like |BN_uadd|, but it pessimally sets |
| // |r->width| = |a->width| + |b->width| + 1. |
| int bn_uadd_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); |
| |
| // bn_usub_consttime behaves like |BN_usub|, but it pessimally sets |
| // |r->width| = |a->width|. |
| int bn_usub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); |
| |
| // bn_abs_sub_consttime sets |r| to the absolute value of |a| - |b|, treating |
| // both inputs as secret. It returns one on success and zero on error. |
| OPENSSL_EXPORT int bn_abs_sub_consttime(BIGNUM *r, const BIGNUM *a, |
| const BIGNUM *b, BN_CTX *ctx); |
| |
| // bn_mul_consttime behaves like |BN_mul|, but it rejects negative inputs and |
| // pessimally sets |r->width| to |a->width| + |b->width|, to avoid leaking |
| // information about |a| and |b|. |
| int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); |
| |
| // bn_sqrt_consttime behaves like |BN_sqrt|, but it pessimally sets |r->width| |
| // to 2*|a->width|, to avoid leaking information about |a| and |b|. |
| int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); |
| |
| // bn_div_consttime behaves like |BN_div|, but it rejects negative inputs and |
| // treats both inputs, including their magnitudes, as secret. It is, as a |
| // result, much slower than |BN_div| and should only be used for rare operations |
| // where Montgomery reduction is not available. |
| // |
| // Note that |quotient->width| will be set pessimally to |numerator->width|. |
| OPENSSL_EXPORT int bn_div_consttime(BIGNUM *quotient, BIGNUM *remainder, |
| const BIGNUM *numerator, |
| const BIGNUM *divisor, BN_CTX *ctx); |
| |
| // bn_is_relatively_prime checks whether GCD(|x|, |y|) is one. On success, it |
| // returns one and sets |*out_relatively_prime| to one if the GCD was one and |
| // zero otherwise. On error, it returns zero. |
| OPENSSL_EXPORT int bn_is_relatively_prime(int *out_relatively_prime, |
| const BIGNUM *x, const BIGNUM *y, |
| BN_CTX *ctx); |
| |
| // bn_lcm_consttime sets |r| to LCM(|a|, |b|). It returns one and success and |
| // zero on error. |a| and |b| are both treated as secret. |
| OPENSSL_EXPORT int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| BN_CTX *ctx); |
| |
| |
| // Constant-time modular arithmetic. |
| // |
| // The following functions implement basic constant-time modular arithmetic. |
| |
| // bn_mod_add_words sets |r| to |a| + |b| (mod |m|), using |tmp| as scratch |
| // space. Each array is |num| words long. |a| and |b| must be < |m|. Any pair of |
| // |r|, |a|, and |b| may alias. |
| void bn_mod_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| const BN_ULONG *m, BN_ULONG *tmp, size_t num); |
| |
| // bn_mod_add_consttime acts like |BN_mod_add_quick| but takes a |BN_CTX|. |
| int bn_mod_add_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| const BIGNUM *m, BN_CTX *ctx); |
| |
| // bn_mod_sub_words sets |r| to |a| - |b| (mod |m|), using |tmp| as scratch |
| // space. Each array is |num| words long. |a| and |b| must be < |m|. Any pair of |
| // |r|, |a|, and |b| may alias. |
| void bn_mod_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| const BN_ULONG *m, BN_ULONG *tmp, size_t num); |
| |
| // bn_mod_sub_consttime acts like |BN_mod_sub_quick| but takes a |BN_CTX|. |
| int bn_mod_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| const BIGNUM *m, BN_CTX *ctx); |
| |
| // bn_mod_lshift1_consttime acts like |BN_mod_lshift1_quick| but takes a |
| // |BN_CTX|. |
| int bn_mod_lshift1_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, |
| BN_CTX *ctx); |
| |
| // bn_mod_lshift_consttime acts like |BN_mod_lshift_quick| but takes a |BN_CTX|. |
| int bn_mod_lshift_consttime(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, |
| BN_CTX *ctx); |
| |
| // bn_mod_inverse_consttime sets |r| to |a|^-1, mod |n|. |a| must be non- |
| // negative and less than |n|. It returns one on success and zero on error. On |
| // failure, if the failure was caused by |a| having no inverse mod |n| then |
| // |*out_no_inverse| will be set to one; otherwise it will be set to zero. |
| // |
| // This function treats both |a| and |n| as secret, provided they are both non- |
| // zero and the inverse exists. It should only be used for even moduli where |
| // none of the less general implementations are applicable. |
| OPENSSL_EXPORT int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse, |
| const BIGNUM *a, const BIGNUM *n, |
| BN_CTX *ctx); |
| |
| // 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); |
| |
| |
| // 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|. |
| void 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. |
| void 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. |
| // |r| and |a| are |num| words long, which must be |mont->N.width|. |a| must be |
| // fully reduced and may alias |r|. |
| void bn_to_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num, |
| const BN_MONT_CTX *mont); |
| |
| // bn_from_montgomery_small sets |r| to |a| translated out of the Montgomery |
| // domain. |r| and |a| are |num_r| and |num_a| words long, respectively. |num_r| |
| // must be |mont->N.width|. |a| must be at most |mont->N|^2 and may alias |r|. |
| // |
| // Unlike most of these functions, only |num_r| is bounded by |
| // |BN_SMALL_MAX_WORDS|. |num_a| may exceed it, but must be at most 2 * |num_r|. |
| void 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. Each array is |num| words long, |
| // which must be |mont->N.width|. Any two of |r|, |a|, and |b| may alias. |a| |
| // and |b| must be reduced on input. |
| void bn_mod_mul_montgomery_small(BN_ULONG *r, const BN_ULONG *a, |
| const BN_ULONG *b, size_t num, |
| 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. |r| and |a| are |num| words long, which must be |
| // |mont->N.width| and 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. |a| must be fully-reduced and may alias with |r|. |
| // |
| // 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. |
| void bn_mod_exp_mont_small(BN_ULONG *r, const BN_ULONG *a, size_t num, |
| const BN_ULONG *p, size_t num_p, |
| const BN_MONT_CTX *mont); |
| |
| // bn_mod_inverse0_prime_mont_small sets |r| to |a|^-1 mod |mont->N|. If |a| is |
| // zero, |r| is set to zero. |mont->N| must be a prime. |r| and |a| are |num| |
| // words long, which must be |mont->N.width| and at most |BN_SMALL_MAX_WORDS|. |
| // |a| must be fully-reduced and may alias |r|. This function runs in time |
| // independent of |a|, but |mont->N| is a public value. |
| void bn_mod_inverse0_prime_mont_small(BN_ULONG *r, const BN_ULONG *a, |
| size_t num, const BN_MONT_CTX *mont); |
| |
| |
| #if defined(__cplusplus) |
| } // extern C |
| #endif |
| |
| #endif // OPENSSL_HEADER_BN_INTERNAL_H |