--- /dev/null
+/* 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
+
+
+#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);
+
+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);
+
+// 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);
+
+// 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_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);
+
+
+// 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_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_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|. 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_one_to_montgomery_small sets |r| to one in Montgomery form. It returns one
+// on success and zero on error. |num_r| must be the length of the modulus,
+// which is |mont->N.top|. This function treats the bit width of the modulus as
+// public.
+int bn_one_to_montgomery_small(BN_ULONG *r, size_t num_r,
+ 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
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