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+/*
+ * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef INNER_H__
+#define INNER_H__
+
+#include <string.h>
+#include <limits.h>
+
+#include "config.h"
+#include "bearssl.h"
+
+/*
+ * On MSVC, disable the warning about applying unary minus on an
+ * unsigned type: it is standard, we do it all the time, and for
+ * good reasons.
+ */
+#if _MSC_VER
+#pragma warning( disable : 4146 )
+#endif
+
+/*
+ * Maximum size for a RSA modulus (in bits). Allocated stack buffers
+ * depend on that size, so this value should be kept small. Currently,
+ * 2048-bit RSA keys offer adequate security, and should still do so for
+ * the next few decades; however, a number of widespread PKI have
+ * already set their root keys to RSA-4096, so we should be able to
+ * process such keys.
+ *
+ * This value MUST be a multiple of 64. This value MUST NOT exceed 47666
+ * (some computations in RSA key generation rely on the factor size being
+ * no more than 23833 bits). RSA key sizes beyond 3072 bits don't make a
+ * lot of sense anyway.
+ */
+#define BR_MAX_RSA_SIZE 4096
+
+/*
+ * Minimum size for a RSA modulus (in bits); this value is used only to
+ * filter out invalid parameters for key pair generation. Normally,
+ * applications should not use RSA keys smaller than 2048 bits; but some
+ * specific cases might need shorter keys, for legacy or research
+ * purposes.
+ */
+#define BR_MIN_RSA_SIZE 512
+
+/*
+ * Maximum size for a RSA factor (in bits). This is for RSA private-key
+ * operations. Default is to support factors up to a bit more than half
+ * the maximum modulus size.
+ *
+ * This value MUST be a multiple of 32.
+ */
+#define BR_MAX_RSA_FACTOR ((BR_MAX_RSA_SIZE + 64) >> 1)
+
+/*
+ * Maximum size for an EC curve (modulus or order), in bits. Size of
+ * stack buffers depends on that parameter. This size MUST be a multiple
+ * of 8 (so that decoding an integer with that many bytes does not
+ * overflow).
+ */
+#define BR_MAX_EC_SIZE 528
+
+/*
+ * Some macros to recognize the current architecture. Right now, we are
+ * interested into automatically recognizing architecture with efficient
+ * 64-bit types so that we may automatically use implementations that
+ * use 64-bit registers in that case. Future versions may detect, e.g.,
+ * availability of SSE2 intrinsics.
+ *
+ * If 'unsigned long' is a 64-bit type, then we assume that 64-bit types
+ * are efficient. Otherwise, we rely on macros that depend on compiler,
+ * OS and architecture. In any case, failure to detect the architecture
+ * as 64-bit means that the 32-bit code will be used, and that code
+ * works also on 64-bit architectures (the 64-bit code may simply be
+ * more efficient).
+ *
+ * The test on 'unsigned long' should already catch most cases, the one
+ * notable exception being Windows code where 'unsigned long' is kept to
+ * 32-bit for compatibility with all the legacy code that liberally uses
+ * the 'DWORD' type for 32-bit values.
+ *
+ * Macro names are taken from: http://nadeausoftware.com/articles/2012/02/c_c_tip_how_detect_processor_type_using_compiler_predefined_macros
+ */
+#ifndef BR_64
+#if ((ULONG_MAX >> 31) >> 31) == 3
+#define BR_64 1
+#elif defined(__ia64) || defined(__itanium__) || defined(_M_IA64)
+#define BR_64 1
+#elif defined(__powerpc64__) || defined(__ppc64__) || defined(__PPC64__) \
+ || defined(__64BIT__) || defined(_LP64) || defined(__LP64__)
+#define BR_64 1
+#elif defined(__sparc64__)
+#define BR_64 1
+#elif defined(__x86_64__) || defined(_M_X64)
+#define BR_64 1
+#elif defined(__aarch64__) || defined(_M_ARM64)
+#define BR_64 1
+#elif defined(__mips64)
+#define BR_64 1
+#endif
+#endif
+
+/*
+ * Set BR_LOMUL on platforms where it makes sense.
+ */
+#ifndef BR_LOMUL
+#if BR_ARMEL_CORTEXM_GCC
+#define BR_LOMUL 1
+#endif
+#endif
+
+/*
+ * Architecture detection.
+ */
+#ifndef BR_i386
+#if __i386__ || _M_IX86
+#define BR_i386 1
+#endif
+#endif
+
+#ifndef BR_amd64
+#if __x86_64__ || _M_X64
+#define BR_amd64 1
+#endif
+#endif
+
+/*
+ * Compiler brand and version.
+ *
+ * Implementations that use intrinsics need to detect the compiler type
+ * and version because some specific actions may be needed to activate
+ * the corresponding opcodes, both for header inclusion, and when using
+ * them in a function.
+ *
+ * BR_GCC, BR_CLANG and BR_MSC will be set to 1 for, respectively, GCC,
+ * Clang and MS Visual C. For each of them, sub-macros will be defined
+ * for versions; each sub-macro is set whenever the compiler version is
+ * at least as recent as the one corresponding to the macro.
+ */
+
+/*
+ * GCC thresholds are on versions 4.4 to 4.9 and 5.0.
+ */
+#ifndef BR_GCC
+#if __GNUC__ && !__clang__
+#define BR_GCC 1
+
+#if __GNUC__ > 4
+#define BR_GCC_5_0 1
+#elif __GNUC__ == 4 && __GNUC_MINOR__ >= 9
+#define BR_GCC_4_9 1
+#elif __GNUC__ == 4 && __GNUC_MINOR__ >= 8
+#define BR_GCC_4_8 1
+#elif __GNUC__ == 4 && __GNUC_MINOR__ >= 7
+#define BR_GCC_4_7 1
+#elif __GNUC__ == 4 && __GNUC_MINOR__ >= 6
+#define BR_GCC_4_6 1
+#elif __GNUC__ == 4 && __GNUC_MINOR__ >= 5
+#define BR_GCC_4_5 1
+#elif __GNUC__ == 4 && __GNUC_MINOR__ >= 4
+#define BR_GCC_4_4 1
+#endif
+
+#if BR_GCC_5_0
+#define BR_GCC_4_9 1
+#endif
+#if BR_GCC_4_9
+#define BR_GCC_4_8 1
+#endif
+#if BR_GCC_4_8
+#define BR_GCC_4_7 1
+#endif
+#if BR_GCC_4_7
+#define BR_GCC_4_6 1
+#endif
+#if BR_GCC_4_6
+#define BR_GCC_4_5 1
+#endif
+#if BR_GCC_4_5
+#define BR_GCC_4_4 1
+#endif
+
+#endif
+#endif
+
+/*
+ * Clang thresholds are on versions 3.7.0 and 3.8.0.
+ */
+#ifndef BR_CLANG
+#if __clang__
+#define BR_CLANG 1
+
+#if __clang_major__ > 3 || (__clang_major__ == 3 && __clang_minor__ >= 8)
+#define BR_CLANG_3_8 1
+#elif __clang_major__ == 3 && __clang_minor__ >= 7
+#define BR_CLANG_3_7 1
+#endif
+
+#if BR_CLANG_3_8
+#define BR_CLANG_3_7 1
+#endif
+
+#endif
+#endif
+
+/*
+ * MS Visual C thresholds are on Visual Studio 2005 to 2015.
+ */
+#ifndef BR_MSC
+#if _MSC_VER
+#define BR_MSC 1
+
+#if _MSC_VER >= 1900
+#define BR_MSC_2015 1
+#elif _MSC_VER >= 1800
+#define BR_MSC_2013 1
+#elif _MSC_VER >= 1700
+#define BR_MSC_2012 1
+#elif _MSC_VER >= 1600
+#define BR_MSC_2010 1
+#elif _MSC_VER >= 1500
+#define BR_MSC_2008 1
+#elif _MSC_VER >= 1400
+#define BR_MSC_2005 1
+#endif
+
+#if BR_MSC_2015
+#define BR_MSC_2013 1
+#endif
+#if BR_MSC_2013
+#define BR_MSC_2012 1
+#endif
+#if BR_MSC_2012
+#define BR_MSC_2010 1
+#endif
+#if BR_MSC_2010
+#define BR_MSC_2008 1
+#endif
+#if BR_MSC_2008
+#define BR_MSC_2005 1
+#endif
+
+#endif
+#endif
+
+/*
+ * GCC 4.4+ and Clang 3.7+ allow tagging specific functions with a
+ * 'target' attribute that activates support for specific opcodes.
+ */
+#if BR_GCC_4_4 || BR_CLANG_3_7
+#define BR_TARGET(x) __attribute__((target(x)))
+#else
+#define BR_TARGET(x)
+#endif
+
+/*
+ * AES-NI intrinsics are available on x86 (32-bit and 64-bit) with
+ * GCC 4.8+, Clang 3.7+ and MSC 2012+.
+ */
+#ifndef BR_AES_X86NI
+#if (BR_i386 || BR_amd64) && (BR_GCC_4_8 || BR_CLANG_3_7 || BR_MSC_2012)
+#define BR_AES_X86NI 1
+#endif
+#endif
+
+/*
+ * SSE2 intrinsics are available on x86 (32-bit and 64-bit) with
+ * GCC 4.4+, Clang 3.7+ and MSC 2005+.
+ */
+#ifndef BR_SSE2
+#if (BR_i386 || BR_amd64) && (BR_GCC_4_4 || BR_CLANG_3_7 || BR_MSC_2005)
+#define BR_SSE2 1
+#endif
+#endif
+
+/*
+ * RDRAND intrinsics are available on x86 (32-bit and 64-bit) with
+ * GCC 4.6+, Clang 3.7+ and MSC 2012+.
+ */
+#ifndef BR_RDRAND
+#if (BR_i386 || BR_amd64) && (BR_GCC_4_6 || BR_CLANG_3_7 || BR_MSC_2012)
+#define BR_RDRAND 1
+#endif
+#endif
+
+/*
+ * Determine type of OS for random number generation. Macro names and
+ * values are documented on:
+ * https://sourceforge.net/p/predef/wiki/OperatingSystems/
+ *
+ * TODO: enrich the list of detected system. Also add detection for
+ * alternate system calls like getentropy(), which are usually
+ * preferable when available.
+ */
+
+#ifndef BR_USE_URANDOM
+#if defined _AIX \
+ || defined __ANDROID__ \
+ || defined __FreeBSD__ \
+ || defined __NetBSD__ \
+ || defined __OpenBSD__ \
+ || defined __DragonFly__ \
+ || defined __linux__ \
+ || (defined __sun && (defined __SVR4 || defined __svr4__)) \
+ || (defined __APPLE__ && defined __MACH__)
+#define BR_USE_URANDOM 1
+#endif
+#endif
+
+#ifndef BR_USE_WIN32_RAND
+#if defined _WIN32 || defined _WIN64
+#define BR_USE_WIN32_RAND 1
+#endif
+#endif
+
+/*
+ * POWER8 crypto support. We rely on compiler macros for the
+ * architecture, since we do not have a reliable, simple way to detect
+ * the required support at runtime (we could try running an opcode, and
+ * trapping the exception or signal on illegal instruction, but this
+ * induces some non-trivial OS dependencies that we would prefer to
+ * avoid if possible).
+ */
+#ifndef BR_POWER8
+#if __GNUC__ && ((_ARCH_PWR8 || _ARCH_PPC) && __CRYPTO__)
+#define BR_POWER8 1
+#endif
+#endif
+
+/*
+ * Detect endinanness on POWER8.
+ */
+#if BR_POWER8
+#if defined BR_POWER8_LE
+#undef BR_POWER8_BE
+#if BR_POWER8_LE
+#define BR_POWER8_BE 0
+#else
+#define BR_POWER8_BE 1
+#endif
+#elif defined BR_POWER8_BE
+#undef BR_POWER8_LE
+#if BR_POWER8_BE
+#define BR_POWER8_LE 0
+#else
+#define BR_POWER8_LE 1
+#endif
+#else
+#if __LITTLE_ENDIAN__
+#define BR_POWER8_LE 1
+#define BR_POWER8_BE 0
+#else
+#define BR_POWER8_LE 0
+#define BR_POWER8_BE 1
+#endif
+#endif
+#endif
+
+/*
+ * Detect support for 128-bit integers.
+ */
+#if !defined BR_INT128 && !defined BR_UMUL128
+#ifdef __SIZEOF_INT128__
+#define BR_INT128 1
+#elif _M_X64
+#define BR_UMUL128 1
+#endif
+#endif
+
+/*
+ * Detect support for unaligned accesses with known endianness.
+ *
+ * x86 (both 32-bit and 64-bit) is little-endian and allows unaligned
+ * accesses.
+ *
+ * POWER/PowerPC allows unaligned accesses when big-endian. POWER8 and
+ * later also allow unaligned accesses when little-endian.
+ */
+#if !defined BR_LE_UNALIGNED && !defined BR_BE_UNALIGNED
+
+#if __i386 || __i386__ || __x86_64__ || _M_IX86 || _M_X64
+#define BR_LE_UNALIGNED 1
+#elif BR_POWER8_BE
+#define BR_BE_UNALIGNED 1
+#elif BR_POWER8_LE
+#define BR_LE_UNALIGNED 1
+#elif (__powerpc__ || __powerpc64__ || _M_PPC || _ARCH_PPC || _ARCH_PPC64) \
+ && __BIG_ENDIAN__
+#define BR_BE_UNALIGNED 1
+#endif
+
+#endif
+
+/*
+ * Detect support for an OS-provided time source.
+ */
+
+#ifndef BR_USE_UNIX_TIME
+#if defined __unix__ || defined __linux__ \
+ || defined _POSIX_SOURCE || defined _POSIX_C_SOURCE \
+ || (defined __APPLE__ && defined __MACH__)
+#define BR_USE_UNIX_TIME 1
+#endif
+#endif
+
+#ifndef BR_USE_WIN32_TIME
+#if defined _WIN32 || defined _WIN64
+#define BR_USE_WIN32_TIME 1
+#endif
+#endif
+
+/* ==================================================================== */
+/*
+ * Encoding/decoding functions.
+ *
+ * 32-bit and 64-bit decoding, both little-endian and big-endian, is
+ * implemented with the inline functions below.
+ *
+ * When allowed by some compile-time options (autodetected or provided),
+ * optimised code is used, to perform direct memory access when the
+ * underlying architecture supports it, both for endianness and
+ * alignment. This, however, may trigger strict aliasing issues; the
+ * code below uses unions to perform (supposedly) safe type punning.
+ * Since the C aliasing rules are relatively complex and were amended,
+ * or at least re-explained with different phrasing, in all successive
+ * versions of the C standard, it is always a bit risky to bet that any
+ * specific version of a C compiler got it right, for some notion of
+ * "right".
+ */
+
+typedef union {
+ uint16_t u;
+ unsigned char b[sizeof(uint16_t)];
+} br_union_u16;
+
+typedef union {
+ uint32_t u;
+ unsigned char b[sizeof(uint32_t)];
+} br_union_u32;
+
+typedef union {
+ uint64_t u;
+ unsigned char b[sizeof(uint64_t)];
+} br_union_u64;
+
+static inline void
+br_enc16le(void *dst, unsigned x)
+{
+#if BR_LE_UNALIGNED
+ ((br_union_u16 *)dst)->u = x;
+#else
+ unsigned char *buf;
+
+ buf = dst;
+ buf[0] = (unsigned char)x;
+ buf[1] = (unsigned char)(x >> 8);
+#endif
+}
+
+static inline void
+br_enc16be(void *dst, unsigned x)
+{
+#if BR_BE_UNALIGNED
+ ((br_union_u16 *)dst)->u = x;
+#else
+ unsigned char *buf;
+
+ buf = dst;
+ buf[0] = (unsigned char)(x >> 8);
+ buf[1] = (unsigned char)x;
+#endif
+}
+
+static inline unsigned
+br_dec16le(const void *src)
+{
+#if BR_LE_UNALIGNED
+ return ((const br_union_u16 *)src)->u;
+#else
+ const unsigned char *buf;
+
+ buf = src;
+ return (unsigned)buf[0] | ((unsigned)buf[1] << 8);
+#endif
+}
+
+static inline unsigned
+br_dec16be(const void *src)
+{
+#if BR_BE_UNALIGNED
+ return ((const br_union_u16 *)src)->u;
+#else
+ const unsigned char *buf;
+
+ buf = src;
+ return ((unsigned)buf[0] << 8) | (unsigned)buf[1];
+#endif
+}
+
+static inline void
+br_enc32le(void *dst, uint32_t x)
+{
+#if BR_LE_UNALIGNED
+ ((br_union_u32 *)dst)->u = x;
+#else
+ unsigned char *buf;
+
+ buf = dst;
+ buf[0] = (unsigned char)x;
+ buf[1] = (unsigned char)(x >> 8);
+ buf[2] = (unsigned char)(x >> 16);
+ buf[3] = (unsigned char)(x >> 24);
+#endif
+}
+
+static inline void
+br_enc32be(void *dst, uint32_t x)
+{
+#if BR_BE_UNALIGNED
+ ((br_union_u32 *)dst)->u = x;
+#else
+ unsigned char *buf;
+
+ buf = dst;
+ buf[0] = (unsigned char)(x >> 24);
+ buf[1] = (unsigned char)(x >> 16);
+ buf[2] = (unsigned char)(x >> 8);
+ buf[3] = (unsigned char)x;
+#endif
+}
+
+static inline uint32_t
+br_dec32le(const void *src)
+{
+#if BR_LE_UNALIGNED
+ return ((const br_union_u32 *)src)->u;
+#else
+ const unsigned char *buf;
+
+ buf = src;
+ return (uint32_t)buf[0]
+ | ((uint32_t)buf[1] << 8)
+ | ((uint32_t)buf[2] << 16)
+ | ((uint32_t)buf[3] << 24);
+#endif
+}
+
+static inline uint32_t
+br_dec32be(const void *src)
+{
+#if BR_BE_UNALIGNED
+ return ((const br_union_u32 *)src)->u;
+#else
+ const unsigned char *buf;
+
+ buf = src;
+ return ((uint32_t)buf[0] << 24)
+ | ((uint32_t)buf[1] << 16)
+ | ((uint32_t)buf[2] << 8)
+ | (uint32_t)buf[3];
+#endif
+}
+
+static inline void
+br_enc64le(void *dst, uint64_t x)
+{
+#if BR_LE_UNALIGNED
+ ((br_union_u64 *)dst)->u = x;
+#else
+ unsigned char *buf;
+
+ buf = dst;
+ br_enc32le(buf, (uint32_t)x);
+ br_enc32le(buf + 4, (uint32_t)(x >> 32));
+#endif
+}
+
+static inline void
+br_enc64be(void *dst, uint64_t x)
+{
+#if BR_BE_UNALIGNED
+ ((br_union_u64 *)dst)->u = x;
+#else
+ unsigned char *buf;
+
+ buf = dst;
+ br_enc32be(buf, (uint32_t)(x >> 32));
+ br_enc32be(buf + 4, (uint32_t)x);
+#endif
+}
+
+static inline uint64_t
+br_dec64le(const void *src)
+{
+#if BR_LE_UNALIGNED
+ return ((const br_union_u64 *)src)->u;
+#else
+ const unsigned char *buf;
+
+ buf = src;
+ return (uint64_t)br_dec32le(buf)
+ | ((uint64_t)br_dec32le(buf + 4) << 32);
+#endif
+}
+
+static inline uint64_t
+br_dec64be(const void *src)
+{
+#if BR_BE_UNALIGNED
+ return ((const br_union_u64 *)src)->u;
+#else
+ const unsigned char *buf;
+
+ buf = src;
+ return ((uint64_t)br_dec32be(buf) << 32)
+ | (uint64_t)br_dec32be(buf + 4);
+#endif
+}
+
+/*
+ * Range decoding and encoding (for several successive values).
+ */
+void br_range_dec16le(uint16_t *v, size_t num, const void *src);
+void br_range_dec16be(uint16_t *v, size_t num, const void *src);
+void br_range_enc16le(void *dst, const uint16_t *v, size_t num);
+void br_range_enc16be(void *dst, const uint16_t *v, size_t num);
+
+void br_range_dec32le(uint32_t *v, size_t num, const void *src);
+void br_range_dec32be(uint32_t *v, size_t num, const void *src);
+void br_range_enc32le(void *dst, const uint32_t *v, size_t num);
+void br_range_enc32be(void *dst, const uint32_t *v, size_t num);
+
+void br_range_dec64le(uint64_t *v, size_t num, const void *src);
+void br_range_dec64be(uint64_t *v, size_t num, const void *src);
+void br_range_enc64le(void *dst, const uint64_t *v, size_t num);
+void br_range_enc64be(void *dst, const uint64_t *v, size_t num);
+
+/*
+ * Byte-swap a 32-bit integer.
+ */
+static inline uint32_t
+br_swap32(uint32_t x)
+{
+ x = ((x & (uint32_t)0x00FF00FF) << 8)
+ | ((x >> 8) & (uint32_t)0x00FF00FF);
+ return (x << 16) | (x >> 16);
+}
+
+/* ==================================================================== */
+/*
+ * Support code for hash functions.
+ */
+
+/*
+ * IV for MD5, SHA-1, SHA-224 and SHA-256.
+ */
+extern const uint32_t br_md5_IV[];
+extern const uint32_t br_sha1_IV[];
+extern const uint32_t br_sha224_IV[];
+extern const uint32_t br_sha256_IV[];
+
+/*
+ * Round functions for MD5, SHA-1, SHA-224 and SHA-256 (SHA-224 and
+ * SHA-256 use the same round function).
+ */
+void br_md5_round(const unsigned char *buf, uint32_t *val);
+void br_sha1_round(const unsigned char *buf, uint32_t *val);
+void br_sha2small_round(const unsigned char *buf, uint32_t *val);
+
+/*
+ * The core function for the TLS PRF. It computes
+ * P_hash(secret, label + seed), and XORs the result into the dst buffer.
+ */
+void br_tls_phash(void *dst, size_t len,
+ const br_hash_class *dig,
+ const void *secret, size_t secret_len, const char *label,
+ size_t seed_num, const br_tls_prf_seed_chunk *seed);
+
+/*
+ * Copy all configured hash implementations from a multihash context
+ * to another.
+ */
+static inline void
+br_multihash_copyimpl(br_multihash_context *dst,
+ const br_multihash_context *src)
+{
+ memcpy((void *)dst->impl, src->impl, sizeof src->impl);
+}
+
+/* ==================================================================== */
+/*
+ * Constant-time primitives. These functions manipulate 32-bit values in
+ * order to provide constant-time comparisons and multiplexers.
+ *
+ * Boolean values (the "ctl" bits) MUST have value 0 or 1.
+ *
+ * Implementation notes:
+ * =====================
+ *
+ * The uintN_t types are unsigned and with width exactly N bits; the C
+ * standard guarantees that computations are performed modulo 2^N, and
+ * there can be no overflow. Negation (unary '-') works on unsigned types
+ * as well.
+ *
+ * The intN_t types are guaranteed to have width exactly N bits, with no
+ * padding bit, and using two's complement representation. Casting
+ * intN_t to uintN_t really is conversion modulo 2^N. Beware that intN_t
+ * types, being signed, trigger implementation-defined behaviour on
+ * overflow (including raising some signal): with GCC, while modular
+ * arithmetics are usually applied, the optimizer may assume that
+ * overflows don't occur (unless the -fwrapv command-line option is
+ * added); Clang has the additional -ftrapv option to explicitly trap on
+ * integer overflow or underflow.
+ */
+
+/*
+ * Negate a boolean.
+ */
+static inline uint32_t
+NOT(uint32_t ctl)
+{
+ return ctl ^ 1;
+}
+
+/*
+ * Multiplexer: returns x if ctl == 1, y if ctl == 0.
+ */
+static inline uint32_t
+MUX(uint32_t ctl, uint32_t x, uint32_t y)
+{
+ return y ^ (-ctl & (x ^ y));
+}
+
+/*
+ * Equality check: returns 1 if x == y, 0 otherwise.
+ */
+static inline uint32_t
+EQ(uint32_t x, uint32_t y)
+{
+ uint32_t q;
+
+ q = x ^ y;
+ return NOT((q | -q) >> 31);
+}
+
+/*
+ * Inequality check: returns 1 if x != y, 0 otherwise.
+ */
+static inline uint32_t
+NEQ(uint32_t x, uint32_t y)
+{
+ uint32_t q;
+
+ q = x ^ y;
+ return (q | -q) >> 31;
+}
+
+/*
+ * Comparison: returns 1 if x > y, 0 otherwise.
+ */
+static inline uint32_t
+GT(uint32_t x, uint32_t y)
+{
+ /*
+ * If both x < 2^31 and x < 2^31, then y-x will have its high
+ * bit set if x > y, cleared otherwise.
+ *
+ * If either x >= 2^31 or y >= 2^31 (but not both), then the
+ * result is the high bit of x.
+ *
+ * If both x >= 2^31 and y >= 2^31, then we can virtually
+ * subtract 2^31 from both, and we are back to the first case.
+ * Since (y-2^31)-(x-2^31) = y-x, the subtraction is already
+ * fine.
+ */
+ uint32_t z;
+
+ z = y - x;
+ return (z ^ ((x ^ y) & (x ^ z))) >> 31;
+}
+
+/*
+ * Other comparisons (greater-or-equal, lower-than, lower-or-equal).
+ */
+#define GE(x, y) NOT(GT(y, x))
+#define LT(x, y) GT(y, x)
+#define LE(x, y) NOT(GT(x, y))
+
+/*
+ * General comparison: returned value is -1, 0 or 1, depending on
+ * whether x is lower than, equal to, or greater than y.
+ */
+static inline int32_t
+CMP(uint32_t x, uint32_t y)
+{
+ return (int32_t)GT(x, y) | -(int32_t)GT(y, x);
+}
+
+/*
+ * Returns 1 if x == 0, 0 otherwise. Take care that the operand is signed.
+ */
+static inline uint32_t
+EQ0(int32_t x)
+{
+ uint32_t q;
+
+ q = (uint32_t)x;
+ return ~(q | -q) >> 31;
+}
+
+/*
+ * Returns 1 if x > 0, 0 otherwise. Take care that the operand is signed.
+ */
+static inline uint32_t
+GT0(int32_t x)
+{
+ /*
+ * High bit of -x is 0 if x == 0, but 1 if x > 0.
+ */
+ uint32_t q;
+
+ q = (uint32_t)x;
+ return (~q & -q) >> 31;
+}
+
+/*
+ * Returns 1 if x >= 0, 0 otherwise. Take care that the operand is signed.
+ */
+static inline uint32_t
+GE0(int32_t x)
+{
+ return ~(uint32_t)x >> 31;
+}
+
+/*
+ * Returns 1 if x < 0, 0 otherwise. Take care that the operand is signed.
+ */
+static inline uint32_t
+LT0(int32_t x)
+{
+ return (uint32_t)x >> 31;
+}
+
+/*
+ * Returns 1 if x <= 0, 0 otherwise. Take care that the operand is signed.
+ */
+static inline uint32_t
+LE0(int32_t x)
+{
+ uint32_t q;
+
+ /*
+ * ~-x has its high bit set if and only if -x is nonnegative (as
+ * a signed int), i.e. x is in the -(2^31-1) to 0 range. We must
+ * do an OR with x itself to account for x = -2^31.
+ */
+ q = (uint32_t)x;
+ return (q | ~-q) >> 31;
+}
+
+/*
+ * Conditional copy: src[] is copied into dst[] if and only if ctl is 1.
+ * dst[] and src[] may overlap completely (but not partially).
+ */
+void br_ccopy(uint32_t ctl, void *dst, const void *src, size_t len);
+
+#define CCOPY br_ccopy
+
+/*
+ * Compute the bit length of a 32-bit integer. Returned value is between 0
+ * and 32 (inclusive).
+ */
+static inline uint32_t
+BIT_LENGTH(uint32_t x)
+{
+ uint32_t k, c;
+
+ k = NEQ(x, 0);
+ c = GT(x, 0xFFFF); x = MUX(c, x >> 16, x); k += c << 4;
+ c = GT(x, 0x00FF); x = MUX(c, x >> 8, x); k += c << 3;
+ c = GT(x, 0x000F); x = MUX(c, x >> 4, x); k += c << 2;
+ c = GT(x, 0x0003); x = MUX(c, x >> 2, x); k += c << 1;
+ k += GT(x, 0x0001);
+ return k;
+}
+
+/*
+ * Compute the minimum of x and y.
+ */
+static inline uint32_t
+MIN(uint32_t x, uint32_t y)
+{
+ return MUX(GT(x, y), y, x);
+}
+
+/*
+ * Compute the maximum of x and y.
+ */
+static inline uint32_t
+MAX(uint32_t x, uint32_t y)
+{
+ return MUX(GT(x, y), x, y);
+}
+
+/*
+ * Multiply two 32-bit integers, with a 64-bit result. This default
+ * implementation assumes that the basic multiplication operator
+ * yields constant-time code.
+ */
+#define MUL(x, y) ((uint64_t)(x) * (uint64_t)(y))
+
+#if BR_CT_MUL31
+
+/*
+ * Alternate implementation of MUL31, that will be constant-time on some
+ * (old) platforms where the default MUL31 is not. Unfortunately, it is
+ * also substantially slower, and yields larger code, on more modern
+ * platforms, which is why it is deactivated by default.
+ *
+ * MUL31_lo() must do some extra work because on some platforms, the
+ * _signed_ multiplication may return early if the top bits are 1.
+ * Simply truncating (casting) the output of MUL31() would not be
+ * sufficient, because the compiler may notice that we keep only the low
+ * word, and then replace automatically the unsigned multiplication with
+ * a signed multiplication opcode.
+ */
+#define MUL31(x, y) ((uint64_t)((x) | (uint32_t)0x80000000) \
+ * (uint64_t)((y) | (uint32_t)0x80000000) \
+ - ((uint64_t)(x) << 31) - ((uint64_t)(y) << 31) \
+ - ((uint64_t)1 << 62))
+static inline uint32_t
+MUL31_lo(uint32_t x, uint32_t y)
+{
+ uint32_t xl, xh;
+ uint32_t yl, yh;
+
+ xl = (x & 0xFFFF) | (uint32_t)0x80000000;
+ xh = (x >> 16) | (uint32_t)0x80000000;
+ yl = (y & 0xFFFF) | (uint32_t)0x80000000;
+ yh = (y >> 16) | (uint32_t)0x80000000;
+ return (xl * yl + ((xl * yh + xh * yl) << 16)) & (uint32_t)0x7FFFFFFF;
+}
+
+#else
+
+/*
+ * Multiply two 31-bit integers, with a 62-bit result. This default
+ * implementation assumes that the basic multiplication operator
+ * yields constant-time code.
+ * The MUL31_lo() macro returns only the low 31 bits of the product.
+ */
+#define MUL31(x, y) ((uint64_t)(x) * (uint64_t)(y))
+#define MUL31_lo(x, y) (((uint32_t)(x) * (uint32_t)(y)) & (uint32_t)0x7FFFFFFF)
+
+#endif
+
+/*
+ * Multiply two words together; the sum of the lengths of the two
+ * operands must not exceed 31 (for instance, one operand may use 16
+ * bits if the other fits on 15). If BR_CT_MUL15 is non-zero, then the
+ * macro will contain some extra operations that help in making the
+ * operation constant-time on some platforms, where the basic 32-bit
+ * multiplication is not constant-time.
+ */
+#if BR_CT_MUL15
+#define MUL15(x, y) (((uint32_t)(x) | (uint32_t)0x80000000) \
+ * ((uint32_t)(y) | (uint32_t)0x80000000) \
+ & (uint32_t)0x7FFFFFFF)
+#else
+#define MUL15(x, y) ((uint32_t)(x) * (uint32_t)(y))
+#endif
+
+/*
+ * Arithmetic right shift (sign bit is copied). What happens when
+ * right-shifting a negative value is _implementation-defined_, so it
+ * does not trigger undefined behaviour, but it is still up to each
+ * compiler to define (and document) what it does. Most/all compilers
+ * will do an arithmetic shift, the sign bit being used to fill the
+ * holes; this is a native operation on the underlying CPU, and it would
+ * make little sense for the compiler to do otherwise. GCC explicitly
+ * documents that it follows that convention.
+ *
+ * Still, if BR_NO_ARITH_SHIFT is defined (and non-zero), then an
+ * alternate version will be used, that does not rely on such
+ * implementation-defined behaviour. Unfortunately, it is also slower
+ * and yields bigger code, which is why it is deactivated by default.
+ */
+#if BR_NO_ARITH_SHIFT
+#define ARSH(x, n) (((uint32_t)(x) >> (n)) \
+ | ((-((uint32_t)(x) >> 31)) << (32 - (n))))
+#else
+#define ARSH(x, n) ((*(int32_t *)&(x)) >> (n))
+#endif
+
+/*
+ * Constant-time division. The dividend hi:lo is divided by the
+ * divisor d; the quotient is returned and the remainder is written
+ * in *r. If hi == d, then the quotient does not fit on 32 bits;
+ * returned value is thus truncated. If hi > d, returned values are
+ * indeterminate.
+ */
+uint32_t br_divrem(uint32_t hi, uint32_t lo, uint32_t d, uint32_t *r);
+
+/*
+ * Wrapper for br_divrem(); the remainder is returned, and the quotient
+ * is discarded.
+ */
+static inline uint32_t
+br_rem(uint32_t hi, uint32_t lo, uint32_t d)
+{
+ uint32_t r;
+
+ br_divrem(hi, lo, d, &r);
+ return r;
+}
+
+/*
+ * Wrapper for br_divrem(); the quotient is returned, and the remainder
+ * is discarded.
+ */
+static inline uint32_t
+br_div(uint32_t hi, uint32_t lo, uint32_t d)
+{
+ uint32_t r;
+
+ return br_divrem(hi, lo, d, &r);
+}
+
+/* ==================================================================== */
+
+/*
+ * Integers 'i32'
+ * --------------
+ *
+ * The 'i32' functions implement computations on big integers using
+ * an internal representation as an array of 32-bit integers. For
+ * an array x[]:
+ * -- x[0] contains the "announced bit length" of the integer
+ * -- x[1], x[2]... contain the value in little-endian order (x[1]
+ * contains the least significant 32 bits)
+ *
+ * Multiplications rely on the elementary 32x32->64 multiplication.
+ *
+ * The announced bit length specifies the number of bits that are
+ * significant in the subsequent 32-bit words. Unused bits in the
+ * last (most significant) word are set to 0; subsequent words are
+ * uninitialized and need not exist at all.
+ *
+ * The execution time and memory access patterns of all computations
+ * depend on the announced bit length, but not on the actual word
+ * values. For modular integers, the announced bit length of any integer
+ * modulo n is equal to the actual bit length of n; thus, computations
+ * on modular integers are "constant-time" (only the modulus length may
+ * leak).
+ */
+
+/*
+ * Compute the actual bit length of an integer. The argument x should
+ * point to the first (least significant) value word of the integer.
+ * The len 'xlen' contains the number of 32-bit words to access.
+ *
+ * CT: value or length of x does not leak.
+ */
+uint32_t br_i32_bit_length(uint32_t *x, size_t xlen);
+
+/*
+ * Decode an integer from its big-endian unsigned representation. The
+ * "true" bit length of the integer is computed, but all words of x[]
+ * corresponding to the full 'len' bytes of the source are set.
+ *
+ * CT: value or length of x does not leak.
+ */
+void br_i32_decode(uint32_t *x, const void *src, size_t len);
+
+/*
+ * Decode an integer from its big-endian unsigned representation. The
+ * integer MUST be lower than m[]; the announced bit length written in
+ * x[] will be equal to that of m[]. All 'len' bytes from the source are
+ * read.
+ *
+ * Returned value is 1 if the decode value fits within the modulus, 0
+ * otherwise. In the latter case, the x[] buffer will be set to 0 (but
+ * still with the announced bit length of m[]).
+ *
+ * CT: value or length of x does not leak. Memory access pattern depends
+ * only of 'len' and the announced bit length of m. Whether x fits or
+ * not does not leak either.
+ */
+uint32_t br_i32_decode_mod(uint32_t *x,
+ const void *src, size_t len, const uint32_t *m);
+
+/*
+ * Reduce an integer (a[]) modulo another (m[]). The result is written
+ * in x[] and its announced bit length is set to be equal to that of m[].
+ *
+ * x[] MUST be distinct from a[] and m[].
+ *
+ * CT: only announced bit lengths leak, not values of x, a or m.
+ */
+void br_i32_reduce(uint32_t *x, const uint32_t *a, const uint32_t *m);
+
+/*
+ * Decode an integer from its big-endian unsigned representation, and
+ * reduce it modulo the provided modulus m[]. The announced bit length
+ * of the result is set to be equal to that of the modulus.
+ *
+ * x[] MUST be distinct from m[].
+ */
+void br_i32_decode_reduce(uint32_t *x,
+ const void *src, size_t len, const uint32_t *m);
+
+/*
+ * Encode an integer into its big-endian unsigned representation. The
+ * output length in bytes is provided (parameter 'len'); if the length
+ * is too short then the integer is appropriately truncated; if it is
+ * too long then the extra bytes are set to 0.
+ */
+void br_i32_encode(void *dst, size_t len, const uint32_t *x);
+
+/*
+ * Multiply x[] by 2^32 and then add integer z, modulo m[]. This
+ * function assumes that x[] and m[] have the same announced bit
+ * length, and the announced bit length of m[] matches its true
+ * bit length.
+ *
+ * x[] and m[] MUST be distinct arrays.
+ *
+ * CT: only the common announced bit length of x and m leaks, not
+ * the values of x, z or m.
+ */
+void br_i32_muladd_small(uint32_t *x, uint32_t z, const uint32_t *m);
+
+/*
+ * Extract one word from an integer. The offset is counted in bits.
+ * The word MUST entirely fit within the word elements corresponding
+ * to the announced bit length of a[].
+ */
+static inline uint32_t
+br_i32_word(const uint32_t *a, uint32_t off)
+{
+ size_t u;
+ unsigned j;
+
+ u = (size_t)(off >> 5) + 1;
+ j = (unsigned)off & 31;
+ if (j == 0) {
+ return a[u];
+ } else {
+ return (a[u] >> j) | (a[u + 1] << (32 - j));
+ }
+}
+
+/*
+ * Test whether an integer is zero.
+ */
+uint32_t br_i32_iszero(const uint32_t *x);
+
+/*
+ * Add b[] to a[] and return the carry (0 or 1). If ctl is 0, then a[]
+ * is unmodified, but the carry is still computed and returned. The
+ * arrays a[] and b[] MUST have the same announced bit length.
+ *
+ * a[] and b[] MAY be the same array, but partial overlap is not allowed.
+ */
+uint32_t br_i32_add(uint32_t *a, const uint32_t *b, uint32_t ctl);
+
+/*
+ * Subtract b[] from a[] and return the carry (0 or 1). If ctl is 0,
+ * then a[] is unmodified, but the carry is still computed and returned.
+ * The arrays a[] and b[] MUST have the same announced bit length.
+ *
+ * a[] and b[] MAY be the same array, but partial overlap is not allowed.
+ */
+uint32_t br_i32_sub(uint32_t *a, const uint32_t *b, uint32_t ctl);
+
+/*
+ * Compute d+a*b, result in d. The initial announced bit length of d[]
+ * MUST match that of a[]. The d[] array MUST be large enough to
+ * accommodate the full result, plus (possibly) an extra word. The
+ * resulting announced bit length of d[] will be the sum of the announced
+ * bit lengths of a[] and b[] (therefore, it may be larger than the actual
+ * bit length of the numerical result).
+ *
+ * a[] and b[] may be the same array. d[] must be disjoint from both a[]
+ * and b[].
+ */
+void br_i32_mulacc(uint32_t *d, const uint32_t *a, const uint32_t *b);
+
+/*
+ * Zeroize an integer. The announced bit length is set to the provided
+ * value, and the corresponding words are set to 0.
+ */
+static inline void
+br_i32_zero(uint32_t *x, uint32_t bit_len)
+{
+ *x ++ = bit_len;
+ memset(x, 0, ((bit_len + 31) >> 5) * sizeof *x);
+}
+
+/*
+ * Compute -(1/x) mod 2^32. If x is even, then this function returns 0.
+ */
+uint32_t br_i32_ninv32(uint32_t x);
+
+/*
+ * Convert a modular integer to Montgomery representation. The integer x[]
+ * MUST be lower than m[], but with the same announced bit length.
+ */
+void br_i32_to_monty(uint32_t *x, const uint32_t *m);
+
+/*
+ * Convert a modular integer back from Montgomery representation. The
+ * integer x[] MUST be lower than m[], but with the same announced bit
+ * length. The "m0i" parameter is equal to -(1/m0) mod 2^32, where m0 is
+ * the least significant value word of m[] (this works only if m[] is
+ * an odd integer).
+ */
+void br_i32_from_monty(uint32_t *x, const uint32_t *m, uint32_t m0i);
+
+/*
+ * Compute a modular Montgomery multiplication. d[] is filled with the
+ * value of x*y/R modulo m[] (where R is the Montgomery factor). The
+ * array d[] MUST be distinct from x[], y[] and m[]. x[] and y[] MUST be
+ * numerically lower than m[]. x[] and y[] MAY be the same array. The
+ * "m0i" parameter is equal to -(1/m0) mod 2^32, where m0 is the least
+ * significant value word of m[] (this works only if m[] is an odd
+ * integer).
+ */
+void br_i32_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y,
+ const uint32_t *m, uint32_t m0i);
+
+/*
+ * Compute a modular exponentiation. x[] MUST be an integer modulo m[]
+ * (same announced bit length, lower value). m[] MUST be odd. The
+ * exponent is in big-endian unsigned notation, over 'elen' bytes. The
+ * "m0i" parameter is equal to -(1/m0) mod 2^32, where m0 is the least
+ * significant value word of m[] (this works only if m[] is an odd
+ * integer). The t1[] and t2[] parameters must be temporary arrays,
+ * each large enough to accommodate an integer with the same size as m[].
+ */
+void br_i32_modpow(uint32_t *x, const unsigned char *e, size_t elen,
+ const uint32_t *m, uint32_t m0i, uint32_t *t1, uint32_t *t2);
+
+/* ==================================================================== */
+
+/*
+ * Integers 'i31'
+ * --------------
+ *
+ * The 'i31' functions implement computations on big integers using
+ * an internal representation as an array of 32-bit integers. For
+ * an array x[]:
+ * -- x[0] encodes the array length and the "announced bit length"
+ * of the integer: namely, if the announced bit length is k,
+ * then x[0] = ((k / 31) << 5) + (k % 31).
+ * -- x[1], x[2]... contain the value in little-endian order, 31
+ * bits per word (x[1] contains the least significant 31 bits).
+ * The upper bit of each word is 0.
+ *
+ * Multiplications rely on the elementary 32x32->64 multiplication.
+ *
+ * The announced bit length specifies the number of bits that are
+ * significant in the subsequent 32-bit words. Unused bits in the
+ * last (most significant) word are set to 0; subsequent words are
+ * uninitialized and need not exist at all.
+ *
+ * The execution time and memory access patterns of all computations
+ * depend on the announced bit length, but not on the actual word
+ * values. For modular integers, the announced bit length of any integer
+ * modulo n is equal to the actual bit length of n; thus, computations
+ * on modular integers are "constant-time" (only the modulus length may
+ * leak).
+ */
+
+/*
+ * Test whether an integer is zero.
+ */
+uint32_t br_i31_iszero(const uint32_t *x);
+
+/*
+ * Add b[] to a[] and return the carry (0 or 1). If ctl is 0, then a[]
+ * is unmodified, but the carry is still computed and returned. The
+ * arrays a[] and b[] MUST have the same announced bit length.
+ *
+ * a[] and b[] MAY be the same array, but partial overlap is not allowed.
+ */
+uint32_t br_i31_add(uint32_t *a, const uint32_t *b, uint32_t ctl);
+
+/*
+ * Subtract b[] from a[] and return the carry (0 or 1). If ctl is 0,
+ * then a[] is unmodified, but the carry is still computed and returned.
+ * The arrays a[] and b[] MUST have the same announced bit length.
+ *
+ * a[] and b[] MAY be the same array, but partial overlap is not allowed.
+ */
+uint32_t br_i31_sub(uint32_t *a, const uint32_t *b, uint32_t ctl);
+
+/*
+ * Compute the ENCODED actual bit length of an integer. The argument x
+ * should point to the first (least significant) value word of the
+ * integer. The len 'xlen' contains the number of 32-bit words to
+ * access. The upper bit of each value word MUST be 0.
+ * Returned value is ((k / 31) << 5) + (k % 31) if the bit length is k.
+ *
+ * CT: value or length of x does not leak.
+ */
+uint32_t br_i31_bit_length(uint32_t *x, size_t xlen);
+
+/*
+ * Decode an integer from its big-endian unsigned representation. The
+ * "true" bit length of the integer is computed and set in the encoded
+ * announced bit length (x[0]), but all words of x[] corresponding to
+ * the full 'len' bytes of the source are set.
+ *
+ * CT: value or length of x does not leak.
+ */
+void br_i31_decode(uint32_t *x, const void *src, size_t len);
+
+/*
+ * Decode an integer from its big-endian unsigned representation. The
+ * integer MUST be lower than m[]; the (encoded) announced bit length
+ * written in x[] will be equal to that of m[]. All 'len' bytes from the
+ * source are read.
+ *
+ * Returned value is 1 if the decode value fits within the modulus, 0
+ * otherwise. In the latter case, the x[] buffer will be set to 0 (but
+ * still with the announced bit length of m[]).
+ *
+ * CT: value or length of x does not leak. Memory access pattern depends
+ * only of 'len' and the announced bit length of m. Whether x fits or
+ * not does not leak either.
+ */
+uint32_t br_i31_decode_mod(uint32_t *x,
+ const void *src, size_t len, const uint32_t *m);
+
+/*
+ * Zeroize an integer. The announced bit length is set to the provided
+ * value, and the corresponding words are set to 0. The ENCODED bit length
+ * is expected here.
+ */
+static inline void
+br_i31_zero(uint32_t *x, uint32_t bit_len)
+{
+ *x ++ = bit_len;
+ memset(x, 0, ((bit_len + 31) >> 5) * sizeof *x);
+}
+
+/*
+ * Right-shift an integer. The shift amount must be lower than 31
+ * bits.
+ */
+void br_i31_rshift(uint32_t *x, int count);
+
+/*
+ * Reduce an integer (a[]) modulo another (m[]). The result is written
+ * in x[] and its announced bit length is set to be equal to that of m[].
+ *
+ * x[] MUST be distinct from a[] and m[].
+ *
+ * CT: only announced bit lengths leak, not values of x, a or m.
+ */
+void br_i31_reduce(uint32_t *x, const uint32_t *a, const uint32_t *m);
+
+/*
+ * Decode an integer from its big-endian unsigned representation, and
+ * reduce it modulo the provided modulus m[]. The announced bit length
+ * of the result is set to be equal to that of the modulus.
+ *
+ * x[] MUST be distinct from m[].
+ */
+void br_i31_decode_reduce(uint32_t *x,
+ const void *src, size_t len, const uint32_t *m);
+
+/*
+ * Multiply x[] by 2^31 and then add integer z, modulo m[]. This
+ * function assumes that x[] and m[] have the same announced bit
+ * length, the announced bit length of m[] matches its true
+ * bit length.
+ *
+ * x[] and m[] MUST be distinct arrays. z MUST fit in 31 bits (upper
+ * bit set to 0).
+ *
+ * CT: only the common announced bit length of x and m leaks, not
+ * the values of x, z or m.
+ */
+void br_i31_muladd_small(uint32_t *x, uint32_t z, const uint32_t *m);
+
+/*
+ * Encode an integer into its big-endian unsigned representation. The
+ * output length in bytes is provided (parameter 'len'); if the length
+ * is too short then the integer is appropriately truncated; if it is
+ * too long then the extra bytes are set to 0.
+ */
+void br_i31_encode(void *dst, size_t len, const uint32_t *x);
+
+/*
+ * Compute -(1/x) mod 2^31. If x is even, then this function returns 0.
+ */
+uint32_t br_i31_ninv31(uint32_t x);
+
+/*
+ * Compute a modular Montgomery multiplication. d[] is filled with the
+ * value of x*y/R modulo m[] (where R is the Montgomery factor). The
+ * array d[] MUST be distinct from x[], y[] and m[]. x[] and y[] MUST be
+ * numerically lower than m[]. x[] and y[] MAY be the same array. The
+ * "m0i" parameter is equal to -(1/m0) mod 2^31, where m0 is the least
+ * significant value word of m[] (this works only if m[] is an odd
+ * integer).
+ */
+void br_i31_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y,
+ const uint32_t *m, uint32_t m0i);
+
+/*
+ * Convert a modular integer to Montgomery representation. The integer x[]
+ * MUST be lower than m[], but with the same announced bit length.
+ */
+void br_i31_to_monty(uint32_t *x, const uint32_t *m);
+
+/*
+ * Convert a modular integer back from Montgomery representation. The
+ * integer x[] MUST be lower than m[], but with the same announced bit
+ * length. The "m0i" parameter is equal to -(1/m0) mod 2^32, where m0 is
+ * the least significant value word of m[] (this works only if m[] is
+ * an odd integer).
+ */
+void br_i31_from_monty(uint32_t *x, const uint32_t *m, uint32_t m0i);
+
+/*
+ * Compute a modular exponentiation. x[] MUST be an integer modulo m[]
+ * (same announced bit length, lower value). m[] MUST be odd. The
+ * exponent is in big-endian unsigned notation, over 'elen' bytes. The
+ * "m0i" parameter is equal to -(1/m0) mod 2^31, where m0 is the least
+ * significant value word of m[] (this works only if m[] is an odd
+ * integer). The t1[] and t2[] parameters must be temporary arrays,
+ * each large enough to accommodate an integer with the same size as m[].
+ */
+void br_i31_modpow(uint32_t *x, const unsigned char *e, size_t elen,
+ const uint32_t *m, uint32_t m0i, uint32_t *t1, uint32_t *t2);
+
+/*
+ * Compute a modular exponentiation. x[] MUST be an integer modulo m[]
+ * (same announced bit length, lower value). m[] MUST be odd. The
+ * exponent is in big-endian unsigned notation, over 'elen' bytes. The
+ * "m0i" parameter is equal to -(1/m0) mod 2^31, where m0 is the least
+ * significant value word of m[] (this works only if m[] is an odd
+ * integer). The tmp[] array is used for temporaries, and has size
+ * 'twlen' words; it must be large enough to accommodate at least two
+ * temporary values with the same size as m[] (including the leading
+ * "bit length" word). If there is room for more temporaries, then this
+ * function may use the extra room for window-based optimisation,
+ * resulting in faster computations.
+ *
+ * Returned value is 1 on success, 0 on error. An error is reported if
+ * the provided tmp[] array is too short.
+ */
+uint32_t br_i31_modpow_opt(uint32_t *x, const unsigned char *e, size_t elen,
+ const uint32_t *m, uint32_t m0i, uint32_t *tmp, size_t twlen);
+
+/*
+ * Compute d+a*b, result in d. The initial announced bit length of d[]
+ * MUST match that of a[]. The d[] array MUST be large enough to
+ * accommodate the full result, plus (possibly) an extra word. The
+ * resulting announced bit length of d[] will be the sum of the announced
+ * bit lengths of a[] and b[] (therefore, it may be larger than the actual
+ * bit length of the numerical result).
+ *
+ * a[] and b[] may be the same array. d[] must be disjoint from both a[]
+ * and b[].
+ */
+void br_i31_mulacc(uint32_t *d, const uint32_t *a, const uint32_t *b);
+
+/*
+ * Compute x/y mod m, result in x. Values x and y must be between 0 and
+ * m-1, and have the same announced bit length as m. Modulus m must be
+ * odd. The "m0i" parameter is equal to -1/m mod 2^31. The array 't'
+ * must point to a temporary area that can hold at least three integers
+ * of the size of m.
+ *
+ * m may not overlap x and y. x and y may overlap each other (this can
+ * be useful to test whether a value is invertible modulo m). t must be
+ * disjoint from all other arrays.
+ *
+ * Returned value is 1 on success, 0 otherwise. Success is attained if
+ * y is invertible modulo m.
+ */
+uint32_t br_i31_moddiv(uint32_t *x, const uint32_t *y,
+ const uint32_t *m, uint32_t m0i, uint32_t *t);
+
+/* ==================================================================== */
+
+/*
+ * FIXME: document "i15" functions.
+ */
+
+static inline void
+br_i15_zero(uint16_t *x, uint16_t bit_len)
+{
+ *x ++ = bit_len;
+ memset(x, 0, ((bit_len + 15) >> 4) * sizeof *x);
+}
+
+uint32_t br_i15_iszero(const uint16_t *x);
+
+uint16_t br_i15_ninv15(uint16_t x);
+
+uint32_t br_i15_add(uint16_t *a, const uint16_t *b, uint32_t ctl);
+
+uint32_t br_i15_sub(uint16_t *a, const uint16_t *b, uint32_t ctl);
+
+void br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m);
+
+void br_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y,
+ const uint16_t *m, uint16_t m0i);
+
+void br_i15_to_monty(uint16_t *x, const uint16_t *m);
+
+void br_i15_modpow(uint16_t *x, const unsigned char *e, size_t elen,
+ const uint16_t *m, uint16_t m0i, uint16_t *t1, uint16_t *t2);
+
+uint32_t br_i15_modpow_opt(uint16_t *x, const unsigned char *e, size_t elen,
+ const uint16_t *m, uint16_t m0i, uint16_t *tmp, size_t twlen);
+
+void br_i15_encode(void *dst, size_t len, const uint16_t *x);
+
+uint32_t br_i15_decode_mod(uint16_t *x,
+ const void *src, size_t len, const uint16_t *m);
+
+void br_i15_rshift(uint16_t *x, int count);
+
+uint32_t br_i15_bit_length(uint16_t *x, size_t xlen);
+
+void br_i15_decode(uint16_t *x, const void *src, size_t len);
+
+void br_i15_from_monty(uint16_t *x, const uint16_t *m, uint16_t m0i);
+
+void br_i15_decode_reduce(uint16_t *x,
+ const void *src, size_t len, const uint16_t *m);
+
+void br_i15_reduce(uint16_t *x, const uint16_t *a, const uint16_t *m);
+
+void br_i15_mulacc(uint16_t *d, const uint16_t *a, const uint16_t *b);
+
+uint32_t br_i15_moddiv(uint16_t *x, const uint16_t *y,
+ const uint16_t *m, uint16_t m0i, uint16_t *t);
+
+/*
+ * Variant of br_i31_modpow_opt() that internally uses 64x64->128
+ * multiplications. It expects the same parameters as br_i31_modpow_opt(),
+ * except that the temporaries should be 64-bit integers, not 32-bit
+ * integers.
+ */
+uint32_t br_i62_modpow_opt(uint32_t *x31, const unsigned char *e, size_t elen,
+ const uint32_t *m31, uint32_t m0i31, uint64_t *tmp, size_t twlen);
+
+/*
+ * Type for a function with the same API as br_i31_modpow_opt() (some
+ * implementations of this type may have stricter alignment requirements
+ * on the temporaries).
+ */
+typedef uint32_t (*br_i31_modpow_opt_type)(uint32_t *x,
+ const unsigned char *e, size_t elen,
+ const uint32_t *m, uint32_t m0i, uint32_t *tmp, size_t twlen);
+
+/*
+ * Wrapper for br_i62_modpow_opt() that uses the same type as
+ * br_i31_modpow_opt(); however, it requires its 'tmp' argument to the
+ * 64-bit aligned.
+ */
+uint32_t br_i62_modpow_opt_as_i31(uint32_t *x,
+ const unsigned char *e, size_t elen,
+ const uint32_t *m, uint32_t m0i, uint32_t *tmp, size_t twlen);
+
+/* ==================================================================== */
+
+static inline size_t
+br_digest_size(const br_hash_class *digest_class)
+{
+ return (size_t)(digest_class->desc >> BR_HASHDESC_OUT_OFF)
+ & BR_HASHDESC_OUT_MASK;
+}
+
+/*
+ * Get the output size (in bytes) of a hash function.
+ */
+size_t br_digest_size_by_ID(int digest_id);
+
+/*
+ * Get the OID (encoded OBJECT IDENTIFIER value, without tag and length)
+ * for a hash function. If digest_id is not a supported digest identifier
+ * (in particular if it is equal to 0, i.e. br_md5sha1_ID), then NULL is
+ * returned and *len is set to 0.
+ */
+const unsigned char *br_digest_OID(int digest_id, size_t *len);
+
+/* ==================================================================== */
+/*
+ * DES support functions.
+ */
+
+/*
+ * Apply DES Initial Permutation.
+ */
+void br_des_do_IP(uint32_t *xl, uint32_t *xr);
+
+/*
+ * Apply DES Final Permutation (inverse of IP).
+ */
+void br_des_do_invIP(uint32_t *xl, uint32_t *xr);
+
+/*
+ * Key schedule unit: for a DES key (8 bytes), compute 16 subkeys. Each
+ * subkey is two 28-bit words represented as two 32-bit words; the PC-2
+ * bit extration is NOT applied.
+ */
+void br_des_keysched_unit(uint32_t *skey, const void *key);
+
+/*
+ * Reversal of 16 DES sub-keys (for decryption).
+ */
+void br_des_rev_skey(uint32_t *skey);
+
+/*
+ * DES/3DES key schedule for 'des_tab' (encryption direction). Returned
+ * value is the number of rounds.
+ */
+unsigned br_des_tab_keysched(uint32_t *skey, const void *key, size_t key_len);
+
+/*
+ * DES/3DES key schedule for 'des_ct' (encryption direction). Returned
+ * value is the number of rounds.
+ */
+unsigned br_des_ct_keysched(uint32_t *skey, const void *key, size_t key_len);
+
+/*
+ * DES/3DES subkey decompression (from the compressed bitsliced subkeys).
+ */
+void br_des_ct_skey_expand(uint32_t *sk_exp,
+ unsigned num_rounds, const uint32_t *skey);
+
+/*
+ * DES/3DES block encryption/decryption ('des_tab').
+ */
+void br_des_tab_process_block(unsigned num_rounds,
+ const uint32_t *skey, void *block);
+
+/*
+ * DES/3DES block encryption/decryption ('des_ct').
+ */
+void br_des_ct_process_block(unsigned num_rounds,
+ const uint32_t *skey, void *block);
+
+/* ==================================================================== */
+/*
+ * AES support functions.
+ */
+
+/*
+ * The AES S-box (256-byte table).
+ */
+extern const unsigned char br_aes_S[];
+
+/*
+ * AES key schedule. skey[] is filled with n+1 128-bit subkeys, where n
+ * is the number of rounds (10 to 14, depending on key size). The number
+ * of rounds is returned. If the key size is invalid (not 16, 24 or 32),
+ * then 0 is returned.
+ *
+ * This implementation uses a 256-byte table and is NOT constant-time.
+ */
+unsigned br_aes_keysched(uint32_t *skey, const void *key, size_t key_len);
+
+/*
+ * AES key schedule for decryption ('aes_big' implementation).
+ */
+unsigned br_aes_big_keysched_inv(uint32_t *skey,
+ const void *key, size_t key_len);
+
+/*
+ * AES block encryption with the 'aes_big' implementation (fast, but
+ * not constant-time). This function encrypts a single block "in place".
+ */
+void br_aes_big_encrypt(unsigned num_rounds, const uint32_t *skey, void *data);
+
+/*
+ * AES block decryption with the 'aes_big' implementation (fast, but
+ * not constant-time). This function decrypts a single block "in place".
+ */
+void br_aes_big_decrypt(unsigned num_rounds, const uint32_t *skey, void *data);
+
+/*
+ * AES block encryption with the 'aes_small' implementation (small, but
+ * slow and not constant-time). This function encrypts a single block
+ * "in place".
+ */
+void br_aes_small_encrypt(unsigned num_rounds,
+ const uint32_t *skey, void *data);
+
+/*
+ * AES block decryption with the 'aes_small' implementation (small, but
+ * slow and not constant-time). This function decrypts a single block
+ * "in place".
+ */
+void br_aes_small_decrypt(unsigned num_rounds,
+ const uint32_t *skey, void *data);
+
+/*
+ * The constant-time implementation is "bitsliced": the 128-bit state is
+ * split over eight 32-bit words q* in the following way:
+ *
+ * -- Input block consists in 16 bytes:
+ * a00 a10 a20 a30 a01 a11 a21 a31 a02 a12 a22 a32 a03 a13 a23 a33
+ * In the terminology of FIPS 197, this is a 4x4 matrix which is read
+ * column by column.
+ *
+ * -- Each byte is split into eight bits which are distributed over the
+ * eight words, at the same rank. Thus, for a byte x at rank k, bit 0
+ * (least significant) of x will be at rank k in q0 (if that bit is b,
+ * then it contributes "b << k" to the value of q0), bit 1 of x will be
+ * at rank k in q1, and so on.
+ *
+ * -- Ranks given to bits are in "row order" and are either all even, or
+ * all odd. Two independent AES states are thus interleaved, one using
+ * the even ranks, the other the odd ranks. Row order means:
+ * a00 a01 a02 a03 a10 a11 a12 a13 a20 a21 a22 a23 a30 a31 a32 a33
+ *
+ * Converting input bytes from two AES blocks to bitslice representation
+ * is done in the following way:
+ * -- Decode first block into the four words q0 q2 q4 q6, in that order,
+ * using little-endian convention.
+ * -- Decode second block into the four words q1 q3 q5 q7, in that order,
+ * using little-endian convention.
+ * -- Call br_aes_ct_ortho().
+ *
+ * Converting back to bytes is done by using the reverse operations. Note
+ * that br_aes_ct_ortho() is its own inverse.
+ */
+
+/*
+ * Perform bytewise orthogonalization of eight 32-bit words. Bytes
+ * of q0..q7 are spread over all words: for a byte x that occurs
+ * at rank i in q[j] (byte x uses bits 8*i to 8*i+7 in q[j]), the bit
+ * of rank k in x (0 <= k <= 7) goes to q[k] at rank 8*i+j.
+ *
+ * This operation is an involution.
+ */
+void br_aes_ct_ortho(uint32_t *q);
+
+/*
+ * The AES S-box, as a bitsliced constant-time version. The input array
+ * consists in eight 32-bit words; 32 S-box instances are computed in
+ * parallel. Bits 0 to 7 of each S-box input (bit 0 is least significant)
+ * are spread over the words 0 to 7, at the same rank.
+ */
+void br_aes_ct_bitslice_Sbox(uint32_t *q);
+
+/*
+ * Like br_aes_bitslice_Sbox(), but for the inverse S-box.
+ */
+void br_aes_ct_bitslice_invSbox(uint32_t *q);
+
+/*
+ * Compute AES encryption on bitsliced data. Since input is stored on
+ * eight 32-bit words, two block encryptions are actually performed
+ * in parallel.
+ */
+void br_aes_ct_bitslice_encrypt(unsigned num_rounds,
+ const uint32_t *skey, uint32_t *q);
+
+/*
+ * Compute AES decryption on bitsliced data. Since input is stored on
+ * eight 32-bit words, two block decryptions are actually performed
+ * in parallel.
+ */
+void br_aes_ct_bitslice_decrypt(unsigned num_rounds,
+ const uint32_t *skey, uint32_t *q);
+
+/*
+ * AES key schedule, constant-time version. skey[] is filled with n+1
+ * 128-bit subkeys, where n is the number of rounds (10 to 14, depending
+ * on key size). The number of rounds is returned. If the key size is
+ * invalid (not 16, 24 or 32), then 0 is returned.
+ */
+unsigned br_aes_ct_keysched(uint32_t *comp_skey,
+ const void *key, size_t key_len);
+
+/*
+ * Expand AES subkeys as produced by br_aes_ct_keysched(), into
+ * a larger array suitable for br_aes_ct_bitslice_encrypt() and
+ * br_aes_ct_bitslice_decrypt().
+ */
+void br_aes_ct_skey_expand(uint32_t *skey,
+ unsigned num_rounds, const uint32_t *comp_skey);
+
+/*
+ * For the ct64 implementation, the same bitslicing technique is used,
+ * but four instances are interleaved. First instance uses bits 0, 4,
+ * 8, 12,... of each word; second instance uses bits 1, 5, 9, 13,...
+ * and so on.
+ */
+
+/*
+ * Perform bytewise orthogonalization of eight 64-bit words. Bytes
+ * of q0..q7 are spread over all words: for a byte x that occurs
+ * at rank i in q[j] (byte x uses bits 8*i to 8*i+7 in q[j]), the bit
+ * of rank k in x (0 <= k <= 7) goes to q[k] at rank 8*i+j.
+ *
+ * This operation is an involution.
+ */
+void br_aes_ct64_ortho(uint64_t *q);
+
+/*
+ * Interleave bytes for an AES input block. If input bytes are
+ * denoted 0123456789ABCDEF, and have been decoded with little-endian
+ * convention (w[0] contains 0123, with '3' being most significant;
+ * w[1] contains 4567, and so on), then output word q0 will be
+ * set to 08192A3B (again little-endian convention) and q1 will
+ * be set to 4C5D6E7F.
+ */
+void br_aes_ct64_interleave_in(uint64_t *q0, uint64_t *q1, const uint32_t *w);
+
+/*
+ * Perform the opposite of br_aes_ct64_interleave_in().
+ */
+void br_aes_ct64_interleave_out(uint32_t *w, uint64_t q0, uint64_t q1);
+
+/*
+ * The AES S-box, as a bitsliced constant-time version. The input array
+ * consists in eight 64-bit words; 64 S-box instances are computed in
+ * parallel. Bits 0 to 7 of each S-box input (bit 0 is least significant)
+ * are spread over the words 0 to 7, at the same rank.
+ */
+void br_aes_ct64_bitslice_Sbox(uint64_t *q);
+
+/*
+ * Like br_aes_bitslice_Sbox(), but for the inverse S-box.
+ */
+void br_aes_ct64_bitslice_invSbox(uint64_t *q);
+
+/*
+ * Compute AES encryption on bitsliced data. Since input is stored on
+ * eight 64-bit words, four block encryptions are actually performed
+ * in parallel.
+ */
+void br_aes_ct64_bitslice_encrypt(unsigned num_rounds,
+ const uint64_t *skey, uint64_t *q);
+
+/*
+ * Compute AES decryption on bitsliced data. Since input is stored on
+ * eight 64-bit words, four block decryptions are actually performed
+ * in parallel.
+ */
+void br_aes_ct64_bitslice_decrypt(unsigned num_rounds,
+ const uint64_t *skey, uint64_t *q);
+
+/*
+ * AES key schedule, constant-time version. skey[] is filled with n+1
+ * 128-bit subkeys, where n is the number of rounds (10 to 14, depending
+ * on key size). The number of rounds is returned. If the key size is
+ * invalid (not 16, 24 or 32), then 0 is returned.
+ */
+unsigned br_aes_ct64_keysched(uint64_t *comp_skey,
+ const void *key, size_t key_len);
+
+/*
+ * Expand AES subkeys as produced by br_aes_ct64_keysched(), into
+ * a larger array suitable for br_aes_ct64_bitslice_encrypt() and
+ * br_aes_ct64_bitslice_decrypt().
+ */
+void br_aes_ct64_skey_expand(uint64_t *skey,
+ unsigned num_rounds, const uint64_t *comp_skey);
+
+/*
+ * Test support for AES-NI opcodes.
+ */
+int br_aes_x86ni_supported(void);
+
+/*
+ * AES key schedule, using x86 AES-NI instructions. This yields the
+ * subkeys in the encryption direction. Number of rounds is returned.
+ * Key size MUST be 16, 24 or 32 bytes; otherwise, 0 is returned.
+ */
+unsigned br_aes_x86ni_keysched_enc(unsigned char *skni,
+ const void *key, size_t len);
+
+/*
+ * AES key schedule, using x86 AES-NI instructions. This yields the
+ * subkeys in the decryption direction. Number of rounds is returned.
+ * Key size MUST be 16, 24 or 32 bytes; otherwise, 0 is returned.
+ */
+unsigned br_aes_x86ni_keysched_dec(unsigned char *skni,
+ const void *key, size_t len);
+
+/*
+ * Test support for AES POWER8 opcodes.
+ */
+int br_aes_pwr8_supported(void);
+
+/*
+ * AES key schedule, using POWER8 instructions. This yields the
+ * subkeys in the encryption direction. Number of rounds is returned.
+ * Key size MUST be 16, 24 or 32 bytes; otherwise, 0 is returned.
+ */
+unsigned br_aes_pwr8_keysched(unsigned char *skni,
+ const void *key, size_t len);
+
+/* ==================================================================== */
+/*
+ * RSA.
+ */
+
+/*
+ * Apply proper PKCS#1 v1.5 padding (for signatures). 'hash_oid' is
+ * the encoded hash function OID, or NULL.
+ */
+uint32_t br_rsa_pkcs1_sig_pad(const unsigned char *hash_oid,
+ const unsigned char *hash, size_t hash_len,
+ uint32_t n_bitlen, unsigned char *x);
+
+/*
+ * Check PKCS#1 v1.5 padding (for signatures). 'hash_oid' is the encoded
+ * hash function OID, or NULL. The provided 'sig' value is _after_ the
+ * modular exponentiation, i.e. it should be the padded hash. On
+ * success, the hashed message is extracted.
+ */
+uint32_t br_rsa_pkcs1_sig_unpad(const unsigned char *sig, size_t sig_len,
+ const unsigned char *hash_oid, size_t hash_len,
+ unsigned char *hash_out);
+
+/*
+ * Apply proper PSS padding. The 'x' buffer is output only: it
+ * receives the value that is to be exponentiated.
+ */
+uint32_t br_rsa_pss_sig_pad(const br_prng_class **rng,
+ const br_hash_class *hf_data, const br_hash_class *hf_mgf1,
+ const unsigned char *hash, size_t salt_len,
+ uint32_t n_bitlen, unsigned char *x);
+
+/*
+ * Check PSS padding. The provided value is the one _after_
+ * the modular exponentiation; it is modified by this function.
+ * This function infers the signature length from the public key
+ * size, i.e. it assumes that this has already been verified (as
+ * part of the exponentiation).
+ */
+uint32_t br_rsa_pss_sig_unpad(
+ const br_hash_class *hf_data, const br_hash_class *hf_mgf1,
+ const unsigned char *hash, size_t salt_len,
+ const br_rsa_public_key *pk, unsigned char *x);
+
+/*
+ * Apply OAEP padding. Returned value is the actual padded string length,
+ * or zero on error.
+ */
+size_t br_rsa_oaep_pad(const br_prng_class **rnd, const br_hash_class *dig,
+ const void *label, size_t label_len, const br_rsa_public_key *pk,
+ void *dst, size_t dst_nax_len, const void *src, size_t src_len);
+
+/*
+ * Unravel and check OAEP padding. If the padding is correct, then 1 is
+ * returned, '*len' is adjusted to the length of the message, and the
+ * data is moved to the start of the 'data' buffer. If the padding is
+ * incorrect, then 0 is returned and '*len' is untouched. Either way,
+ * the complete buffer contents are altered.
+ */
+uint32_t br_rsa_oaep_unpad(const br_hash_class *dig,
+ const void *label, size_t label_len, void *data, size_t *len);
+
+/*
+ * Compute MGF1 for a given seed, and XOR the output into the provided
+ * buffer.
+ */
+void br_mgf1_xor(void *data, size_t len,
+ const br_hash_class *dig, const void *seed, size_t seed_len);
+
+/*
+ * Inner function for RSA key generation; used by the "i31" and "i62"
+ * implementations.
+ */
+uint32_t br_rsa_i31_keygen_inner(const br_prng_class **rng,
+ br_rsa_private_key *sk, void *kbuf_priv,
+ br_rsa_public_key *pk, void *kbuf_pub,
+ unsigned size, uint32_t pubexp, br_i31_modpow_opt_type mp31);
+
+/* ==================================================================== */
+/*
+ * Elliptic curves.
+ */
+
+/*
+ * Type for generic EC parameters: curve order (unsigned big-endian
+ * encoding) and encoded conventional generator.
+ */
+typedef struct {
+ int curve;
+ const unsigned char *order;
+ size_t order_len;
+ const unsigned char *generator;
+ size_t generator_len;
+} br_ec_curve_def;
+
+extern const br_ec_curve_def br_secp256r1;
+extern const br_ec_curve_def br_secp384r1;
+extern const br_ec_curve_def br_secp521r1;
+
+/*
+ * For Curve25519, the advertised "order" really is 2^255-1, since the
+ * point multipliction function really works over arbitrary 255-bit
+ * scalars. This value is only meant as a hint for ECDH key generation;
+ * only ECDSA uses the exact curve order, and ECDSA is not used with
+ * that specific curve.
+ */
+extern const br_ec_curve_def br_curve25519;
+
+/*
+ * Decode some bytes as an i31 integer, with truncation (corresponding
+ * to the 'bits2int' operation in RFC 6979). The target ENCODED bit
+ * length is provided as last parameter. The resulting value will have
+ * this declared bit length, and consists the big-endian unsigned decoding
+ * of exactly that many bits in the source (capped at the source length).
+ */
+void br_ecdsa_i31_bits2int(uint32_t *x,
+ const void *src, size_t len, uint32_t ebitlen);
+
+/*
+ * Decode some bytes as an i15 integer, with truncation (corresponding
+ * to the 'bits2int' operation in RFC 6979). The target ENCODED bit
+ * length is provided as last parameter. The resulting value will have
+ * this declared bit length, and consists the big-endian unsigned decoding
+ * of exactly that many bits in the source (capped at the source length).
+ */
+void br_ecdsa_i15_bits2int(uint16_t *x,
+ const void *src, size_t len, uint32_t ebitlen);
+
+/* ==================================================================== */
+/*
+ * ASN.1 support functions.
+ */
+
+/*
+ * A br_asn1_uint structure contains encoding information about an
+ * INTEGER nonnegative value: pointer to the integer contents (unsigned
+ * big-endian representation), length of the integer contents,
+ * and length of the encoded value. The data shall have minimal length:
+ * - If the integer value is zero, then 'len' must be zero.
+ * - If the integer value is not zero, then data[0] must be non-zero.
+ *
+ * Under these conditions, 'asn1len' is necessarily equal to either len
+ * or len+1.
+ */
+typedef struct {
+ const unsigned char *data;
+ size_t len;
+ size_t asn1len;
+} br_asn1_uint;
+
+/*
+ * Given an encoded integer (unsigned big-endian, with possible leading
+ * bytes of value 0), returned the "prepared INTEGER" structure.
+ */
+br_asn1_uint br_asn1_uint_prepare(const void *xdata, size_t xlen);
+
+/*
+ * Encode an ASN.1 length. The length of the encoded length is returned.
+ * If 'dest' is NULL, then no encoding is performed, but the length of
+ * the encoded length is still computed and returned.
+ */
+size_t br_asn1_encode_length(void *dest, size_t len);
+
+/*
+ * Convenient macro for computing lengths of lengths.
+ */
+#define len_of_len(len) br_asn1_encode_length(NULL, len)
+
+/*
+ * Encode a (prepared) ASN.1 INTEGER. The encoded length is returned.
+ * If 'dest' is NULL, then no encoding is performed, but the length of
+ * the encoded integer is still computed and returned.
+ */
+size_t br_asn1_encode_uint(void *dest, br_asn1_uint pp);
+
+/*
+ * Get the OID that identifies an elliptic curve. Returned value is
+ * the DER-encoded OID, with the length (always one byte) but without
+ * the tag. Thus, the first byte of the returned buffer contains the
+ * number of subsequent bytes in the value. If the curve is not
+ * recognised, NULL is returned.
+ */
+const unsigned char *br_get_curve_OID(int curve);
+
+/*
+ * Inner function for EC private key encoding. This is equivalent to
+ * the API function br_encode_ec_raw_der(), except for an extra
+ * parameter: if 'include_curve_oid' is zero, then the curve OID is
+ * _not_ included in the output blob (this is for PKCS#8 support).
+ */
+size_t br_encode_ec_raw_der_inner(void *dest,
+ const br_ec_private_key *sk, const br_ec_public_key *pk,
+ int include_curve_oid);
+
+/* ==================================================================== */
+/*
+ * SSL/TLS support functions.
+ */
+
+/*
+ * Record types.
+ */
+#define BR_SSL_CHANGE_CIPHER_SPEC 20
+#define BR_SSL_ALERT 21
+#define BR_SSL_HANDSHAKE 22
+#define BR_SSL_APPLICATION_DATA 23
+
+/*
+ * Handshake message types.
+ */
+#define BR_SSL_HELLO_REQUEST 0
+#define BR_SSL_CLIENT_HELLO 1
+#define BR_SSL_SERVER_HELLO 2
+#define BR_SSL_CERTIFICATE 11
+#define BR_SSL_SERVER_KEY_EXCHANGE 12
+#define BR_SSL_CERTIFICATE_REQUEST 13
+#define BR_SSL_SERVER_HELLO_DONE 14
+#define BR_SSL_CERTIFICATE_VERIFY 15
+#define BR_SSL_CLIENT_KEY_EXCHANGE 16
+#define BR_SSL_FINISHED 20
+
+/*
+ * Alert levels.
+ */
+#define BR_LEVEL_WARNING 1
+#define BR_LEVEL_FATAL 2
+
+/*
+ * Low-level I/O state.
+ */
+#define BR_IO_FAILED 0
+#define BR_IO_IN 1
+#define BR_IO_OUT 2
+#define BR_IO_INOUT 3
+
+/*
+ * Mark a SSL engine as failed. The provided error code is recorded if
+ * the engine was not already marked as failed. If 'err' is 0, then the
+ * engine is marked as closed (without error).
+ */
+void br_ssl_engine_fail(br_ssl_engine_context *cc, int err);
+
+/*
+ * Test whether the engine is closed (normally or as a failure).
+ */
+static inline int
+br_ssl_engine_closed(const br_ssl_engine_context *cc)
+{
+ return cc->iomode == BR_IO_FAILED;
+}
+
+/*
+ * Configure a new maximum fragment length. If possible, the maximum
+ * length for outgoing records is immediately adjusted (if there are
+ * not already too many buffered bytes for that).
+ */
+void br_ssl_engine_new_max_frag_len(
+ br_ssl_engine_context *rc, unsigned max_frag_len);
+
+/*
+ * Test whether the current incoming record has been fully received
+ * or not. This functions returns 0 only if a complete record header
+ * has been received, but some of the (possibly encrypted) payload
+ * has not yet been obtained.
+ */
+int br_ssl_engine_recvrec_finished(const br_ssl_engine_context *rc);
+
+/*
+ * Flush the current record (if not empty). This is meant to be called
+ * from the handshake processor only.
+ */
+void br_ssl_engine_flush_record(br_ssl_engine_context *cc);
+
+/*
+ * Test whether there is some accumulated payload to send.
+ */
+static inline int
+br_ssl_engine_has_pld_to_send(const br_ssl_engine_context *rc)
+{
+ return rc->oxa != rc->oxb && rc->oxa != rc->oxc;
+}
+
+/*
+ * Initialize RNG in engine. Returned value is 1 on success, 0 on error.
+ * This function will try to use the OS-provided RNG, if available. If
+ * there is no OS-provided RNG, or if it failed, and no entropy was
+ * injected by the caller, then a failure will be reported. On error,
+ * the context error code is set.
+ */
+int br_ssl_engine_init_rand(br_ssl_engine_context *cc);
+
+/*
+ * Reset the handshake-related parts of the engine.
+ */
+void br_ssl_engine_hs_reset(br_ssl_engine_context *cc,
+ void (*hsinit)(void *), void (*hsrun)(void *));
+
+/*
+ * Get the PRF to use for this context, for the provided PRF hash
+ * function ID.
+ */
+br_tls_prf_impl br_ssl_engine_get_PRF(br_ssl_engine_context *cc, int prf_id);
+
+/*
+ * Consume the provided pre-master secret and compute the corresponding
+ * master secret. The 'prf_id' is the ID of the hash function to use
+ * with the TLS 1.2 PRF (ignored if the version is TLS 1.0 or 1.1).
+ */
+void br_ssl_engine_compute_master(br_ssl_engine_context *cc,
+ int prf_id, const void *pms, size_t len);
+
+/*
+ * Switch to CBC decryption for incoming records.
+ * cc the engine context
+ * is_client non-zero for a client, zero for a server
+ * prf_id id of hash function for PRF (ignored if not TLS 1.2+)
+ * mac_id id of hash function for HMAC
+ * bc_impl block cipher implementation (CBC decryption)
+ * cipher_key_len block cipher key length (in bytes)
+ */
+void br_ssl_engine_switch_cbc_in(br_ssl_engine_context *cc,
+ int is_client, int prf_id, int mac_id,
+ const br_block_cbcdec_class *bc_impl, size_t cipher_key_len);
+
+/*
+ * Switch to CBC encryption for outgoing records.
+ * cc the engine context
+ * is_client non-zero for a client, zero for a server
+ * prf_id id of hash function for PRF (ignored if not TLS 1.2+)
+ * mac_id id of hash function for HMAC
+ * bc_impl block cipher implementation (CBC encryption)
+ * cipher_key_len block cipher key length (in bytes)
+ */
+void br_ssl_engine_switch_cbc_out(br_ssl_engine_context *cc,
+ int is_client, int prf_id, int mac_id,
+ const br_block_cbcenc_class *bc_impl, size_t cipher_key_len);
+
+/*
+ * Switch to GCM decryption for incoming records.
+ * cc the engine context
+ * is_client non-zero for a client, zero for a server
+ * prf_id id of hash function for PRF
+ * bc_impl block cipher implementation (CTR)
+ * cipher_key_len block cipher key length (in bytes)
+ */
+void br_ssl_engine_switch_gcm_in(br_ssl_engine_context *cc,
+ int is_client, int prf_id,
+ const br_block_ctr_class *bc_impl, size_t cipher_key_len);
+
+/*
+ * Switch to GCM encryption for outgoing records.
+ * cc the engine context
+ * is_client non-zero for a client, zero for a server
+ * prf_id id of hash function for PRF
+ * bc_impl block cipher implementation (CTR)
+ * cipher_key_len block cipher key length (in bytes)
+ */
+void br_ssl_engine_switch_gcm_out(br_ssl_engine_context *cc,
+ int is_client, int prf_id,
+ const br_block_ctr_class *bc_impl, size_t cipher_key_len);
+
+/*
+ * Switch to ChaCha20+Poly1305 decryption for incoming records.
+ * cc the engine context
+ * is_client non-zero for a client, zero for a server
+ * prf_id id of hash function for PRF
+ */
+void br_ssl_engine_switch_chapol_in(br_ssl_engine_context *cc,
+ int is_client, int prf_id);
+
+/*
+ * Switch to ChaCha20+Poly1305 encryption for outgoing records.
+ * cc the engine context
+ * is_client non-zero for a client, zero for a server
+ * prf_id id of hash function for PRF
+ */
+void br_ssl_engine_switch_chapol_out(br_ssl_engine_context *cc,
+ int is_client, int prf_id);
+
+/*
+ * Switch to CCM decryption for incoming records.
+ * cc the engine context
+ * is_client non-zero for a client, zero for a server
+ * prf_id id of hash function for PRF
+ * bc_impl block cipher implementation (CTR+CBC)
+ * cipher_key_len block cipher key length (in bytes)
+ * tag_len tag length (in bytes)
+ */
+void br_ssl_engine_switch_ccm_in(br_ssl_engine_context *cc,
+ int is_client, int prf_id,
+ const br_block_ctrcbc_class *bc_impl,
+ size_t cipher_key_len, size_t tag_len);
+
+/*
+ * Switch to GCM encryption for outgoing records.
+ * cc the engine context
+ * is_client non-zero for a client, zero for a server
+ * prf_id id of hash function for PRF
+ * bc_impl block cipher implementation (CTR+CBC)
+ * cipher_key_len block cipher key length (in bytes)
+ * tag_len tag length (in bytes)
+ */
+void br_ssl_engine_switch_ccm_out(br_ssl_engine_context *cc,
+ int is_client, int prf_id,
+ const br_block_ctrcbc_class *bc_impl,
+ size_t cipher_key_len, size_t tag_len);
+
+/*
+ * Calls to T0-generated code.
+ */
+void br_ssl_hs_client_init_main(void *ctx);
+void br_ssl_hs_client_run(void *ctx);
+void br_ssl_hs_server_init_main(void *ctx);
+void br_ssl_hs_server_run(void *ctx);
+
+/*
+ * Get the hash function to use for signatures, given a bit mask of
+ * supported hash functions. This implements a strict choice order
+ * (namely SHA-256, SHA-384, SHA-512, SHA-224, SHA-1). If the mask
+ * does not document support of any of these hash functions, then this
+ * functions returns 0.
+ */
+int br_ssl_choose_hash(unsigned bf);
+
+/* ==================================================================== */
+
+/*
+ * PowerPC / POWER assembly stuff. The special BR_POWER_ASM_MACROS macro
+ * must be defined before including this file; this is done by source
+ * files that use some inline assembly for PowerPC / POWER machines.
+ */
+
+#if BR_POWER_ASM_MACROS
+
+#define lxvw4x(xt, ra, rb) lxvw4x_(xt, ra, rb)
+#define stxvw4x(xt, ra, rb) stxvw4x_(xt, ra, rb)
+
+#define bdnz(foo) bdnz_(foo)
+#define bdz(foo) bdz_(foo)
+#define beq(foo) beq_(foo)
+
+#define li(rx, value) li_(rx, value)
+#define addi(rx, ra, imm) addi_(rx, ra, imm)
+#define cmpldi(rx, imm) cmpldi_(rx, imm)
+#define mtctr(rx) mtctr_(rx)
+#define vspltb(vrt, vrb, uim) vspltb_(vrt, vrb, uim)
+#define vspltw(vrt, vrb, uim) vspltw_(vrt, vrb, uim)
+#define vspltisb(vrt, imm) vspltisb_(vrt, imm)
+#define vspltisw(vrt, imm) vspltisw_(vrt, imm)
+#define vrlw(vrt, vra, vrb) vrlw_(vrt, vra, vrb)
+#define vsbox(vrt, vra) vsbox_(vrt, vra)
+#define vxor(vrt, vra, vrb) vxor_(vrt, vra, vrb)
+#define vand(vrt, vra, vrb) vand_(vrt, vra, vrb)
+#define vsro(vrt, vra, vrb) vsro_(vrt, vra, vrb)
+#define vsl(vrt, vra, vrb) vsl_(vrt, vra, vrb)
+#define vsldoi(vt, va, vb, sh) vsldoi_(vt, va, vb, sh)
+#define vsr(vrt, vra, vrb) vsr_(vrt, vra, vrb)
+#define vaddcuw(vrt, vra, vrb) vaddcuw_(vrt, vra, vrb)
+#define vadduwm(vrt, vra, vrb) vadduwm_(vrt, vra, vrb)
+#define vsububm(vrt, vra, vrb) vsububm_(vrt, vra, vrb)
+#define vsubuwm(vrt, vra, vrb) vsubuwm_(vrt, vra, vrb)
+#define vsrw(vrt, vra, vrb) vsrw_(vrt, vra, vrb)
+#define vcipher(vt, va, vb) vcipher_(vt, va, vb)
+#define vcipherlast(vt, va, vb) vcipherlast_(vt, va, vb)
+#define vncipher(vt, va, vb) vncipher_(vt, va, vb)
+#define vncipherlast(vt, va, vb) vncipherlast_(vt, va, vb)
+#define vperm(vt, va, vb, vc) vperm_(vt, va, vb, vc)
+#define vpmsumd(vt, va, vb) vpmsumd_(vt, va, vb)
+#define xxpermdi(vt, va, vb, d) xxpermdi_(vt, va, vb, d)
+
+#define lxvw4x_(xt, ra, rb) "\tlxvw4x\t" #xt "," #ra "," #rb "\n"
+#define stxvw4x_(xt, ra, rb) "\tstxvw4x\t" #xt "," #ra "," #rb "\n"
+
+#define label(foo) #foo "%=:\n"
+#define bdnz_(foo) "\tbdnz\t" #foo "%=\n"
+#define bdz_(foo) "\tbdz\t" #foo "%=\n"
+#define beq_(foo) "\tbeq\t" #foo "%=\n"
+
+#define li_(rx, value) "\tli\t" #rx "," #value "\n"
+#define addi_(rx, ra, imm) "\taddi\t" #rx "," #ra "," #imm "\n"
+#define cmpldi_(rx, imm) "\tcmpldi\t" #rx "," #imm "\n"
+#define mtctr_(rx) "\tmtctr\t" #rx "\n"
+#define vspltb_(vrt, vrb, uim) "\tvspltb\t" #vrt "," #vrb "," #uim "\n"
+#define vspltw_(vrt, vrb, uim) "\tvspltw\t" #vrt "," #vrb "," #uim "\n"
+#define vspltisb_(vrt, imm) "\tvspltisb\t" #vrt "," #imm "\n"
+#define vspltisw_(vrt, imm) "\tvspltisw\t" #vrt "," #imm "\n"
+#define vrlw_(vrt, vra, vrb) "\tvrlw\t" #vrt "," #vra "," #vrb "\n"
+#define vsbox_(vrt, vra) "\tvsbox\t" #vrt "," #vra "\n"
+#define vxor_(vrt, vra, vrb) "\tvxor\t" #vrt "," #vra "," #vrb "\n"
+#define vand_(vrt, vra, vrb) "\tvand\t" #vrt "," #vra "," #vrb "\n"
+#define vsro_(vrt, vra, vrb) "\tvsro\t" #vrt "," #vra "," #vrb "\n"
+#define vsl_(vrt, vra, vrb) "\tvsl\t" #vrt "," #vra "," #vrb "\n"
+#define vsldoi_(vt, va, vb, sh) "\tvsldoi\t" #vt "," #va "," #vb "," #sh "\n"
+#define vsr_(vrt, vra, vrb) "\tvsr\t" #vrt "," #vra "," #vrb "\n"
+#define vaddcuw_(vrt, vra, vrb) "\tvaddcuw\t" #vrt "," #vra "," #vrb "\n"
+#define vadduwm_(vrt, vra, vrb) "\tvadduwm\t" #vrt "," #vra "," #vrb "\n"
+#define vsububm_(vrt, vra, vrb) "\tvsububm\t" #vrt "," #vra "," #vrb "\n"
+#define vsubuwm_(vrt, vra, vrb) "\tvsubuwm\t" #vrt "," #vra "," #vrb "\n"
+#define vsrw_(vrt, vra, vrb) "\tvsrw\t" #vrt "," #vra "," #vrb "\n"
+#define vcipher_(vt, va, vb) "\tvcipher\t" #vt "," #va "," #vb "\n"
+#define vcipherlast_(vt, va, vb) "\tvcipherlast\t" #vt "," #va "," #vb "\n"
+#define vncipher_(vt, va, vb) "\tvncipher\t" #vt "," #va "," #vb "\n"
+#define vncipherlast_(vt, va, vb) "\tvncipherlast\t" #vt "," #va "," #vb "\n"
+#define vperm_(vt, va, vb, vc) "\tvperm\t" #vt "," #va "," #vb "," #vc "\n"
+#define vpmsumd_(vt, va, vb) "\tvpmsumd\t" #vt "," #va "," #vb "\n"
+#define xxpermdi_(vt, va, vb, d) "\txxpermdi\t" #vt "," #va "," #vb "," #d "\n"
+
+#endif
+
+/* ==================================================================== */
+/*
+ * Special "activate intrinsics" code, needed for some compiler versions.
+ * This is defined at the end of this file, so that it won't impact any
+ * of the inline functions defined previously; and it is controlled by
+ * a specific macro defined in the caller code.
+ *
+ * Calling code conventions:
+ *
+ * - Caller must define BR_ENABLE_INTRINSICS before including "inner.h".
+ * - Functions that use intrinsics must be enclosed in an "enabled"
+ * region (between BR_TARGETS_X86_UP and BR_TARGETS_X86_DOWN).
+ * - Functions that use intrinsics must be tagged with the appropriate
+ * BR_TARGET().
+ */
+
+#if BR_ENABLE_INTRINSICS && (BR_GCC_4_4 || BR_CLANG_3_7 || BR_MSC_2005)
+
+/*
+ * x86 intrinsics (both 32-bit and 64-bit).
+ */
+#if BR_i386 || BR_amd64
+
+/*
+ * On GCC before version 5.0, we need to use the pragma to enable the
+ * target options globally, because the 'target' function attribute
+ * appears to be unreliable. Before 4.6 we must also avoid the
+ * push_options / pop_options mechanism, because it tends to trigger
+ * some internal compiler errors.
+ */
+#if BR_GCC && !BR_GCC_5_0
+#if BR_GCC_4_6
+#define BR_TARGETS_X86_UP \
+ _Pragma("GCC push_options") \
+ _Pragma("GCC target(\"sse2,ssse3,sse4.1,aes,pclmul,rdrnd\")")
+#define BR_TARGETS_X86_DOWN \
+ _Pragma("GCC pop_options")
+#else
+#define BR_TARGETS_X86_UP \
+ _Pragma("GCC target(\"sse2,ssse3,sse4.1,aes,pclmul\")")
+#define BR_TARGETS_X86_DOWN
+#endif
+#pragma GCC diagnostic ignored "-Wpsabi"
+#endif
+
+#if BR_CLANG && !BR_CLANG_3_8
+#undef __SSE2__
+#undef __SSE3__
+#undef __SSSE3__
+#undef __SSE4_1__
+#undef __AES__
+#undef __PCLMUL__
+#undef __RDRND__
+#define __SSE2__ 1
+#define __SSE3__ 1
+#define __SSSE3__ 1
+#define __SSE4_1__ 1
+#define __AES__ 1
+#define __PCLMUL__ 1
+#define __RDRND__ 1
+#endif
+
+#ifndef BR_TARGETS_X86_UP
+#define BR_TARGETS_X86_UP
+#endif
+#ifndef BR_TARGETS_X86_DOWN
+#define BR_TARGETS_X86_DOWN
+#endif
+
+#if BR_GCC || BR_CLANG
+BR_TARGETS_X86_UP
+#include <x86intrin.h>
+#include <cpuid.h>
+#define br_bswap32 __builtin_bswap32
+BR_TARGETS_X86_DOWN
+#endif
+
+#if BR_MSC
+#include <stdlib.h>
+#include <intrin.h>
+#include <immintrin.h>
+#define br_bswap32 _byteswap_ulong
+#endif
+
+static inline int
+br_cpuid(uint32_t mask_eax, uint32_t mask_ebx,
+ uint32_t mask_ecx, uint32_t mask_edx)
+{
+#if BR_GCC || BR_CLANG
+ unsigned eax, ebx, ecx, edx;
+
+ if (__get_cpuid(1, &eax, &ebx, &ecx, &edx)) {
+ if ((eax & mask_eax) == mask_eax
+ && (ebx & mask_ebx) == mask_ebx
+ && (ecx & mask_ecx) == mask_ecx
+ && (edx & mask_edx) == mask_edx)
+ {
+ return 1;
+ }
+ }
+#elif BR_MSC
+ int info[4];
+
+ __cpuid(info, 1);
+ if (((uint32_t)info[0] & mask_eax) == mask_eax
+ && ((uint32_t)info[1] & mask_ebx) == mask_ebx
+ && ((uint32_t)info[2] & mask_ecx) == mask_ecx
+ && ((uint32_t)info[3] & mask_edx) == mask_edx)
+ {
+ return 1;
+ }
+#endif
+ return 0;
+}
+
+#endif
+
+#endif
+
+/* ==================================================================== */
+
+#endif