502 lines
13 KiB
C
502 lines
13 KiB
C
/* TomsFastMath, a fast ISO C bignum library.
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*
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* This project is meant to fill in where LibTomMath
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* falls short. That is speed ;-)
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*
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* This project is public domain and free for all purposes.
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*
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* Tom St Denis, tomstdenis@gmail.com
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*/
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#ifndef TFM_H_
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#define TFM_H_
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#include <stdio.h>
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#include <string.h>
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#include <stdlib.h>
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#include <ctype.h>
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#include <limits.h>
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/* 0xMaMiPaXX
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* Major
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* Minor
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* Patch
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* XX - undefined
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*/
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#define TFM_VERSION 0x000D0100
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#define TFM_VERSION_S "v0.13.1"
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#ifndef MIN
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#define MIN(x,y) ((x)<(y)?(x):(y))
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#endif
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#ifndef MAX
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#define MAX(x,y) ((x)>(y)?(x):(y))
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#endif
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/* externally define this symbol to ignore the default settings, useful for changing the build from the make process */
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#ifndef TFM_ALREADY_SET
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/* do we want the large set of small multiplications ?
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Enable these if you are going to be doing a lot of small (<= 16 digit) multiplications say in ECC
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Or if you're on a 64-bit machine doing RSA as a 1024-bit integer == 16 digits ;-)
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*/
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#define TFM_SMALL_SET
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/* do we want huge code
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Enable these if you are doing 20, 24, 28, 32, 48, 64 digit multiplications (useful for RSA)
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Less important on 64-bit machines as 32 digits == 2048 bits
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*/
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#if 0
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#define TFM_MUL3
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#define TFM_MUL4
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#define TFM_MUL6
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#define TFM_MUL7
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#define TFM_MUL8
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#define TFM_MUL9
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#define TFM_MUL12
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#define TFM_MUL17
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#endif
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#define TFM_MUL20
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#define TFM_MUL24
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#define TFM_MUL28
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#define TFM_MUL32
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#define TFM_MUL48
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#define TFM_MUL64
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#if 0
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#define TFM_SQR3
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#define TFM_SQR4
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#define TFM_SQR6
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#define TFM_SQR7
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#define TFM_SQR8
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#define TFM_SQR9
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#define TFM_SQR12
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#define TFM_SQR17
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#endif
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#define TFM_SQR20
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#define TFM_SQR24
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#define TFM_SQR28
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#define TFM_SQR32
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#define TFM_SQR48
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#define TFM_SQR64
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/* do we want some overflow checks
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Not required if you make sure your numbers are within range (e.g. by default a modulus for fp_exptmod() can only be upto 2048 bits long)
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*/
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/* #define TFM_CHECK */
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/* Is the target a P4 Prescott
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*/
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/* #define TFM_PRESCOTT */
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/* Do we want timing resistant fp_exptmod() ?
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* This makes it slower but also timing invariant with respect to the exponent
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*/
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/* #define TFM_TIMING_RESISTANT */
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#endif
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/* Max size of any number in bits. Basically the largest size you will be multiplying
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* should be half [or smaller] of FP_MAX_SIZE-four_digit
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*
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* You can externally define this or it defaults to 4096-bits [allowing multiplications upto 2048x2048 bits ]
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*/
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#ifndef FP_MAX_SIZE
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// Increase max size of TomsFastMath's numbers from 4096-bits to 8192-bits.
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// 8192-bits was the previous maximum size, but was reduced to 4096 bits (the default) accidentally when the library was updated.
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// The higher size is required for RSA certificate verification.
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#define FP_MAX_SIZE (8192+(8*DIGIT_BIT))
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#endif
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/* will this lib work? */
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#if (CHAR_BIT & 7)
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#error CHAR_BIT must be a multiple of eight.
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#endif
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#if FP_MAX_SIZE % CHAR_BIT
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#error FP_MAX_SIZE must be a multiple of CHAR_BIT
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#endif
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#if __SIZEOF_LONG__ == 8
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#define FP_64BIT
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#endif
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/* autodetect x86-64 and make sure we are using 64-bit digits with x86-64 asm */
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#if defined(__x86_64__)
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#if defined(TFM_X86) || defined(TFM_SSE2) || defined(TFM_ARM)
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#error x86-64 detected, x86-32/SSE2/ARM optimizations are not valid!
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#endif
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#if !defined(TFM_X86_64) && !defined(TFM_NO_ASM)
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#define TFM_X86_64
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#endif
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#endif
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#if defined(TFM_X86_64)
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#if !defined(FP_64BIT)
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#define FP_64BIT
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#endif
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#endif
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/* try to detect x86-32 */
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#if defined(__i386__) && !defined(TFM_SSE2)
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#if defined(TFM_X86_64) || defined(TFM_ARM)
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#error x86-32 detected, x86-64/ARM optimizations are not valid!
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#endif
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#if !defined(TFM_X86) && !defined(TFM_NO_ASM)
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#define TFM_X86
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#endif
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#endif
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/* make sure we're 32-bit for x86-32/sse/arm/ppc32 */
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#if (defined(TFM_X86) || defined(TFM_SSE2) || defined(TFM_ARM) || defined(TFM_PPC32)) && defined(FP_64BIT)
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#warning x86-32, SSE2 and ARM, PPC32 optimizations require 32-bit digits (undefining)
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#undef FP_64BIT
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#endif
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/* multi asms? */
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#ifdef TFM_X86
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#define TFM_ASM
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#endif
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#ifdef TFM_X86_64
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#ifdef TFM_ASM
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#error TFM_ASM already defined!
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#endif
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#define TFM_ASM
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#endif
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#ifdef TFM_SSE2
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#ifdef TFM_ASM
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#error TFM_ASM already defined!
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#endif
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#define TFM_ASM
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#endif
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#ifdef TFM_ARM
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#ifdef TFM_ASM
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#error TFM_ASM already defined!
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#endif
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#define TFM_ASM
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#endif
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#ifdef TFM_PPC32
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#ifdef TFM_ASM
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#error TFM_ASM already defined!
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#endif
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#define TFM_ASM
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#endif
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#ifdef TFM_PPC64
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#ifdef TFM_ASM
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#error TFM_ASM already defined!
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#endif
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#define TFM_ASM
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#endif
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#ifdef TFM_AVR32
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#ifdef TFM_ASM
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#error TFM_ASM already defined!
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#endif
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#define TFM_ASM
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#endif
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/* we want no asm? */
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#ifdef TFM_NO_ASM
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#undef TFM_X86
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#undef TFM_X86_64
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#undef TFM_SSE2
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#undef TFM_ARM
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#undef TFM_PPC32
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#undef TFM_PPC64
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#undef TFM_AVR32
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#undef TFM_ASM
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#endif
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/* ECC helpers */
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#ifdef TFM_ECC192
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#ifdef FP_64BIT
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#define TFM_MUL3
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#define TFM_SQR3
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#else
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#define TFM_MUL6
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#define TFM_SQR6
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#endif
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#endif
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#ifdef TFM_ECC224
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#ifdef FP_64BIT
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#define TFM_MUL4
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#define TFM_SQR4
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#else
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#define TFM_MUL7
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#define TFM_SQR7
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#endif
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#endif
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#ifdef TFM_ECC256
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#ifdef FP_64BIT
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#define TFM_MUL4
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#define TFM_SQR4
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#else
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#define TFM_MUL8
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#define TFM_SQR8
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#endif
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#endif
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#ifdef TFM_ECC384
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#ifdef FP_64BIT
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#define TFM_MUL6
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#define TFM_SQR6
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#else
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#define TFM_MUL12
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#define TFM_SQR12
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#endif
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#endif
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#ifdef TFM_ECC521
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#ifdef FP_64BIT
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#define TFM_MUL9
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#define TFM_SQR9
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#else
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#define TFM_MUL17
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#define TFM_SQR17
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#endif
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#endif
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/* use arc4random on platforms that support it */
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#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
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#define FP_GEN_RANDOM() arc4random()
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#define FP_GEN_RANDOM_MAX 0xffffffff
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#endif
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/* use rand() as fall-back if there's no better rand function */
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#ifndef FP_GEN_RANDOM
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#define FP_GEN_RANDOM() rand()
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#define FP_GEN_RANDOM_MAX RAND_MAX
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#endif
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/* some default configurations.
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*/
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#if defined(FP_64BIT)
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/* for GCC only on supported platforms */
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#ifndef CRYPT
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typedef unsigned long long ulong64;
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#endif /* CRYPT */
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typedef ulong64 fp_digit;
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#define SIZEOF_FP_DIGIT 8
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typedef unsigned long fp_word __attribute__ ((mode(TI)));
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#else
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/* this is to make porting into LibTomCrypt easier :-) */
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#ifndef CRYPT
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#if defined(_MSC_VER) || defined(__BORLANDC__)
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typedef unsigned __int64 ulong64;
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typedef signed __int64 long64;
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#else
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typedef unsigned long long ulong64;
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typedef signed long long long64;
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#endif /* defined(_MSC_VER) ... */
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#endif /* CRYPT */
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typedef unsigned int fp_digit;
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#define SIZEOF_FP_DIGIT 4
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typedef ulong64 fp_word;
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#endif /* FP_64BIT */
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/* # of digits this is */
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#define DIGIT_BIT ((CHAR_BIT) * SIZEOF_FP_DIGIT)
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#define FP_MASK (fp_digit)(-1)
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#define FP_SIZE (FP_MAX_SIZE/DIGIT_BIT)
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/* signs */
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#define FP_ZPOS 0
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#define FP_NEG 1
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/* return codes */
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#define FP_OKAY 0
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#define FP_VAL 1
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#define FP_MEM 2
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/* equalities */
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#define FP_LT -1 /* less than */
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#define FP_EQ 0 /* equal to */
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#define FP_GT 1 /* greater than */
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/* replies */
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#define FP_YES 1 /* yes response */
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#define FP_NO 0 /* no response */
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/* a FP type */
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typedef struct {
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fp_digit dp[FP_SIZE];
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int used,
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sign;
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} fp_int;
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/* functions */
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/* returns a TFM ident string useful for debugging... */
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const char *fp_ident(void);
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/* initialize [or zero] an fp int */
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#define fp_init(a) (void)memset((a), 0, sizeof(fp_int))
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#define fp_zero(a) fp_init(a)
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/* zero/even/odd ? */
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#define fp_iszero(a) (((a)->used == 0) ? FP_YES : FP_NO)
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#define fp_iseven(a) (((a)->used >= 0 && (((a)->dp[0] & 1) == 0)) ? FP_YES : FP_NO)
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#define fp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? FP_YES : FP_NO)
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/* set to a small digit */
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void fp_set(fp_int *a, fp_digit b);
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/* makes a pseudo-random int of a given size */
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void fp_rand(fp_int *a, int digits);
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/* copy from a to b */
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#define fp_copy(a, b) (void)(((a) != (b)) && memcpy((b), (a), sizeof(fp_int)))
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#define fp_init_copy(a, b) fp_copy(b, a)
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/* clamp digits */
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#define fp_clamp(a) { while ((a)->used && (a)->dp[(a)->used-1] == 0) --((a)->used); (a)->sign = (a)->used ? (a)->sign : FP_ZPOS; }
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/* negate and absolute */
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#define fp_neg(a, b) { fp_copy(a, b); (b)->sign ^= 1; fp_clamp(b); }
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#define fp_abs(a, b) { fp_copy(a, b); (b)->sign = 0; }
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/* right shift x digits */
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void fp_rshd(fp_int *a, int x);
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/* left shift x digits */
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void fp_lshd(fp_int *a, int x);
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/* signed comparison */
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int fp_cmp(fp_int *a, fp_int *b);
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/* unsigned comparison */
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int fp_cmp_mag(fp_int *a, fp_int *b);
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/* power of 2 operations */
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void fp_div_2d(fp_int *a, int b, fp_int *c, fp_int *d);
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void fp_mod_2d(fp_int *a, int b, fp_int *c);
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void fp_mul_2d(fp_int *a, int b, fp_int *c);
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void fp_2expt (fp_int *a, int b);
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void fp_mul_2(fp_int *a, fp_int *c);
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void fp_div_2(fp_int *a, fp_int *c);
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/* Counts the number of lsbs which are zero before the first zero bit */
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int fp_cnt_lsb(fp_int *a);
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/* c = a + b */
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void fp_add(fp_int *a, fp_int *b, fp_int *c);
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/* c = a - b */
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void fp_sub(fp_int *a, fp_int *b, fp_int *c);
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/* c = a * b */
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void fp_mul(fp_int *a, fp_int *b, fp_int *c);
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/* b = a*a */
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void fp_sqr(fp_int *a, fp_int *b);
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/* a/b => cb + d == a */
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int fp_div(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
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/* c = a mod b, 0 <= c < b */
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int fp_mod(fp_int *a, fp_int *b, fp_int *c);
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/* compare against a single digit */
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int fp_cmp_d(fp_int *a, fp_digit b);
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/* c = a + b */
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void fp_add_d(fp_int *a, fp_digit b, fp_int *c);
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/* c = a - b */
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void fp_sub_d(fp_int *a, fp_digit b, fp_int *c);
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/* c = a * b */
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void fp_mul_d(fp_int *a, fp_digit b, fp_int *c);
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/* a/b => cb + d == a */
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int fp_div_d(fp_int *a, fp_digit b, fp_int *c, fp_digit *d);
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/* c = a mod b, 0 <= c < b */
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int fp_mod_d(fp_int *a, fp_digit b, fp_digit *c);
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/* ---> number theory <--- */
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/* d = a + b (mod c) */
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int fp_addmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
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/* d = a - b (mod c) */
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int fp_submod(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
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/* d = a * b (mod c) */
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int fp_mulmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
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/* c = a * a (mod b) */
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int fp_sqrmod(fp_int *a, fp_int *b, fp_int *c);
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/* c = 1/a (mod b) */
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int fp_invmod(fp_int *a, fp_int *b, fp_int *c);
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/* c = (a, b) */
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void fp_gcd(fp_int *a, fp_int *b, fp_int *c);
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/* c = [a, b] */
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void fp_lcm(fp_int *a, fp_int *b, fp_int *c);
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/* setups the montgomery reduction */
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int fp_montgomery_setup(fp_int *a, fp_digit *mp);
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/* computes a = B**n mod b without division or multiplication useful for
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* normalizing numbers in a Montgomery system.
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*/
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void fp_montgomery_calc_normalization(fp_int *a, fp_int *b);
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/* computes x/R == x (mod N) via Montgomery Reduction */
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void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp);
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/* d = a**b (mod c) */
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int fp_exptmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
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/* primality stuff */
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/* perform a Miller-Rabin test of a to the base b and store result in "result" */
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void fp_prime_miller_rabin (fp_int * a, fp_int * b, int *result);
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#define FP_PRIME_SIZE 256
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/* 256 trial divisions + 8 Miller-Rabins, returns FP_YES if probable prime */
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int fp_isprime(fp_int *a);
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/* extended version of fp_isprime, do 't' Miller-Rabins instead of only 8 */
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int fp_isprime_ex(fp_int *a, int t);
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/* Primality generation flags */
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#define TFM_PRIME_BBS 0x0001 /* BBS style prime */
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#define TFM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
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#define TFM_PRIME_2MSB_OFF 0x0004 /* force 2nd MSB to 0 */
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#define TFM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
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/* callback for fp_prime_random, should fill dst with random bytes and return how many read [upto len] */
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typedef int tfm_prime_callback(unsigned char *dst, int len, void *dat);
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#define fp_prime_random(a, t, size, bbs, cb, dat) fp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?TFM_PRIME_BBS:0, cb, dat)
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int fp_prime_random_ex(fp_int *a, int t, int size, int flags, tfm_prime_callback cb, void *dat);
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/* radix conersions */
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int fp_count_bits(fp_int *a);
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int fp_unsigned_bin_size(fp_int *a);
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void fp_read_unsigned_bin(fp_int *a, const unsigned char *b, int c);
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void fp_to_unsigned_bin(fp_int *a, unsigned char *b);
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int fp_signed_bin_size(fp_int *a);
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void fp_read_signed_bin(fp_int *a, const unsigned char *b, int c);
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void fp_to_signed_bin(fp_int *a, unsigned char *b);
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int fp_read_radix(fp_int *a, const char *str, int radix);
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int fp_radix_size(fp_int *a, int radix, int *size);
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int fp_toradix(fp_int *a, char *str, int radix);
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int fp_toradix_n(fp_int * a, char *str, int radix, int maxlen);
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#endif
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/* $Source$ */
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/* $Revision$ */
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/* $Date$ */
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