#include "BigNumLibInternal.h"

Macros
#define	OC_BN_MAX_VAL ((OC_BN_WORD)0U - 1U)

Functions
	STATIC_ASSERT (OC_BN_WORD_SIZE==sizeof(UINT32)\|\|OC_BN_WORD_SIZE==sizeof(UINT64), "OC_BN_WORD_SIZE and OC_BN_WORD_NUM_BITS usages must be adapted.")

OC_BN_WORD	BigNumSwapWord (IN OC_BN_WORD Word)

STATIC VOID	BigNumLeftShiftWords (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWordsResult, IN CONST OC_BN_WORD A, IN OC_BN_NUM_WORDS NumWordsA, IN UINTN Exponent)

STATIC VOID	BigNumLeftShiftWordsAndBits (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWordsResult, IN CONST OC_BN_WORD A, IN OC_BN_NUM_WORDS NumWordsA, IN UINTN NumWords, IN UINT8 NumBits)

STATIC VOID	BigNumLeftShift (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWordsResult, IN CONST OC_BN_WORD A, IN OC_BN_NUM_WORDS NumWordsA, IN UINTN Exponent)

STATIC VOID	BigNumRightShiftWords (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWordsResult, IN CONST OC_BN_WORD A, IN OC_BN_NUM_WORDS NumWordsA, IN UINTN Exponent)

STATIC VOID	BigNumRightShiftBitsSmall (IN OUT OC_BN_WORD *A, IN OC_BN_NUM_WORDS NumWords, IN UINT8 Exponent)

STATIC VOID	BigNumRightShiftWordsAndBits (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWordsResult, IN CONST OC_BN_WORD A, IN OC_BN_NUM_WORDS NumWordsA, IN UINTN NumWords, IN UINT8 NumBits)

STATIC VOID	BigNumRightShift (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWordsResult, IN CONST OC_BN_WORD A, IN OC_BN_NUM_WORDS NumWordsA, IN UINTN Exponent)

OC_BN_WORD	BigNumWordMul (OUT OC_BN_WORD *Hi, IN OC_BN_WORD A, IN OC_BN_WORD B)

VOID	BigNumSub (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWords, IN CONST OC_BN_WORD A, IN CONST OC_BN_WORD *B)

STATIC UINT8	BigNumSignificantBitsWord (IN OC_BN_WORD Word)

STATIC OC_BN_NUM_WORDS	BigNumMostSignificantWord (IN CONST OC_BN_WORD *A, IN OC_BN_NUM_WORDS NumWords)

OC_BN_NUM_BITS	BigNumSignificantBits (IN CONST OC_BN_WORD *A, IN OC_BN_NUM_WORDS NumWords)

VOID	BigNumOrWord (IN OUT OC_BN_WORD *A, IN OC_BN_NUM_WORDS NumWords, IN OC_BN_WORD Value, IN UINTN Exponent)

INTN	BigNumCmp (IN CONST OC_BN_WORD A, IN OC_BN_NUM_WORDS NumWords, IN CONST OC_BN_WORD B)

VOID	BigNumMod (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWordsRest, IN CONST OC_BN_WORD A, IN OC_BN_NUM_WORDS NumWordsA, IN CONST OC_BN_WORD B, IN OC_BN_WORD Scratch)

VOID	BigNumParseBuffer (IN OUT OC_BN_WORD Result, IN OC_BN_NUM_WORDS NumWords, IN CONST UINT8 Buffer, IN UINTN BufferSize)

Macro Definition Documentation

◆ OC_BN_MAX_VAL

#define OC_BN_MAX_VAL ((OC_BN_WORD)0U - 1U)

This library performs unsigned arbitrary precision arithmetic operations. All results are returned into caller-provided buffers. The caller is responsible to ensure the buffers can hold a value of the precision it desires. Too large results will be truncated without further notification for public APIs.

https://github.com/kokke/tiny-bignum-c has served as a template for several algorithmic ideas.

This code is not to be considered general-purpose but solely to support cryptographic operations such as RSA encryption. As such, there are arbitrary limitations, such as requirement of equal precision, to limit the complexity of the operations to the bare minimum required to support such use caes.

SECURITY: Currently, no security measures have been taken. This code is vulnerable to both timing and side channel attacks for value leakage. However, its current purpose is the verification of public binaries with public certificates, for which this is perfectly acceptable, especially in regards to performance.

This program and the accompanying materials are licensed and made available under the terms and conditions of the BSD License which accompanies this distribution. The full text of the license may be found at http://opensource.org/licenses/bsd-license.php

THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS, WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.

Definition at line 36 of file BigNumPrimitives.c.

Function Documentation

◆ BigNumCmp()

INTN BigNumCmp	(	IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWords,
		IN CONST OC_BN_WORD *	B )

Returns the relative order of A and B. A and B must have the same precision.

Parameters

[in]	A	The first number to compare.
[in]	NumWords	The number of Words to compare.
[in]	B	The second number to compare.

Return values

<	0 A is lower than B.
0	A is as big as B.
>	0 A is greater than B.

Definition at line 540 of file BigNumPrimitives.c.

◆ BigNumLeftShift()

STATIC VOID BigNumLeftShift	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWordsResult,
		IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWordsA,
		IN UINTN	Exponent )

Calculates the left-shift of A by Exponent Bits.

Parameters

[in,out]	Result	The buffer to return the result into.
[in]	NumWordsResult	The number of Words of Result.
[in]	A	The number to shift.
[in]	NumWordsA	The number of Words of A.
[in]	Exponent	The amount of Bits to shift by.

Definition at line 165 of file BigNumPrimitives.c.

◆ BigNumLeftShiftWords()

STATIC VOID BigNumLeftShiftWords	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWordsResult,
		IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWordsA,
		IN UINTN	Exponent )

Shifts A left by Exponent Words.

Parameters

[in,out]	Result	The buffer to return the result into.
[in]	NumWordsResult	The number of Words of Result.
[in,out]	A	The number to be word-shifted.
[in]	NumWordsA	The number of Words of A.
[in]	Exponent	The Word shift exponent.

Definition at line 71 of file BigNumPrimitives.c.

◆ BigNumLeftShiftWordsAndBits()

STATIC VOID BigNumLeftShiftWordsAndBits	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWordsResult,
		IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWordsA,
		IN UINTN	NumWords,
		IN UINT8	NumBits )

Shifts A left by Exponent Bits for 0 < Exponent < #Bits(Word). Result must have the exact precision to carry the result.

Parameters

[in,out]	Result	The buffer to return the result into.
[in]	NumWordsResult	The number of Words of Result.
[in]	A	The base.
[in]	NumWordsA	The number of Words of A.
[in]	NumWords	The Word shift exponent.
[in]	NumBits	The Bit shift exponent.

Definition at line 110 of file BigNumPrimitives.c.

◆ BigNumMod()

VOID BigNumMod	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWordsRest,
		IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWordsA,
		IN CONST OC_BN_WORD *	B,
		IN OC_BN_WORD *	Scratch )

Calculates the remainder of A and B.

Parameters

[in,out]	Result	The buffer to return the result into.
[in]	NumWordsRest	The number of Words of Result and B.
[in]	A	The dividend.
[in]	NumWordsA	The number of Words of A.
[in]	B	The divisor.
[in]	Scratch	Scratch buffer 2 * OC_BN_SIZE (NumWordsA).

Definition at line 566 of file BigNumPrimitives.c.

◆ BigNumMostSignificantWord()

STATIC OC_BN_NUM_WORDS BigNumMostSignificantWord	(	IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWords )

Returns the most significant word index of A.

Parameters

[in]	A	The number to gather the most significant Word index of.
[in]	NumWords	The number of Words of A.

Returns: The index of the most significant Word in A.

Definition at line 481 of file BigNumPrimitives.c.

◆ BigNumOrWord()

VOID BigNumOrWord	(	IN OUT OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWords,
		IN OC_BN_WORD	Value,
		IN UINTN	Exponent )

Calculates the binary union of A and (Value << Exponent).

Parameters

[in,out]	A	The number to OR with and store the result into.
[in]	NumWords	The number of Words of A.
[in]	Value	The Word value to OR with.
[in]	Exponent	The Word shift exponent.

Definition at line 518 of file BigNumPrimitives.c.

◆ BigNumParseBuffer()

VOID BigNumParseBuffer	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWords,
		IN CONST UINT8 *	Buffer,
		IN UINTN	BufferSize )

Parses a data array into a number. The buffer size must be a multiple of the Word size. The length of Result must precisely fit the required size.

Parameters

[in,out]	Result	The buffer to store the result in.
[in]	NumWords	The number of Words of Result.
[in]	Buffer	The buffer to parse.
[in]	BufferSize	The size, in bytes, of Buffer.

Definition at line 748 of file BigNumPrimitives.c.

◆ BigNumRightShift()

STATIC VOID BigNumRightShift	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWordsResult,
		IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWordsA,
		IN UINTN	Exponent )

Calculates the right-shift of A by Exponent Bits.

Parameters

[in,out]	Result	The buffer to return the result into.
[in]	NumWordsResult	The number of Words of Result.
[in]	A	The number to shift.
[in]	NumWordsA	The number of Words of A.
[in]	Exponent	The amount of Bits to shift by.

Definition at line 335 of file BigNumPrimitives.c.

◆ BigNumRightShiftBitsSmall()

STATIC VOID BigNumRightShiftBitsSmall	(	IN OUT OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWords,
		IN UINT8	Exponent )

Shifts A right by Exponent Bits for 0 < Exponent < #Bits(Word).

Parameters

[in,out]	A	The base.
[in]	NumWords	The number of Words of A.
[in]	Exponent	The Bit shift exponent.

Definition at line 239 of file BigNumPrimitives.c.

◆ BigNumRightShiftWords()

STATIC VOID BigNumRightShiftWords	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWordsResult,
		IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWordsA,
		IN UINTN	Exponent )

Shifts A right by Exponent Words.

Parameters

[in,out]	Result	The buffer to return the result into.
[in]	NumWordsResult	The number of Words of Result.
[in,out]	A	The number to be word-shifted.
[in]	NumWordsA	The number of Words of A.
[in]	Exponent	The Word shift exponent.

Definition at line 210 of file BigNumPrimitives.c.

◆ BigNumRightShiftWordsAndBits()

STATIC VOID BigNumRightShiftWordsAndBits	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWordsResult,
		IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWordsA,
		IN UINTN	NumWords,
		IN UINT8	NumBits )

Shifts A right by Exponent Bits for 0 < Exponent < #Bits(Word).

Parameters

[in,out]	Result	The buffer to return the result into.
[in]	NumWordsResult	The number of Words of Result.
[in]	A	The base.
[in]	NumWordsA	The number of Words of A.
[in]	NumWords	The Word shift exponent.
[in]	NumBits	The Bit shift exponent.

Definition at line 276 of file BigNumPrimitives.c.

◆ BigNumSignificantBits()

OC_BN_NUM_BITS BigNumSignificantBits	(	IN CONST OC_BN_WORD *	A,
		IN OC_BN_NUM_WORDS	NumWords )

Returns the number of significant bits in a number. Logically matches OpenSSL's BN_num_bits.

Parameters

[in]	A	The number to gather the number of significant bits of.
[in]	NumWords	The number of Words of A.

Returns: The number of significant bits in A.

Definition at line 503 of file BigNumPrimitives.c.

◆ BigNumSignificantBitsWord()

STATIC UINT8 BigNumSignificantBitsWord ( IN OC_BN_WORD Word )

Returns the number of significant bits in a Word.

Parameters

[in] Word The word to gather the number of significant bits of.

Returns: The number of significant bits in Word.

Definition at line 449 of file BigNumPrimitives.c.

◆ BigNumSub()

VOID BigNumSub	(	IN OUT OC_BN_WORD *	Result,
		IN OC_BN_NUM_WORDS	NumWords,
		IN CONST OC_BN_WORD *	A,
		IN CONST OC_BN_WORD *	B )

Calulates the difference of A and B. A must have the same precision as B. Result must have a precision at most as bit as A and B.

Parameters

[in,out]	Result	The buffer to return the result into.
[in]	NumWords	The number of Words of Result, minimum number of Words of A and B.
[in]	A	The minuend.
[in]	B	The subtrahend.

Definition at line 404 of file BigNumPrimitives.c.

◆ BigNumSwapWord()

OC_BN_WORD BigNumSwapWord ( IN OC_BN_WORD Word )

Swaps the byte order of Word.

Parameters

[in] Word The Word to swap.

Returns: The byte-swapped value of Word.

Definition at line 44 of file BigNumPrimitives.c.

◆ BigNumWordMul()

OC_BN_WORD BigNumWordMul	(	OUT OC_BN_WORD *	Hi,
		IN OC_BN_WORD	A,
		IN OC_BN_WORD	B )

Calculates the product of A and B.

Parameters

[out]	Hi	Buffer in which the high Word of the result is returned.
[in]	A	The multiplicant.
[in]	B	The multiplier.

Returns: The low Word of the result.

Definition at line 379 of file BigNumPrimitives.c.

◆ STATIC_ASSERT()

STATIC_ASSERT	(	OC_BN_WORD_SIZE	= =sizeof(UINT32)\|\|OC_BN_WORD_SIZE==sizeof(UINT64),
		"OC_BN_WORD_SIZE and OC_BN_WORD_NUM_BITS usages must be adapted."	)

Macros

Functions

Macro Definition Documentation

◆ OC_BN_MAX_VAL

Function Documentation

◆ BigNumCmp()

◆ BigNumLeftShift()

◆ BigNumLeftShiftWords()

◆ BigNumLeftShiftWordsAndBits()

◆ BigNumMod()

◆ BigNumMostSignificantWord()

◆ BigNumOrWord()

◆ BigNumParseBuffer()

◆ BigNumRightShift()

◆ BigNumRightShiftBitsSmall()

◆ BigNumRightShiftWords()

◆ BigNumRightShiftWordsAndBits()

◆ BigNumSignificantBits()

◆ BigNumSignificantBitsWord()

◆ BigNumSub()

◆ BigNumSwapWord()

◆ BigNumWordMul()

◆ STATIC_ASSERT()