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[crypto] Eliminate temporary carry space for big integer multiplication

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An n-bit multiplication product may be added to up to two n-bit
integers without exceeding the range of a (2n)-bit integer:

  (2^n - 1)*(2^n - 1) + (2^n - 1) + (2^n - 1) = 2^(2n) - 1

Exploit this to perform big integer multiplication in constant time
without requiring the caller to provide temporary carry space.

Signed-off-by: Michael Brown <mcb30@ipxe.org>
This commit is contained in:
Michael Brown
2024-09-26 16:24:57 +01:00
parent 8844a3d546
commit 3f4f843920
9 changed files with 111 additions and 197 deletions
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12
src/tests/bigint_test.c
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@@ -173,8 +173,7 @@ void bigint_multiply_sample ( const bigint_element_t *multiplicand0,
unsigned int multiplicand_size,
const bigint_element_t *multiplier0,
unsigned int multiplier_size,
bigint_element_t *result0,
bigint_element_t *carry0 ) {
bigint_element_t *result0 ) {
unsigned int result_size = ( multiplicand_size + multiplier_size );
const bigint_t ( multiplicand_size ) __attribute__ (( may_alias ))
*multiplicand = ( ( const void * ) multiplicand0 );
@@ -182,10 +181,8 @@ void bigint_multiply_sample ( const bigint_element_t *multiplicand0,
*multiplier = ( ( const void * ) multiplier0 );
bigint_t ( result_size ) __attribute__ (( may_alias ))
*result = ( ( void * ) result0 );
bigint_t ( result_size ) __attribute__ (( may_alias ))
*carry = ( ( void * ) carry0 );
bigint_multiply ( multiplicand, multiplier, result, carry );
bigint_multiply ( multiplicand, multiplier, result );
}
void bigint_mod_multiply_sample ( const bigint_element_t *multiplicand0,
@@ -498,14 +495,11 @@ void bigint_mod_exp_sample ( const bigint_element_t *base0,
bigint_t ( multiplicand_size ) multiplicand_temp; \
bigint_t ( multiplier_size ) multiplier_temp; \
bigint_t ( multiplicand_size + multiplier_size ) result_temp; \
bigint_t ( multiplicand_size + multiplier_size ) carry_temp; \
{} /* Fix emacs alignment */ \
\
assert ( bigint_size ( &result_temp ) == \
( bigint_size ( &multiplicand_temp ) + \
bigint_size ( &multiplier_temp ) ) ); \
assert ( bigint_size ( &carry_temp ) == \
bigint_size ( &result_temp ) ); \
bigint_init ( &multiplicand_temp, multiplicand_raw, \
sizeof ( multiplicand_raw ) ); \
bigint_init ( &multiplier_temp, multiplier_raw, \
@@ -514,7 +508,7 @@ void bigint_mod_exp_sample ( const bigint_element_t *base0,
DBG_HDA ( 0, &multiplicand_temp, sizeof ( multiplicand_temp ) );\
DBG_HDA ( 0, &multiplier_temp, sizeof ( multiplier_temp ) ); \
bigint_multiply ( &multiplicand_temp, &multiplier_temp, \
&result_temp, &carry_temp ); \
&result_temp ); \
DBG_HDA ( 0, &result_temp, sizeof ( result_temp ) ); \
bigint_done ( &result_temp, result_raw, sizeof ( result_raw ) );\
\