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https://github.com/ipxe/ipxe
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[crypto] Eliminate temporary carry space for big integer multiplication
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
@@ -314,7 +314,7 @@ bigint_done_raw ( const uint32_t *value0, unsigned int size __unused,
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*
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* @v multiplicand Multiplicand element
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* @v multiplier Multiplier element
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* @v result Result element pair
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* @v result Result element
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* @v carry Carry element
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*/
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static inline __attribute__ (( always_inline )) void
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@@ -324,19 +324,20 @@ bigint_multiply_one ( const uint32_t multiplicand, const uint32_t multiplier,
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uint32_t discard_high;
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__asm__ __volatile__ ( /* Perform multiplication */
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"umull %0, %1, %5, %6\n\t"
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"umull %0, %1, %4, %5\n\t"
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/* Accumulate result */
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"adds %2, %0\n\t"
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"adcs %3, %1\n\t"
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"adc %1, #0\n\t"
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/* Accumulate carry (cannot overflow) */
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"adc %4, #0\n\t"
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"adds %2, %3\n\t"
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"adc %3, %1, #0\n\t"
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: "=r" ( discard_low ),
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"=r" ( discard_high ),
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"+r" ( result[0] ),
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"+r" ( result[1] ),
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"+r" ( *result ),
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"+r" ( *carry )
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: "r" ( multiplicand ),
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"r" ( multiplier ) );
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"r" ( multiplier )
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: "cc" );
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}
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#endif /* _BITS_BIGINT_H */
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@@ -315,7 +315,7 @@ bigint_done_raw ( const uint64_t *value0, unsigned int size __unused,
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*
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* @v multiplicand Multiplicand element
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* @v multiplier Multiplier element
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* @v result Result element pair
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* @v result Result element
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* @v carry Carry element
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*/
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static inline __attribute__ (( always_inline )) void
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@@ -325,20 +325,21 @@ bigint_multiply_one ( const uint64_t multiplicand, const uint64_t multiplier,
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uint64_t discard_high;
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__asm__ __volatile__ ( /* Perform multiplication */
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"mul %0, %5, %6\n\t"
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"umulh %1, %5, %6\n\t"
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"mul %0, %4, %5\n\t"
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"umulh %1, %4, %5\n\t"
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/* Accumulate result */
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"adds %2, %2, %0\n\t"
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"adcs %3, %3, %1\n\t"
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"adc %1, %1, xzr\n\t"
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/* Accumulate carry (cannot overflow) */
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"adc %4, %4, xzr\n\t"
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"adds %2, %2, %3\n\t"
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"adc %3, %1, xzr\n\t"
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: "=&r" ( discard_low ),
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"=r" ( discard_high ),
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"+r" ( result[0] ),
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"+r" ( result[1] ),
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"+r" ( *result ),
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"+r" ( *carry )
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: "r" ( multiplicand ),
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"r" ( multiplier ) );
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"r" ( multiplier )
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: "cc" );
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}
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#endif /* _BITS_BIGINT_H */
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@@ -362,7 +362,7 @@ bigint_done_raw ( const uint64_t *value0, unsigned int size __unused,
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*
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* @v multiplicand Multiplicand element
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* @v multiplier Multiplier element
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* @v result Result element pair
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* @v result Result element
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* @v carry Carry element
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*/
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static inline __attribute__ (( always_inline )) void
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@@ -373,23 +373,20 @@ bigint_multiply_one ( const uint64_t multiplicand, const uint64_t multiplier,
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uint64_t discard_carry;
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__asm__ __volatile__ ( /* Perform multiplication */
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"mul.d %0, %6, %7\n\t"
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"mulh.du %1, %6, %7\n\t"
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"mul.d %0, %5, %6\n\t"
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"mulh.du %1, %5, %6\n\t"
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/* Accumulate low half */
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"add.d %3, %3, %0\n\t"
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"sltu %2, %3, %0\n\t"
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/* Add carry to high half (cannot overflow) */
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"add.d %1, %1, %2\n\t"
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/* Accumulate high half */
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"add.d %4, %4, %1\n\t"
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"sltu %2, %4, %1\n\t"
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/* Accumulate carry (cannot overflow) */
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"add.d %5, %5, %2\n\t"
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"add.d %3, %3, %4\n\t"
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"sltu %2, %3, %4\n\t"
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"add.d %4, %1, %2\n\t"
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: "=&r" ( discard_low ),
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"=r" ( discard_high ),
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"=r" ( discard_carry ),
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"+r" ( result[0] ),
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"+r" ( result[1] ),
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"+r" ( *result ),
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"+r" ( *carry )
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: "r" ( multiplicand ),
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"r" ( multiplier ) );
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@@ -358,7 +358,7 @@ bigint_done_raw ( const unsigned long *value0, unsigned int size __unused,
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*
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* @v multiplicand Multiplicand element
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* @v multiplier Multiplier element
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* @v result Result element pair
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* @v result Result element
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* @v carry Carry element
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*/
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static inline __attribute__ (( always_inline )) void
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@@ -370,23 +370,20 @@ bigint_multiply_one ( const unsigned long multiplicand,
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unsigned long discard_carry;
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__asm__ __volatile__ ( /* Perform multiplication */
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"mulhu %1, %6, %7\n\t"
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"mul %0, %6, %7\n\t"
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"mulhu %1, %5, %6\n\t"
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"mul %0, %5, %6\n\t"
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/* Accumulate low half */
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"add %3, %3, %0\n\t"
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"sltu %2, %3, %0\n\t"
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/* Add carry to high half (cannot overflow) */
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"add %1, %1, %2\n\t"
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/* Accumulate high half */
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"add %4, %4, %1\n\t"
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"sltu %2, %4, %1\n\t"
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/* Accumulate carry (cannot overflow) */
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"add %5, %5, %2\n\t"
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"add %3, %3, %4\n\t"
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"sltu %2, %3, %4\n\t"
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"add %4, %1, %2\n\t"
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: "=r" ( discard_low ),
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"=&r" ( discard_high ),
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"=r" ( discard_carry ),
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"+r" ( result[0] ),
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"+r" ( result[1] ),
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"+r" ( *result ),
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"+r" ( *carry )
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: "r" ( multiplicand ),
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"r" ( multiplier ) );
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@@ -327,29 +327,28 @@ bigint_done_raw ( const uint32_t *value0, unsigned int size __unused,
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*
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* @v multiplicand Multiplicand element
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* @v multiplier Multiplier element
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* @v result Result element pair
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* @v result Result element
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* @v carry Carry element
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*/
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static inline __attribute__ (( always_inline )) void
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bigint_multiply_one ( const uint32_t multiplicand, const uint32_t multiplier,
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uint32_t *result, uint32_t *carry ) {
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uint32_t discard_a;
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uint32_t discard_d;
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__asm__ __volatile__ ( /* Perform multiplication */
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"mull %6\n\t"
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"mull %3\n\t"
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/* Accumulate carry */
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"addl %5, %0\n\t"
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"adcl $0, %1\n\t"
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/* Accumulate result */
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"addl %0, %2\n\t"
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"adcl %1, %3\n\t"
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/* Accumulate carry (cannot overflow) */
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"adcl $0, %4\n\t"
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: "=a" ( discard_a ),
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"=d" ( discard_d ),
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"+m" ( result[0] ),
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"+m" ( result[1] ),
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"+m" ( *carry )
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: "0" ( multiplicand ),
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"g" ( multiplier ) );
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"adcl $0, %1\n\t"
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: "=&a" ( discard_a ),
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"=&d" ( *carry ),
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"+m" ( *result )
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: "g" ( multiplicand ),
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"0" ( multiplier ),
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"r" ( *carry ) );
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}
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#endif /* _BITS_BIGINT_H */
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