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Multi-exponentiation algorithm based on binary GCD computation and its application to side-channel countermeasure

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A series of algorithms for evaluation of multi-exponentiation are proposed based on the binary greatest common divisor algorithm. The proposed algorithms are inversion free and have the capability to evaluate double or multi-exponentiation with non-fixed base numbers and exponents. They can also be employed in developing side-channel countermeasures. For n-bit double and triple exponentiation, they achieve the average complexity of 1.53n and 1.75n multiplications (including squarings), respectively. The proposed algorithms can be very useful for the implementation of many public-key cryptosystems on small devices with limited memory space, e.g., smart cards.

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Correspondence to Sung-Ming Yen.

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C.-N. Chen is now with Nanyang Technological University, Singapore and most of this work was done while he was at National Central University, Taiwan.

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Yen, SM., Chen, CN. & Moon, S. Multi-exponentiation algorithm based on binary GCD computation and its application to side-channel countermeasure. J Cryptogr Eng 2, 99–110 (2012).

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