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

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 1.53 n and 1.75 n 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.