Performance comparison of some addition chain methods based on integer family

Mohd Fadzil, Abdul Kadir and Mustafa, Mamat and Mohamad Afendee, Mohamed and Mohamad, R and Muhammed, A (2019) Performance comparison of some addition chain methods based on integer family. In: International Conference on Information Science and Applications, ICISA 2018;, 25 June 2018, Kowloon; Hong Kong;.

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Abstract

A generalized version of an addition chain problem, in which one must find a chain that simultaneously satisfies a sequence on integer in ascending order, is NP-complete. There is no known algorithm which can calculate an optimal addition chain for a given number with any guarantees of reasonable timing or small memory usage. Several methods were introduced to calculate relatively short chain and they are most used to support scalar multiplication operation tailored to limited computational resources in elliptic curve cryptography. In reality, one method is no better than the other except on certain occasions and only for specific integers. In this studies, we evaluate some existing addition chain methods against each other for their competitive performance by categorizing integers into various groups as the input. This result can be used as a benchmark for which method is suitable in which condition anticipated.

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