Performance Comparison of Some Addition Chain Methods Based on Integer Family

Abdul Kadir, Prof. Madya Dr. Mohd Fadzil and Mamat, Prof. Dr. Mustafa and Mohamed, Prof. Madya Dr. Mohamad Afendee (2019) Performance Comparison of Some Addition Chain Methods Based on Integer Family. In: Information Science and Applications 2018. Springer, Singapore, pp. 211-218. ISBN 978-981-13-1056-0

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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. These is no known algorithm which can calculate on 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 resource 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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