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A fast optimal parallel algorithm for a short addition chain

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Abstract

Given a natural number e, an addition chain for e is a finite sequence of numbers having the following properties: (1) the first number is one, (2) every element is the sum of two earlier elements, and (3) the given number occurs at the end of the sequence. We introduce a fast optimal algorithm to generate a chain of short length for the number e of n-bits. The algorithm is based on the right–left binary strategy and barrel shifter circuit. The algorithm uses \(O((\frac{n}{\log {n}})^2)\) processors and runs in \(O((\log {n})^2)\) time under exclusive read exclusive write parallel random access machine.

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Acknowledgements

The author would like to thank the editor and referees for their valuable comments to improve this presentation.

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Authors and Affiliations

  1. Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt

    Hazem M. Bahig

  2. Computer Science and Engineering College, Hail University, Hail, Kingdom of Saudi Arabia

    Hazem M. Bahig

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  1. Hazem M. Bahig
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Correspondence to Hazem M. Bahig.

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Bahig, H.M. A fast optimal parallel algorithm for a short addition chain. J Supercomput 74, 324–333 (2018). https://doi.org/10.1007/s11227-017-2129-0

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  • DOI: https://doi.org/10.1007/s11227-017-2129-0

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