EFFICIENT GENERATION OF SHORTEST ADDITION-MULTIPLICATION CHAINS | Zendy

Hatem M. Bahig | Zendy; A. E. A. Mahran | Zendy

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EFFICIENT GENERATION OF SHORTEST ADDITION-MULTIPLICATION CHAINS

Author(s) -

Hatem M. Bahig,

A. E. A. Mahran

Publication year - 2018

Publication title -

journal of the egyptian mathematical society

Language(s) - English

Resource type - Journals

eISSN - 2090-9128

pISSN - 1110-256X

DOI - 10.21608/joems.2018.2691.1052

Subject(s) - mathematics , multiplication (music) , arithmetic , combinatorics

The aim of this paper is to generalize some results on addition chains to addition-multiplication chains. The pa-per concerns with generating shortest addition-multiplication chains. It rst presents two methods for generating shortaddition-multiplication chains. Second, it presents an algorithm for generating a shortest addition-multiplication chain.Then it proposes three main improvements for generating a shortest addition-multiplication chain. The practical resultsshow that the proposed improvements reduce, on the average, the running time and storage of the algorithm by about95% and 35% respectively for data range 12 20 bits. Similar practical results are obtained for generating all shortestaddition-multiplication chains. Finally, the paper discusses how to apply the algorithm to obtain some results that havebeen uncovered previously.

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