The alternating greedy expansion and applications to computing digit expansions from left-to-right in cryptography

Authors:
Clemens Heuberger;Rajendra Katti;Helmut Prodinger;Xiaoyu Ruan
Affiliations:
Institut für Mathematik B, Technische Universität Graz, Graz, Austria;Department of Electrical and Computer Engineering, North Dakota State University, Fargo, North Dakota;The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa;Department of Electrical and Computer Engineering, North Dakota State University, Fargo, North Dakota
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

The central topic of this paper is the alternating greedy expansion of integers, which is defined to be a binary expansion with digits {0, ±1} with the property that the nonzero digits have alternating signs. We collect known results about this alternating greedy expansion and complement it with other useful properties and algorithms. In the second part, we apply it to give an algorithm for computing a joint expansion of d integers of minimal joint Hamming weight from left to right, i.e., from the column with the most significant bits towards the column with the least significant bits. Furthermore, we also compute an expansion equivalent to the so-caled w-NAF from left to right using the alternating greedy expansion.