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Analysis of the Binary Asymmetric Joint Sparse Form

Published online by Cambridge University Press:  14 July 2014

CLEMENS HEUBERGER  and
SARA KROPF
CLEMENS HEUBERGER
Affiliation:
Institut für Mathematik, Alpen-Adria-Universität Klagenfurt, Universitätsstraße 65–67, 9020 Klagenfurt am Wörthersee, Austria and Institut für Optimierung und Diskrete Mathematik (Math B), TU Graz, Steyrergasse 30, 8010 Graz, Austria (e-mail: clemens.heuberger@aau.at)
SARA KROPF
Affiliation:
Institut für Mathematik, Alpen-Adria-Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt am Wörthersee, Austria (e-mail: sara.kropf@aau.at)
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Abstract

We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of non-zero digit vectors. This leads to efficient linear combination algorithms in abelian groups, which are used in elliptic curve cryptography, for instance.

If the digit set is a set of contiguous integers containing zero, a special syntactical condition is known to minimize the weight. We analyse the optimal weight of all non-negative integer vectors with maximum entry less than N. The expectation and the variance are given with a main term and a periodic fluctuation in the second-order term. Finally, we prove asymptotic normality.

Keywords

Primary 11A63Secondary 94A6068W4060F05
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 6: Honouring the Memory of Philippe Flajolet - Part 2 , November 2014 , pp. 1087 - 1113
Copyright
Copyright © Cambridge University Press 2014 

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