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Abstract
We consider digital expansions to the base of an algebraic integer τ. For a , the set of admissible digits consists of 0 and one representative of every residue class modulo which is not divisible by τ. The resulting redundancy is avoided by imposing the width-w non-adjacency condition. Such constructs can be efficiently used in elliptic curve cryptography in conjunction with Koblitz curves. The present work deals with analysing the number of occurrences of a fixed non-zero digit. In the general setting, we study all w-NAFs of given length of the expansion (expectation, variance, central limit theorem). In the case of an imaginary quadratic τ and the digit set of minimal norm representatives, the analysis is much more refined. The proof follows Delangeʼs method. We also show that each element of has a w-NAF in that setting.
Original language | English |
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Pages (from-to) | 1752-1808 |
Journal | Journal of Number Theory |
Volume | 133 |
DOIs | |
Publication status | Published - 2013 |
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
- Application
- Theoretical
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Dive into the research topics of 'Analysis of width-w non-adjacent forms to imaginary quadratic bases'. Together they form a unique fingerprint.Projects
- 1 Finished
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Analytic Combinatorics: Analytic Combinatorics and Probabilistic Number Theory
Wagner, S. (Co-Investigator (CoI)), Madritsch, M. (Co-Investigator (CoI)), Aistleitner, C. (Co-Investigator (CoI)), Barat, G. (Co-Investigator (CoI)), Thuswaldner, J. (Principal Investigator (PI)), Grabner, P. (Principal Investigator (PI)), Van De Woestijne, C. E. (Co-Investigator (CoI)), Heuberger, C. (Principal Investigator (PI)), Brauchart, J. (Co-Investigator (CoI)), Berkes, I. (Principal Investigator (PI)), Filipin, A. (Co-Investigator (CoI)), Zeiner, M. (Co-Investigator (CoI)) & Tichy, R. (Principal Investigator (PI))
1/01/06 → 31/07/12
Project: Research project