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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., Madritsch, M., Aistleitner, C., Barat, G., Thuswaldner, J., Grabner, P., Van De Woestijne, C. E., Heuberger, C., Brauchart, J., Berkes, I., Filipin, A., Zeiner, M. & Tichy, R.
1/01/06 → 31/07/12
Project: Research project