کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6415632 | 1335746 | 2013 | 57 صفحه PDF | دانلود رایگان |
We consider digital expansions to the base of an algebraic integer Ï. For a w⩾2, the set of admissible digits consists of 0 and one representative of every residue class modulo Ïw which is not divisible by Ï. 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 Ï 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 Z[Ï] has a w-NAF in that setting.
Journal: Journal of Number Theory - Volume 133, Issue 5, May 2013, Pages 1752-1808