1. Nonadjacent Radix-τ Expansions of Integers in Euclidean Imaginary Quadratic Number Fields
- Author
-
V. Kumar Murty, Guangwu Xu, and Ian F. Blake
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,Algebraic number field ,01 natural sciences ,Quadratic equation ,0103 physical sciences ,Euclidean geometry ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Point (geometry) ,Radix ,010307 mathematical physics ,0101 mathematics ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Mathematics - Abstract
In his seminal papers, Koblitz proposed curves for cryptographic use. For fast operations on these curves, these papers also initiated a study of the radix-τ expansion of integers in the number fields and . The (window) nonadjacent form of τ -expansion of integers in was first investigated by Solinas. For integers in , the nonadjacent form and the window nonadjacent form of the τ -expansion were studied. These are used for efficient point multiplications on Koblitz curves. In this paper, we complete the picture by producing the (window) nonadjacent radix-τ expansions for integers in all Euclidean imaginary quadratic number fields.
- Published
- 2008