Analysis of Digital Expansions of Minimal Weight - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2012

Analysis of Digital Expansions of Minimal Weight

Abstract

Extending an idea of Suppakitpaisarn, Edahiro and Imai, a dynamic programming approach for computing digital expansions of minimal weight is transformed into an asymptotic analysis of minimal weight expansions. The minimal weight of an optimal expansion of a random input of length $\ell$ is shown to be asymptotically normally distributed under suitable conditions. After discussing the general framework, we focus on expansions to the base of $\tau$, where $\tau$ is a root of the polynomial $X^2- \mu X + 2$ for $\mu \in \{ \pm 1\}$. As the Frobenius endomorphism on a binary Koblitz curve fulfils the same equation, digit expansions to the base of this $\tau$ can be used for scalar multiplication and linear combination in elliptic curve cryptosystems over these curves.
Fichier principal
Vignette du fichier
dmAQ0131.pdf (371.23 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01197230 , version 1 (11-09-2015)

Identifiers

Cite

Florian Heigl, Clemens Heuberger. Analysis of Digital Expansions of Minimal Weight. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. pp.399-412, ⟨10.46298/dmtcs.3009⟩. ⟨hal-01197230⟩

Collections

INSMI TDS-MACS
163 View
469 Download

Altmetric

Share

Gmail Facebook X LinkedIn More