Optimality of the width-\(w\) non-adjacent form: general characterisation and the case of imaginary quadratic bases

DOI10.5802/jtnb.840zbMath1282.11005arXiv1110.0966OpenAlexW2074720715MaRDI QIDQ394267

Daniel Krenn, Clemens Heuberger

Publication date: 24 January 2014

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.0966

zbMATH Keywords

optimalityFrobenius endomorphismelliptic curve cryptographyHamming weightscalar multiplicationKoblitz curvesredundant digit setswidth-\(w\) non-adjacent forms\(\tau \)-adic expansionsimaginary quadratic bases

Mathematics Subject Classification ID

Cryptography (94A60) Radix representation; digital problems (11A63) Algebraic numbers; rings of algebraic integers (11R04) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (5)

Analysis of the width-\(w\) non-adjacent form in conjunction with hyperelliptic curve cryptography and with lattices ⋮ Non-minimality of the width-$w$ non-adjacent form in conjunction with trace one $\tau $-adic digit expansions and Koblitz curves in characteristic two ⋮ Existence and optimality of \(w\)-non-adjacent forms with an algebraic integer base ⋮ On the minimal Hamming weight of a multi-base representation ⋮ Some properties of \(\tau\)-adic expansions on hyperelliptic Koblitz curves

Uses Software

• SageMath

Cites Work

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• Minimality and other properties of the width-𝑤 nonadjacent form
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