On the number of optimal base 2 representations of integers

DOI10.1007/s10623-005-6158-yzbMath1261.11003OpenAlexW2091645886MaRDI QIDQ851731

Clemens Heuberger, Peter J. Grabner

Publication date: 22 November 2006

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-005-6158-y

zbMATH Keywords

elliptic curve cryptographyminimal Hamming weightSigned digit expansions

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Data encryption (aspects in computer science) (68P25) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Radix representation; digital problems (11A63) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Arithmetic codes (94B40)

Related Items (13)

Dynamical directions in numeration ⋮ Analysis of Summatory Functions of Regular Sequences: Transducer and Pascal's Rhombus ⋮ Purity results for some arithmetically defined measures ⋮ Numeration and discrete dynamical systems ⋮ Unnamed Item ⋮ Redundancy of minimal weight expansions in Pisot bases ⋮ ON THE BINARY DIGITS OF ALGEBRAIC NUMBERS ⋮ Binary signed-digit integers and the Stern diatomic sequence ⋮ On \(q\)-quasiadditive and \(q\)-quasimultiplicative functions ⋮ On the minimal Hamming weight of a multi-base representation ⋮ Minimal weight expansions in Pisot bases ⋮ Asymptotic analysis of regular sequences ⋮ Matching for random systems with an application to minimal weight expansions

Cites Work

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• Mellin transforms and asymptotics: Digital sums
• Digital sums and divide-and-conquer recurrences: Fourier expansions and absolute convergence
• On the number of odd binomial coefficients
• The state of elliptic curve cryptography
• Analysis of alternative digit sets for nonadjacent representations
• Minimal expansions in redundant number systems: Fibonacci bases and greedy algorithms
• A Survey of Fast Exponentiation Methods
• Functional iterations and stopping times for Brownian motion on the Sierpiński gasket
• On a Family of Symmetric Bernoulli Convolutions

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