Minimality and other properties of the width-𝑤 nonadjacent form

DOI10.1090/S0025-5718-05-01769-2zbMath1091.94026OpenAlexW2000840326MaRDI QIDQ5713234

James A. Muir, Douglas R. Stinson

Publication date: 12 December 2005

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-05-01769-2

zbMATH Keywords

minimal weightelliptic curve arithmeticefficient integer representation

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50) Arithmetic codes (94B40)

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Speeding up the Elliptic Curve Scalar Multiplication Using Non Adjacent Form ⋮ Optimality of the width-\(w\) non-adjacent form: general characterisation and the case of imaginary quadratic bases ⋮ Redundant \(\tau \)-adic expansions. II: Non-optimality and chaotic behaviour ⋮ Balanced non-adjacent forms ⋮ Non-minimality of the width-$w$ non-adjacent form in conjunction with trace one $\tau $-adic digit expansions and Koblitz curves in characteristic two ⋮ POWER CIRCUITS, EXPONENTIAL ALGEBRA, AND TIME COMPLEXITY ⋮ Factor-4 and 6 compression of cyclotomic subgroups of and ⋮ On the minimal Hamming weight of a multi-base representation ⋮ On the low Hamming weight discrete logarithm problem for nonadjacent representations ⋮ Minimal weight and colexicographically minimal integer representations ⋮ Minimal weight expansions in Pisot bases ⋮ A New Type of 2-Block Collisions in MD5 ⋮ Fast elliptic curve point multiplication based on window non-adjacent form method ⋮ Variances and covariances in the central limit theorem for the output of a transducer

Cites Work

• Analysis of the sliding window powering algorithm
• Efficient arithmetic on Koblitz curves
• The alternating greedy expansion and applications to computing digit expansions from left-to-right in cryptography
• A Survey of Fast Exponentiation Methods
• Advances in Cryptology – CRYPTO 2004
• Topics in Cryptology – CT-RSA 2005
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