Displaying similar documents to “Signed bits and fast exponentiation”

Efficient Computing of some Vector Operations over GF(3) and GF(4)

Bouyukliev, Iliya, Bakoev, Valentin (2008)

Serdica Journal of Computing

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The problem of efficient computing of the affine vector operations (addition of two vectors and multiplication of a vector by a scalar over GF (q)), and also the weight of a given vector, is important for many problems in coding theory, cryptography, VLSI technology etc. In this paper we propose a new way of representing vectors over GF (3) and GF (4) and we describe an efficient performance of these affine operations. Computing weights of binary vectors is also discussed.

Efficient computation of addition chains

F. Bergeron, J. Berstel, S. Brlek (1994)

Journal de théorie des nombres de Bordeaux

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The aim of this paper is to present a unifying approach to the computation of short addition chains. Our method is based upon continued fraction expansions. Most of the popular methods for the generation of addition chains, such as the binary method, the factor method, etc..., fit in our framework. However, we present new and better algorithms. We give a general upper bound for the complexity of continued fraction methods, as a function of a chosen strategy, thus the total number of...

On the number of binary signed digit representations of a given weight

Jiří Tůma, Jiří Vábek (2015)

Commentationes Mathematicae Universitatis Carolinae

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Binary signed digit representations (BSDR’s) of integers have been studied since the 1950’s. Their study was originally motivated by multiplication and division algorithms for integers and later by arithmetics on elliptic curves. Our paper is motivated by differential cryptanalysis of hash functions. We give an upper bound for the number of BSDR’s of a given weight. Our result improves the upper bound on the number of BSDR’s with minimal weight stated by Grabner and Heuberger in On the...