منابع مشابه
Counting Optimal Joint Digit Expansions
This paper deals with pairs of integers, written in base two expansions using digits 0,±1. Representations with minimal Hamming weight (number of non-zero pairs of digits) are of special importance because of applications in Cryptography. The interest here is to count the number of such optimal representations.
متن کاملGrowth Rate for Beta-expansions
Let β > 1 and let m > β be an integer. Each x ∈ Iβ := [0, m−1 β−1 ] can be represented in the form x = ∞ ∑ k=1 εkβ −k, where εk ∈ {0, 1, . . . , m − 1} for all k (a β-expansion of x). It is known that a.e. x ∈ Iβ has a continuum of distinct β-expansions. In this paper we prove that if β is a Pisot number, then for a.e. x this continuum has one and the same growth rate. We also link this rate to...
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This paper investigates representations of real numbers with an arbitrary negative base −β < −1, which we call the (−β)-expansions. They arise from the orbits of the (−β)-transformation which is a natural modification of the β-transformation. We show some fundamental properties of (−β)-expansions, each of which corresponds to a well-known fact of ordinary β-expansions. In particular, we charact...
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This paper studies τ -adic expansions of scalars, which are important in the design of scalar multiplication algorithms on Koblitz Curves, and are less understood than their binary counterparts. At Crypto ’97 Solinas introduced the width-w τ -adic non-adjacent form for use with Koblitz curves. It is an expansion of integers z = P` i=0 ziτ , where τ is a quadratic integer depending on the curve,...
متن کاملDaniel KRENN Digit Expansions with Applications in Cryptography
Efficient scalar multiplication in Abelian groups (which is an important operation in public key cryptography) can be performed using digit expansions. Apart from rational integer bases (double-and-add algorithm), imaginary quadratic integer bases are of interest for elliptic curve cryptography, because the Frobenius endomorphism fulfils a quadratic equation. One strategy for improving the effi...
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ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2020
ISSN: 0236-5294,1588-2632
DOI: 10.1007/s10474-020-01032-7