Simplicity conditions for binary orthogonal arrays

It is known that correlation-immune (CI) Boolean functions used in the framework of side channel attacks need to have low Hamming weights. The supports of CI functions are (equivalently) simple orthogonal arrays, when their elements are written as rows of an array. The minimum Hamming weight of a CI...

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Vydáno v:Designs, codes, and cryptography Ročník 91; číslo 1; s. 151 - 163
Hlavní autoři: Carlet, Claude, Kiss, Rebeka, Nagy, Gábor P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.01.2023
Springer Nature B.V
Springer Verlag
Témata:
Arrays
Boolean
Boolean functions
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Fourier transforms
Mathematics
Orthogonal arrays
Boolean function
Correlation-immune
Rao’s bound
Linear programming bound
Orthogonal array
05B05
ISSN:0925-1022, 1573-7586
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Shrnutí:It is known that correlation-immune (CI) Boolean functions used in the framework of side channel attacks need to have low Hamming weights. The supports of CI functions are (equivalently) simple orthogonal arrays, when their elements are written as rows of an array. The minimum Hamming weight of a CI function is then the same as the minimum number of rows in a simple orthogonal array. In this paper, we use Rao’s Bound to give a sufficient condition on the number of rows, for a binary orthogonal array (OA) to be simple. We apply this result for determining the minimum number of rows in all simple binary orthogonal arrays of strengths 2 and 3; we show that this minimum is the same in such case as for all OA, and we extend this observation to some OA of strengths 4 and 5. This allows us to reply positively, in the case of strengths 2 and 3, to a question raised by the first author and X. Chen on the monotonicity of the minimum Hamming weight of 2-CI Boolean functions, and to partially reply positively to the same question in the case of strengths 4 and 5.
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ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-022-01105-4