Algebraically degenerate approximations of boolean functions PDF

Автори:A.N. Alekseychuk, S.N. Konyushok

A.N. Alekseychuk, S.N. Konyushok

UDC 519.7

Algebraic degenerate approximations of Boolean functions / Alekseychuk A.N., Konyushok S.N. // Cybernetika i sistemny analiz.

Properties of k-dimensional approximations of Boolean functions are investigated. One of main results is the theorem on the structure of k-dimensional functions whose degree equals d and whose distance from a given Boolean function of n variables is no longer than 2 n-d (1-ε), 1 ≤ d ≤ k ≤ n, ε∈ (0, 1) This theorem considerably strengthens the well-known P. Gopalan result and makes it possible to considerably increase the efficiency of his algorithm for constructing all the mentioned k-dimensional Boolean functions.

Refs: 12 titles.

Keywords:

correlation cryptanalysis, degenerate Boolean function, k-dimensional function, Walsh–Hadamard transform, finding k-dimensional approximations of Boolean functions

Author Affiliations

Institute of Special Communications and Information Protection, National Technical University of Ukraine "Kyiv Polytechnic Institute", Kyiv, Ukraine

References

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Cybernetics and Systems Analysis

November 2014, Volume 50, Issue 6, pp 817-828

Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 3–14, November–December, 2014