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Connections Between Nonlinearity and Restrictions, Terms and Hypergraphs of Boolean Functions

By Xian-mo Zhang

Abstract

Abstract | This paper studies nonlinear characteristics of (Boolean) functions which are important in cryptography. Main contributions of this paper are: (1) we show that the restriction of a function on a coset has signi cant in uence on cryptographic properties of the function, (2) we identify relationships between the nonlinearity of a function and the distribution of terms in the polynomial representation of the function, (3) we prove that cycles of odd length in the terms, as well as quadratic terms, in a function play an important role in determining the nonlinearity of the function. Results in this paperwillcontribute to the study of new cryptanalytic attacks on encryption algorithms, and counter-measures against such attacks

Publisher: Press
Year: 1998
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.247
Provided by: CiteSeerX
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