Connections between nonlinearity and restrictions, terms and hypergraphs of Boolean functions

Xian Mo Zhang, Yuliang Zheng, H. Imai

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

1 Citation (Scopus)

Abstract

This paper studies nonlinear characteristics of (Boolean) functions which are important in cryptography. The main contributions of this paper are: (1) we show that the restriction of a function on a coset has significant influence 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 paper will contribute to the study of new cryptanalytic attacks on encryption algorithms, and counter-measures against such attacks.

Original languageEnglish
Title of host publicationProceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998
Pages439
Number of pages1
DOIs
Publication statusPublished - 1998
Event1998 IEEE International Symposium on Information Theory, ISIT - 1998 - Cambridge, United States
Duration: 16 Aug 199821 Aug 1998

Other

Other1998 IEEE International Symposium on Information Theory, ISIT - 1998
CountryUnited States
CityCambridge
Period16/08/9821/08/98

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