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

Author

Zhang, Xian-Mo ; Zheng, Yuliang ; Imai, Hideki

Author_Institution

Sch. of Inf. Technol. & Comput. Sci., Wollongong Univ., NSW, Australia

fYear

1998

fDate

16-21 Aug 1998

Firstpage

439

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

Keywords

Boolean functions; cryptography; graph theory; nonlinear functions; polynomials; Boolean functions; countermeasures; cryptanalytic attacks; cryptographic properties; cryptography; distribution of terms; encryption algorithms; hypergraphs; nonlinear characteristics; nonlinearity; polynomial representation; quadratic terms; restrictions; Australia; Boolean functions; Cryptography; Ear; Hamming distance; Polynomials;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on

Conference_Location

Cambridge, MA

Print_ISBN

0-7803-5000-6

Type

conf

DOI

10.1109/ISIT.1998.709044

Filename

709044