On nonlinearity and global avalanche characteristics of vector Boolean functions

다국어 초록 (Multilingual Abstract)

It is well known that the nonlinearity of vector Boolean func-tions F on n-dimensional vector space GF n to GF m is boundedabove by 2 n 1 2n2 1. In this paper we derive upper bounds and alower bound on the nonlinearity of vector Boolean functions in terms ofauto-correlations. Strengths and weaknesses of each bounds are examined.Also, we modify the notions of the sum-of-square indicator and absoluteindicator for Boolean functions to the case of vector Boolean functionsto measure global avalanche characteristics of vector Boolean functions.Using those indicators we compare the global avalanche characteristics ofDES(Data Encryption System) and Rijndael.

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