The Degree of Two Classes of 3rd Order Correlation Immune Symmetric Boolean Functions

Jie PENG  Haibin KAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.1   pp.365-370
Publication Date: 2014/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.365
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Cryptography and Information Security
symmetric Boolean function,  correlation immune,  correlation attack,  algebraic degree,  

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Two classes of 3rd order correlation immune symmetric Boolean functions have been constructed respectively in [1] and [2], in which some interesting phenomena of the algebraic degree have been observed as well. However, a good explanation has not been given. In this paper, we obtain the formulas for the degree of these functions, which can well explain the behavior of their degree.