A Class of 1-Resilient Functions in Odd Variables with High Nonlinearity and Suboptimal Algebraic Immunity

Yusong DU  Fangguo ZHANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.1   pp.417-420
Publication Date: 2012/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.417
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
stream ciphers,  algebraic attacks,  Boolean functions,  algebraic immunity,  nonlinearity,  resiliency,  

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Based on Tu-Deng's conjecture and the Tu-Deng function, in 2010, X. Tang et al. proposed a class of Boolean functions in even variables with optimal algebraic degree, very high nonlinearity and optimal algebraic immunity. In this corresponding, we consider the concatenation of Tang's function and another Boolean function, and study its cryptographic properties. With this idea, we propose a class of 1-resilient Boolean functions in odd variables with optimal algebraic degree, good nonlinearity and suboptimal algebraic immunity based on Tu-Deng's conjecture.