Computer Science ›› 2016, Vol. 43 ›› Issue (11): 230-233.doi: 10.11896/j.issn.1002-137X.2016.11.045

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Highest Nonlinearity Rotation Symmetric Boolean Functions and Optimal Algebraic Immunity Function

HUANG Jing-lian and WANG Zhuo   

  • Online:2018-12-01 Published:2018-12-01

Abstract: In this paper,we studied the cryptographic properties of RSBFs,including the highest number of propagation,the highest nonlinearity and algebraic immunity,and also studied the problems of the existence and the construction of the optimal algebraic immunity function.Using the derivative and the e-derivative of the Boolean functions,we proved that there exist RSBFs whose nonlinearity is the highest,and verified the existence of a type of RSBFs from Bent functions whose propagation reaches n degree.Moreover,we also proved the existence of RSBFs with algebraic immunity by one-order or higher than two-order.We constructed inhomogeneous complete RSBFs with the optimal algebraic immunity and a large number of the optimal algebraic immunity Boolean functions from rotation symmetric Bent functions,and proved the existence of the two types of functions.Meanwhile,we also obtained inhomogeneous complete RSBFs with correlation immunity.

Key words: RSBFs,Bent function,Derivative,Optimal algebraic immunity function,Correlation immunity

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