Computer Science ›› 2016, Vol. 43 ›› Issue (7): 166-170.doi: 10.11896/j.issn.1002-137X.2016.07.030

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H Boolean Functions with Divided into Two Parts and High Nonlinearity Boolean Functions

HUANG Jing-lian, WANG Zhuo and LI Juan   

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

Abstract: Using the derivative of the Boolean functions and the e-derivative defined by ourselves as research tools,we studied the cryptographic properties of a class of H Boolean function which satisfy one degree propagation and are divi-ded into the product of two subfunctions,including nonlinearity,correlation immunity and algebraic immunity and so on.We achieved the relationship between the correlation immunity of this kind of H Boolean function and the two subfunctions,and also arrived at a conclusion on the correlation immunity of this kind of H Boolean function which can reach n2 -1.Moreover,we obtained the relationship between the lowest algebraic degree annihilator of this kind of an H Boolean function and the two subfunctions.Further,using e-derivative and derivative of a Boolean function,we constructed a cluster of H Boolean function which has the nonlinearity 2n-2+2n-3,the correlation immunity and 2-order algebraic immunity from obtained H Boolean functions.In this way,we resolved the problem of improving the nonlinearity of a Boolean function,and the existence problem of a Boolean function having higher nonlinearity,propagation,correlation immunity and higher algebraic immunity.

Key words: H Boolean functions,2-divide,e-derivative,Nonlinearity,Algebraic immunity,Correlation immunity

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