Computer Science ›› 2015, Vol. 42 ›› Issue (3): 153-157.doi: 10.11896/j.issn.1002-137X.2015.03.032

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On Relationship of Algebraic Degree,Correlation Immunity and Algebraic Immunity for a Class of H Boolean Functions

HUANG Jing-lian, WANG Zhuo and LI Juan   

  • Online:2018-11-14 Published:2018-11-14

Abstract: Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools,we studied the relationship of algebraic degree,algebraic immunity and correlation immunity for H Boolean functions with a specific Hamming weight.We obtained the algebraic degree of the e-derivative which is a component of H Boolean functions deciding the algebraic degree of H Boolean functions.Besides,we determined the e-derivative of H Boolean functions which is closely related to the order of the algebraic immunity of H Boolean functions.We also checked the e-derivative of H Boolean functions which can put algebraic immunity,annihilators,correlation immunity and algebraic degree of H Boolean functions together.Meanwhile,we also deduced two kinds of methods which are formula method and cascade method.By using these two methods we could solve annihilators of the lowest algebraic degree of H Boolean functions.

Key words: H Boolean functions,e-derivative,Derivative,Algebraic degree,Algebraic immunity,Correlation immunity,Relationship

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