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The Characteristic of Spectrum and Self-correlation of Some Boolean Fuctions Linearly Equivalent to Specific Cryptographic Functions

Yang Rui,Zeng Bensheng,Li Shiqu

Strategic Study of CAE 2005, Volume 7, Issue 11, Pages 60-65

Abstract:

The paper made an analysis of the similarities and differences about the cryptographic properties of two Boolean functions in the sense of linearly equivalence, and obtained a sufficient and necessary condition about a Boolean function linearly equivalent to some m order correlation-immune Boolean function. It also obtained a sufficient and necessary condition about a Boolean function linearly equivalent to some Boolean function satisfying the k order propagation criterion. Moreover, it showed an example,in which a given Boolean function, that is not correlation-immuned and does not satisfy the propagation criterion can be constructed into a correlation-immuned Boolean function that can satisfy the propagation criterion and is linearly equivalent to the former one.

Keywords： equivalence Walsh cycle spectrum self-correlation function correlation-immunity propagation criterion SAC