On Algebraic Immunity of Weight Symmetric H Boolean Functions

Abstract:

Using the derivative of Boolean functions and the e-derivative defined by ourselves as research tools, we discuss the relationship among a variety of cryptographic properties of the weight symmetric H Boolean functions in the range of the weight with the existence of H Boolean functions. We also study algebraic immunity and correlation immunity of the weight symmetric H Boolean functions and the balanced H Boolean functions. We obtain that the weight symmetric H Boolean function should have the same algebraic immunity, correlation immunity, propagation degree and nonlinearity. Besides, we determine that there exist several kinds of H Boolean functions with resilient, algebraic immunity and optimal algebraic immunity. The above results not only provide a theoretical basis for reducing nearly half of workload when studying the cryptographic properties of H Boolean function, but also provide a new research method for the study of secure cryptographic property of Boolean functions. Such researches are important in cryptographic primitive designs.

• Periodical: Applied Mechanics and Materials (Volume 643)
• Pages: 124-129
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.643.124
• Online since: September 2014
• Authors: Jing Lian Huang*, Zhuo Wang, Juan Li
• Keywords: Algebraic Immunity, Derivative, E-Derivative, H Boolean Function, Weight Symmetric

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