On the value distributions of Walsh spectrums of quadratic Plateaued functions

Authors:
Xuelian Li;Yupu Hu;Juntao Gao
Affiliations:
Department of Applied Mathematics of Xidian University, Xi'an, Shaanxi Province 710071, China;School of Telecommunication and Engineering of Xidian University, Xi'an, Shaanxi Province 710071, China;School of Telecommunication and Engineering of Xidian University, Xi'an, Shaanxi Province 710071, China and State Key Laboratory of Information Security, Graduate University of Chinese Academy of ...
Venue:
Computers and Electrical Engineering
Year:
2011

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Abstract

Plateaued functions have many cryptographically desirable properties, and have been used in cryptography and coding theory. However the properties of Plateaued functions have not been completely determined yet. Since many cryptographic properties can be estimated or evaluated by the value distribution of Walsh spectrum, it is essential to determine the value distribution of Walsh spectrum of a given Plateaued function. Based on the properties of trace functions and quadratic forms, this paper investigates the value distributions of Walsh spectrums of quadratic Plateaued functions of the form Tr(R(x)) with n variables. Firstly, we give all possible value distributions of Walsh spectrums of the functions. Furthermore, we proceed to determine the value distributions of Walsh spectrums of the functions on condition that the coefficients of R(x) belong to some given sets. Our results can be used to estimate the nonlinearities of these functions and their resiliency orders.