Spectrum Distribution Characteristics of kth-Order Generalized Quasi-Bent Functions over Ring ZpReport as inadecuate




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Nonlinearity criterion is one of the most important criteria of nonlinear combined functions in the design of Cryptographic system, and it is necessary to investigate the nonlinearity of kth-order generalized quasi-Bent functions over ring Zp in order to study its application to Cryptography and coding theory. In this paper, the spectrum distribution characteristics of kth-order generalized quasi-Bent functions over ring Zp is proposed by using the knowledge of algebraic number theory, followed by the coincide ratio of such functions with all affine functions. The results in the paper offer much reference in the further study of the application of kth-order generalized quasi-Bent functions over ring Zp in the fields of Cryptography design and coding theory.

KEYWORDS

kth-order generalized quasi-Bent functions; Chrestenson cyclic spectrum;nonlinearity criterion; algebraic integers;

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Author: Jihong Teng, Xiaoying Huang, Xinran Li, Xiyong Zhang

Source: http://www.scirp.org/



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