Construction of Quadratic Bent Functions over Finite Fields

doi:10.13190/jbupt.201003.52.zhangfr

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2010, Vol. 33 ›› Issue (3): 52-56.doi: 10.13190/jbupt.201003.52.zhangfr

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Construction of Quadratic Bent Functions over Finite Fields

ZHANG Feng-rong¹, GAO Jun-tao¹, HU Yu-pu¹, XIE Min^1,2

(1. Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi'an 710071, China; 
2. Key Laboratory of Information Security Technology in Guangdong (Guangzhou Uni
versity), Guangzhou 510405, China)

Received:2009-09-07 Revised:2009-11-20 Online:2010-06-28 Published:2010-05-14

Abstract

Abstract:

A sufficient and necessary condition that a quadratic polynomial function is a bent function was

presented by Ma W P, et al. in 2005. In the same year, Charpin P, et al proposed a sufficient and

necessary condition that a polynomial function is a quadratic semi-Bent function with three

trace terms in a paper. Corollary 5,6 of the former and Theorem 5,6 of the latter are not quite right

by further investigating these conditions. Based on the theory of quadratic polynomial over finite

fields, the correct conditions are presented. Moreover, some quadratic bent functions with three or

four trace terms are constructed. Finally, a new method for constructing bent functions in polynomial

forms is provided by using bent functions of two trace terms and permutation of polynomial.

Key words: cryptographic functions, Boolean functions, bent functions, maximum nonlinearity

ZHANG Feng-rong, GAO Jun-tao, HU Yu-pu, XIE Min. Construction of Quadratic Bent Functions over Finite Fields[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2010, 33(3): 52-56.

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Construction of Quadratic Bent Functions over Finite Fields

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