Effective Construction of a Class of Bent Quadratic Boolean Functions

2013/08/13 by Chunming Tang, Yanfeng Qi, Tang, Chunming +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT

paper · pdf · doi:10.48550/arxiv.1308.2798

arxiv created 2013/08/13 · openalex publication_date 2013/08/13 · arxiv updated 2013/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the characterization of the bentness of quadratic Boolean functions of the form f(x)=∑_i=1^(m)/(2)-1 Trⁿ₁(c_ix^1+2^ei)+ Tr₁^n/2(c_m/2x^1+2^n/2) , where n=me, m is even and c_i∈ GF(2^e). For a general m, it is difficult to determine the bentness of these functions. We present the bentness of quadratic Boolean function for two cases: m=2^vp^r and m=2^vpq, where p and q are two distinct primes. Further, we give the enumeration of quadratic bent functions for the case m=2^vpq.

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