Two Classes of Crooked Multinomials Inequivalent to Power Functions

2011/11/05 by Xue-Ying Duan, Xueying Duan, Qichun Wang +2
Computer Science · Mathematics · #Coding theory and cryptography #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Mathematical and Theoretical Analysis #advanced mathematical theories #cs.CR

paper · pdf · doi:10.48550/arxiv.1111.1328

arxiv created 2011/11/05 · openalex publication_date 2011/11/05 · arxiv updated 2011/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that crooked functions can be used to construct many interesting combinatorial objects, and a quadratic function is crooked if and only if it is almost perfect nonlinear (APN). In this paper, we introduce two infinite classes of quadratic crooked multinomials on fields of order 2^2m. One class of APN functions constructed in [7] is a particular case of the one we construct in Theorem 1. Moreover, we prove that the two classes of crooked functions constructed in this paper are EA inequivalent to power functions and conjecture that CCZ inequivalence between them also holds.

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