A note on the differential spectrum of a class of locally APN functions

2025/01/08 by Yan, Haode, Ren, Ketong · 2 citations
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2501.04233

Abstract

Let \gf_pⁿ denote the finite field containing pⁿ elements, where n is a positive integer and p is a prime. The function f_u(x)=x^(pn+3)/(2)+ux² over \gf_pⁿ[x] with u∈\gf_pⁿ∖\0,±1\ was recently studied by Budaghyan and Pal in \citeBudaghyan2024ArithmetizationorientedAP, whose differential uniformity is at most 5 when pⁿ≡3~(mod~4). In this paper, we study the differential uniformity and the differential spectrum of f_u for u=±1. We first give some properties of the differential spectrum of any cryptographic function. Moreover, by solving some systems of equations over finite fields, we express the differential spectrum of f_±1 in terms of the quadratic character sums.

Cited by

• Locally-APN Binomials with Low Boomerang Uniformity in Odd Characteristic
• On Differential and Boomerang Properties of a Class of Binomials over Finite Fields of Odd Characteristic

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