Further investigation on differential properties of the generalized Ness-Helleseth function

扫码查看

原文链接

NETL
NSTL

外文摘要：Let n be an odd positive integer, p be an odd prime with p ≡ 3 (mod 4), d_1 = p~n-1/2-1 and d_2 = p~n - 2. The function defined by f_u(x) = ux~(d_1) + x~(d_2) is called the generalized Ness-Helleseth function over F_(p~n), where u ∈ F_(p~n). It was initially studied by Ness and Helleseth in the ternary case. In this paper, for p~n ≡ 3 (mod 4) and p~n ≥ 7, we provide the necessary and sufficient condition for f_u(x) to be an APN function. In addition, for each u satisfying χ(u + 1) = χ(u - 1), the differential spectrum of f_u(x) is investigated, and it is expressed in terms of some quadratic character sums of cubic polynomials, where χ(·) denotes the quadratic character of F_(p~n).

外文关键词：

Quadratic characterAPN functionDifferential cryptanalysisDifferential uniformityDifferential spectrum

作者：

Yongbo Xia、Chunlei Li、Furong Bao、Shaoping Chen、Tor Helleseth

展开 >

作者单位：

School of Mathematics and Statistics, and also with the Hubei Key Laboratory of Intelligent Wireless Communications, South-Central Minzu University, Wuhan 430074, China

Department of Informatics, University of Bergen, 5020 Bergen, Norway

School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China

Hubei Key Laboratory of Intelligent Wireless Communications, South-Central Minzu University, Wuhan 430074, China

展开 >

出版年：

2025

DOI：

10.1007/s10623-024-01525-4

Designs, codes and cryptography

ISSN：0925-1022

年,卷(期)：2025.93(6)