密码学报（中英文）2025，Vol.12Issue(5)：982-1002,21.DOI:10.13868/j.cnki.jcr.000805
(广义)几乎完全非线性函数的研究进展
Recent Progress in(Generalization)Almost Perfect Nonlinear Functions
摘要
Abstract
Almost perfect nonlinear(APN)functions defined over the finite field F2n exhibit opti-mal differential uniformity,offering the strongest known resistance against differential attacks.Beyond cryptography,APN functions and their generalizations play significant roles in coding theory,sequence design,and finite geometry,among other theoretical domains.This study provides a systematic review of current advances in APN functions and their generalizations.The survey is structured along two primary dimensions:(1)classical APN functions,encompassing studies over finite fields of even char-acteristic,odd characteristic,and the ring of integers;and(2)generalized APN functions over finite fields,including GAPN functions,APcN functions,and local APN functions.Finally,we conclude by proposing open problems in the study of APN functions and generalized APN functions that are worthy of further research.关键词
几乎完全非线性函数/广义几乎完全非线性函数/几乎完全c-非线性函数/局部几乎完全非线性函数Key words
almost perfect nonlinear function/generalization almost perfect nonlinear function/almost perfect c-nonlinear function/local almost perfect nonlinear function分类
计算机与自动化引用本文复制引用
王彦平..(广义)几乎完全非线性函数的研究进展[J].密码学报（中英文）,2025,12(5):982-1002,21.基金项目
国家自然科学基金(12361107) （12361107）
兰州市青年科技人才创新项目(2023-QN-105)National Natural Science Foundation of China(12361107) （2023-QN-105）
Lanzhou Youth Scientific and Technological Talents Innovation Project(2023-QN-105) （2023-QN-105）
