中南民族大学学报（自然科学版）2024，Vol.43Issue(1)：126-132,7.DOI:10.20056/j.cnki.ZNMDZK.20240117
一类低差分均匀度幂函数的差分谱
Differential spectra of a class of power functions with low differential uniformity
摘要
Abstract
The differential spectra of a class of power functions f(x)= xpn-3/2 over finite field Fpn with low differential uniformity are described,where p and n satisfy pn ≡ 3(mod 4)and pn≠ 27.By studying the differential equation of f(x),the necessary and sufficient conditions for which the differential equation f(x+1)-f(x)=b has exactly two solutions are given.Furthermore the number of elements b∈Fpn that satisfies the condition is calculated.Based on the obtained results,the differential spectra of these power functions are determined.关键词
有限域/差分均匀度/差分谱/差分方程Key words
finite field/differential uniformity/differential spectrum/differential equation分类
数理科学引用本文复制引用
夏永波,包福荣,彭丽娜..一类低差分均匀度幂函数的差分谱[J].中南民族大学学报（自然科学版）,2024,43(1):126-132,7.基金项目
国家自然科学基金资助项目(62171479) （62171479）
中南民族大学研究生学术创新基金资助项目(3212023sycxjj004) （3212023sycxjj004）
