报告题目：On the Niho type locally-APN power functions and their boomerang spectrum
报告时间：2023年10月30日下午14：00-14：50
报告地点：金沙威尼斯欢乐娱人城犀浦校区7教7510
报告人：李念
摘要：In this talk, we focus on the concept of locally-APN-ness introduced by Blondeau, Canteaut, and Charpin, which makes the corpus of S-boxes somehow larger regarding their differential uniformity and, therefore, more suitable candidates against the differential attack (or their variants). Specifically, given two coprime positive integers m and k such that gcd(2^m+1,2^k+1)=1, we investigate the locally-APN-ness property of an infinite family of Niho type power functions in the form F(x)=x^{s(2^m-1)+1} over the finite field F_{2^n} for s=(2^k+1)^{-1}, where (2^k+1)^{-1} denotes the multiplicative inverse modulo 2^m+1. By employing finer studies of the number of solutions of certain equations over finite fields (with even characteristic) as well as some subtle manipulations of solving some equations, we prove that F(x) is locally APN and determine its differential spectrum. It is worth noting that computer experiments show that this class of locally-APN power functions covers all Niho type locally-APN power functions for 2<= m<=10.
报告人简介：李念，湖北大学教授，博士生导师。主要研究密码、编码及其相关的数学理论。主持国家自然科学基金2项、湖北省杰青等省部级基金5项，代表性成果发表在国内外重要学术期刊IEEE TIT、DCC等上。2017年和2019年分别入选湖北省人才支持计划，2022年获湖北省自然科学奖一等奖（第三完成人）。
