报告题目：On the Niho type locally-APN power functions and their boomerang spectrum

报告专家：李念教授 （湖北大学）

报告时间：2023年4月26日（周三）下午15:00-16:00

报告地点：腾讯会议：445-644-414

主办单位：曲阜师范大学澳门威斯尼斯615人官方

报告摘要：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. In addition, we also determine the boomerang spectrum of F(x) by using its differential spectrum, which particularly generalizes a recent result by Yan, Zhang, and Li.

专家简介： 李念，湖北大学教授，博士生导师。2013年于西南交通大学获博士学位，导师唐小虎教授；博士期间在挪威卑尔根大学联合培养两年，导师Tor Helleseth院士；随后三年先后于香港科技大学和挪威卑尔根大学继续从事关于代数编码与密码方面的博士后和研究员工作，合作导师为熊茂胜和Lilya Budaghyan教授。主要研究密码、编码及其相关的数学理论。近年来在密码函数、线性码、序列设计等领域做出了⼀系列成果，主持国家自然科学基金2项、湖北省杰青等省部级基金3项，代表性成果发表在国内外重要学术期刊《IEEE Transactions on Information Theory》、《Designs, Codes and Cryptography》和《Finite Fields and Their Applications》等上。2017年和2019年分别入选湖北省楚天学者计划和湖北省百人计划。