報告題目：On the Niho type locally-APN power functions and their boomerang spectrum

報告時間：2023年10月30日下午14：00-14：50

報告地點(diǎn)：kaiyun開云官方網(wǎng)站犀浦校區(qū)7教7510

報告人：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.

報告人簡介：李念，湖北大學(xué)教授，博士生導(dǎo)師。主要研究密碼、編碼及其相關(guān)的數(shù)學(xué)理論。主持國家自然科學(xué)基金2項、湖北省杰青等省部級基金5項，代表性成果發(fā)表在國內(nèi)外重要學(xué)術(shù)期刊IEEE TIT、DCC等上。2017年和2019年分別入選湖北省人才支持計劃，2022年獲湖北省自然科學(xué)獎一等獎（第三完成人）。