报告题目：Further Cryptographic Properties of the?Multiplicative Inverse Function?

报 告 人：唐灯（上海交通大学）

报告时间：2022年4月13日（星期三），16;00-18:00

报告地点：腾讯会议ID：510 599 331；会议密码：123456

报告摘要：Differential analysis is an important cryptanalytic technique on block ciphers. In one form, this measures the probability of occurrence of the differences between certain input vectors and the corresponding output vectors. For this analysis, the constituent S-boxes of a block cipher need to be studied carefully. In this direction, we derive further cryptographic properties of the multiplicative inverse function, especially the ones related to higher order differentials. This improves some theoretical results of Boukerrou et al. [ToSC 2020(1)]. Further, we prove that the multiplicative inverse function defined over the finite field ?has an error (bias) in its second order differential spectrum with probability , and that error occurs in more than one place. Next, we analyze the Gowers uniformity norm of S-boxes, which is also a measure connected to higher order approximations. Finally, the bounds related to the nonlinearity profile of the multiplicative inverse function are derived using both Gowers ?norm and Walsh--Hadamard spectrum. Some of our findings here provide slightly improved bounds over the work of Carlet [IEEE-IT, 2008]. These theoretical insights might have implications towards non-randomness of a block cipher, where the multiplicative inverse function is used as a primitive.

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数学科学学院

2022年4月2日

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报告人简介：唐灯，上海交通大学长聘教轨副教授、博士生导师。2015年分别获得法国巴黎第八大学应用数学博士学位和西南交通大学信息安全博士学位。2015年7月加入西南交通大学数学学院，2019年12月加入上海交通大学网络空间安全学院。主要研究方向为对称密码算法分析、大数据安全与隐私保护、代数编码及其应用。在国内外重要学术期刊和会议发表研究论文三十余篇，含第一/通讯作者 IEEE Transactions on Information Forensics and Security、IEEE Transactions on Information Theory、Designs, Codes and Cryptography、SIAM Journal on Discrete Mathematics、Cryptography and Communications 期刊论文十余篇。主持国家自然科学基金面上项目和青年科学基金项目、装备预研国防科技重点实验室基金项目等。获得中国密码学会2019年密码算法学术会议最佳论文奖、全国密码算法设计竞赛分组密码算法三等奖、IEEE成都分会2014年最佳学生论文奖。