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

主讲人：唐灯（上海交通大学）

报告时间：12月8日（周三）下午15:30-16:30

报告地点：腾讯会议 ID： 556-434-569

主办单位：金沙集团wwW3354CC

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 inputs vectors and the corresponding outputs vectors. For this analysis, the constituent S-boxes of block ciphers need to be studied carefully. In this direction, we derive further cryptographic properties of inverse function, especially higher-order differential properties here. This improves certain results of Boukerrou et al. We prove that inverse function defined over $\mathbb F_{2^n}$ has an error (bias) in its second-order differential spectrum with probability $\frac{1}{2^{n-2}}$, and that error occurs in more than one places. To the best of our knowledge, this result was not known earlier. Further, for the first time, we analyze the Gowers uniformity norm of S-boxes which is also a measure of resistance to higher order approximations. Finally, the bounds related to the nonlinearity profile of multiplicative inverse function are derived using both Gowers $U_3$ norm and Walsh--Hadamard spectrum. All our results might have implications towards non-randomness of a block cipher where the inverse function is used as a primitive.

主讲人简介：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。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四十余篇。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、密码科学技术国家重点实验室开放课题等。主研国家重点研发计划项目、国家自然科学基金重点项目等。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。