理学院数理讲坛（2014年第二十七——二十九讲）
报告第27讲：
报 告 人：Yuliang Zheng (University of North Carolina)
报告题目：Collision Accessible One-Way Hash Functions
报告时间：2014年6月11日上午8:30－9:15
报告地点：理学院北楼311报告厅
Abstract:
A "sibling intractable function family (SIFF)" is a collection ofone-way hash functions that admit two seemingly contradictory properties: on one hand, it is infeasible for an attacker, who is given k siblings that are known to be hashed/mapped to the same output, to find a new sibling that is also hashed to the same output; one the other hand, it is easy to pick a function from amongst all those candidate hash functions that force given k input values to be hashed to the same output. In this talk, I will review SIFF and show how it can be further extended to a broader class of hash functions. I will also discuss some interesting applications of such functions, including access control and multi-recipient encryption in a heterogeneous environment.
Biography:
Professor Yuliang Zheng is known as the father of signcryption technology which is now an international standard for data security. His pioneering research into immunizing public key encryption against adaptive attacks has been embodied in numerous international standards for public key cryptography, including those from ISO, IEEE and IETF. Professor Zheng's contributions to nonlinear Boolean functions have found applications in both applied mathematics and data security. An internationally recognized authority in cryptography and network security, Professor Zheng has published over 200 scholarly articles and books on security and holds a multiple number of patents in cyber security. He plays an active leadership role in international research communities, serving as the Chair of the Steering Committee of the Public Key Cryptography (PKC) conferences sponsored by the International Association for Cryptologic Research.
报告第28讲：
报 告 人：Shuhong Gao（Clemson University）
报告题目：Recent progress on computing Groebner bases
报告时间：2014年6月11日上午9:20－10:05
报告地点：理学院北楼311报告厅
Abstract:
Polynomial systems are ubiquitous in Mathematics, Sciences and Engineerings, and Groebner basis theory is one of the most powerful tools for solving polynomial systems from practice. Buchberger (1965) gave the first algorithm for computing Groebner bases and introduced some simple criterions for detecting useless S-pairs. Faugere (2002) presented the F5 algorithm which is significantly much faster than Buchberger's algorithm and can detect all useless S-pairs for regular sequences of homogeneous polynomials. In recent years, there has been extensive effort trying to simply F5 and to give a rigorous mathematical foundation for F5. In this talk, we present a simple criterion for strong Groebner bases that contain Groebner bases for both ideals and the related syzygy modules. This criterion can detect all useless J-pairs (without performing any reduction) for any sequence of polynomials, thus yielding an efficient algorithm for computing Groebner bases and a simple proof of finite termination of the algorithm. This is a joint work with Frank Volny IV (National Security Agency) and Mingsheng Wang (Chinese Academy of Sciences).
Short Bio：
Shuhong Gao received his BS (1983) and MS (1986) from Department of Mathematics, Sichuan University, China, and PhD degree (1993) from Department of Combinatorics and Optimization, University of Waterloo, Canada. From 1993 to 1995, he was an NSERC Postdoctoral Fellow in Department of Computer Science, University of Toronto, Canada. He joined Clemson University, USA, in 1995 as an assistant professor in Mathematical Sciences, and was promoted to associate professor in 2000 and to full professor in 2002. Professor Gao has published over 60 papers in the areas of combinatorial design theory, finite fields, coding theory, cryptography, symbolic computation, and computational algebraic geometry. His research has been supported by grants from NSA, NSF and ONR. More information about his research and teaching can be found at //www.math.clemson.edu/~sgao.
报告第29讲：
报 告 人：胡磊（中国科学院信息工程研究所）
报告题目：密码学中的随机数发生器及其攻击
报告时间：2014年6月11日上午10:10－11:55
报告地点：理学院北楼311报告厅
报告人简介：教授，博士生导师。1988年毕业于北京大学数学系，获学士学位，1991年毕业于北京大学数学系，获硕士学位，1994年毕业于中国科学院系统科学研究所，获博士学位。2001年入选中国科学院“百人计划”。先后主持了国家自然科学基金项目、国家863计划项目和国家密码发展基金项目共7个，在国内外权威期刊和国际学术会议上发表论文40余篇。早期参加的信息安全技术应用获得两项技术转让，2000年完成的“组合函数与组合网络的密码学特性及其构造”项目获得2002年国家密码科技进步奖（省、部级）二等奖。主要研究兴趣为：多变量公钥密码、代数密码分析、椭圆曲线公钥密码与基于双线性映射的密码学、伪随机序列设计、密码函数、理论密码学、密码学在网络安全中的应用。主要研究方向为：理论密码学（可证安全密码学）、密码序列、椭圆曲线公钥密码、密码函数、快速软件密码算法设计、密码学相关组合理论、密码学在网络等新型网络安全中的应用。2001年以后，主持5个国家自然科学基金项目、国家863项目和国家密码发展基金项目。在国内外权威刊物上发表论文30余篇，获2002年国家密码科技进步奖励（省、部级）二等奖。
欢迎各位老师和学生参加！