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[2018.6.1-8.31] 数学与系统科学青年精英学术活动季
举办时间:2018年6月-8月    地点:北京

为增进国内外优秀青年科研人才与系统科学研究所的相互了解与学术合作,系统科学研究所将于2018年6—8月举办为期一个季度的“数学与系统科学青年精英学术活动季”。活动期间,将邀请20位左右近年获得博士学位的系统科学相关领域优秀青年学者来访,并作短课程和学术报告。以下是短课程、学术报告和报告人的相关信息:

 

[六月]

Tao Huang(黄涛),(Nanyang Technological University, Singapore)

6月6日上午10:00-11:00

A Survey on the CAESAR Finalist

【Abstract】In this talk, I will do a survey on the authenticated encryption schemes in the finalist of the CAESAR competition, which are ACORN, Ascon, AEGIS, MORUS, OCB, COLM and Deoxys-II. The seven authenticated encryption schemes are divided into three categories according to their use cases: for lightweight applications, for high performance applications and for defense in depth. For each design, the latest specification, the design method and the features will be discussed. The software and hardware performance data will also be discussed for each use case.

6月7日上午11:00-12:00

Boomerany Connectivity Table: A New Cryptanalysis Tools

【Abstract】A boomerang attack is a cryptanalysis framework that regards a block cipher E as the composition of two sub-ciphers E_1 and E_0 and builds a particular characteristic for E with probability p^2q^2 by combining differential characteristics for E_0 and E_1 with probability p and q, respectively. Crucially the validity of this figure is under the assumption that the characteristics for E_0 and E_1 can be chosen independently. Indeed, Murphy has shown that independently chosen characteristics may turn out to be incompatible. On the other hand, several researchers observed that the probability can be improved to p or q around the boundary between E_0 and E_1 by considering a positive dependency of the two characteristics, e.g. the ladder switch and S-box switch by Biryukov and Khovratovich. This phenomenon was later formalised by Dunkelman et al. as a sandwich attack that regards E as E_1\circ E_m \circ E_0, where E_m satisfies some differential propagation among four texts with probability r, and the entire probability is p^2q^2r.

We revisit the issue of dependency of two characteristics in E_m, and propose a new tool called Boomerang Connectivity Table (BCT), which evaluates r in a systematic and easy-to-understand way when E_m is composed of a single S-box layer. With the BCT, previous observations on the S-box including the incompatibility, the ladder switch and the S-box switch are represented in a unified manner. Moreover, the BCT can detect a new switching effect, which shows that the probability around the boundary may be even higher than p or q. To illustrate the power of the BCT-based analysis, we improve boomerang attacks against Deoxys-BC, and disclose the mechanism behind an unsolved probability amplification for generating a quartet in SKINNY. Lastly, we discuss the issue of searching for S-boxes having good BCT and extending the analysis to modular addition.

 

Bohua Zhan(詹博华),(Technical University of Munich, Germany)

6月28日15:15-16:15,  6月29日15:15-16:15

Introduction to Interactive Theorem Proving

【Abstract】Interactive theorem proving studies the construction of formal proofs on the computer with human guidance. It can be applied to formally verify results in both mathematics and computer science. Formalizations in mathematics can serve one of several purposes: verify potentially controversial results in mathematical research, support verification of computer programs and systems, and as an aid to teaching proofs in mathematics.

In this series of two talks, I will give an introduction to the field of interactive theorem proving, with a focus on formalizations in mathematics. The talks will be self-contained, and no background in logic is assumed.

In the first talk, I will begin by reviewing the basic concepts of the field, then describe some major recent results in formalization of mathematics. In the second talk, I will discuss the important concept of proof automation, and my own work in this area. Finally, I will suggest some ideas for future work.

 

Xianchang Meng(孟宪昌),(Centre de Recherches Mathématiques in Montréal, Canada)

6月26日14:00-15:00, 6月27日9:30-10:30, 6月28日14:00-15:00

The Distribution of Certain Restricted Numbers

【Abstract】Chebyshev noticed that there seems to be more number of primes congruent to 3 mod 4 than those congruent to 1 mod 4. Questions related to the distribution of prime numbers among different arithmetic progressions are known as ``Prime Race Problems". I will introduce some generalizations of the prime number races: 1) the distribution of products of k primes in different arithmetic progressions; the results are different if we count the number of prime factors with multiplicity or not; 2) a generalization of a very recent result of Dummit, Granville, and Kisilevsky who studied the distribution of products of two primes pq with p, q both from the residue class 3 mod 4; 3) Function field version of prime number races. Probabilistic method is a very useful tool to study prime number races. If time permits, I may mention how to improve the error term in the counting function of k-free numbers using probabilistic method under some reasonable conjectures.

 

Liangjie Ye(叶亮节),(RISC, Johannes Kepler University, Austria)

时间:6月26日15:15-16:15, 6月27日10:45-11:45, 6月29日14:00-15:00

Computer Algebra Algorithms for Proving Jacobi Theta Function Relations

【Abstract】This talk will be focused on proving Jacobi theta function identities. In the past centuries, many number theorists, e.g., Ramanujan, Hardy, Rademacher, Berndt, Borwein, etc., have proved a substantial amount of theta function relations by hand. There was no general method for proving such relations, and the computation in their proofs are usually tedious. Thanks to symbolic computation, now we have developed some computer algebra algorithms to prove and produce rich classes of such identities automatically. In this talk, I will present a nutshell of our research on this topic. I will also demonstrate a Mathematica package called ``ThetaFunctions" equipped with our algorithms.

 

七月
 
八月
 

 

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