基于整数的全同态加密体制的研究

DGHV体制是在对Gentry的基于理想格的全同态加密体制进行简化的基础上提出的,但该体制仅能对单比特的明文的加解密,并且效率不够高。2013年,Jean—Sebastien等人对DGHV体制进行了改进,完成了对明文序列的加解密。本文以改进的DGHV算法为基础,分析了改进DGHV算法的思路和方法,并对相应的压缩算法和自举算法进行了分析,给出了正确性证明和安全性证明,最后指出了改进的DGHV算法的主要优势。     

Gaussian sum approximation for non-linear fixed-point prediction

Fixed-point prediction is the estimation of the state of a system at a future fixed time based on a noisy measurement with sequence length that increases with current time. A recursive algorithm for generating fixed-point prediction is given using the integrated form of the chain rule. For non-linear systems no general filter solution exists ; thus a gaussian sum approximation is developed. The method provides a numerical approximation for the time-dependant a posteriori density from which a filter can be generated.     

Barbalat引理及其在系统稳定性分析中的应用

概述了Barbalat引理最常见的几种基本形式及其变形形式，研究了该引理各种形式之间的相互关系，并给出了各自的适用范围．通过3个例子讨论了Barbalat引理在分析系统的渐近收敛性、自适应控制设计和Lp稳定中的应用．     

Sharp lower bounds on the extractable randomness from non-uniform sources

Extraction of uniform randomness from (noisy) non-uniform sources is an important primitive in many security applications, e.g. (pseudo-)random number generators, privacy-preserving biometrics, and key storage based on Physical Unclonable Functions. Generic extraction methods exist, using universal hash functions. There is a trade-off between the length of the extracted bit string and the uniformity of the string. In the literature there are proven lower bounds on this length as a function of the desired uniformity. The best known bound involves a quantity known as smooth min-entropy. Unfortunately, there exist at least three definitions of smooth entropy. In this paper we compare three of these definitions, and we derive improved lower bounds on the extractable randomness.We also investigate the use of almost universal hash functions, which are slightly worse at extracting randomness than universal hash functions, but are preferable in practice because they require far less resources in devices. We show that using them has negligible effect on the extractable randomness.     

Decidability of the termination problem for completely specified protocols

Summary In this paper, we present a new class of protocols called completely specified protocols. Each protocol is represented as a system of Communicating Finite State Machines. The class of completely specified protocols is such that each message that can be received by a Finite State Machine, can also be received in every local state of the Finite State Machine. These protocols are important because they allow for modelling unbounded fifo channels and make it possible to decide the Termination Problem, that is whether the reachability tree is finite or not. An example of our techniques is given using a practical problem concerning link protocols. Alain Finkel is a Professor of Computer Science at the Ecole Normale Supérieure of Cachan. His research is concerned with the models of concurrency and the practical possibilities to verify and to validate distributed systems. He is also interested by the cognitive interfaces.     

线性程序的Ranking函数自动合成

针对判定一个程序终止性的经典方法Ranking函数法,运用半代数系统的概念,把程序终止性问题转换为求半代数系统的Ranking函数.然后运用符号计算工具DISCOV-ERER和Farkas引理,求出函数参数存在的充分必要条件,并根据符号计算理论的方法自动合成Ranking函数.通过计算代数理论的证明和试验的验证,并与其他方法做了比较,这种方法是高效合理的.     

An Even Closer Integration of Linear Arithmetic into Inductive Theorem Proving

To broaden the scope of decision procedures for linear arithmetic, they have to be integrated into theorem provers. Successful approaches e.g. in NQTHM or ACL2 suggest a close integration scheme which augments the decision procedures with lemmas about user-defined operators. We propose an even closer integration providing feedback about the state of the decision procedure in terms of entailed formulas for three reasons: First, to provide detailed proof objects for proof checking and archiving. Second, to analyze and improve the interaction between the decision procedure and the theorem prover. Third, to investigate whether the communication of the state of a failed proof attempt to the human user with the comprehensible standard GUI mechanisms of the theorem prover can enhance the speculation of auxiliary lemmas.     

基于用户兴趣的元搜索结果合成算法研究

元搜索引擎将为用户提供更全面的搜索结果信息,但在庞大的搜索结果中快速找到自己感兴趣的结果并非易事.针对查询结果合成问题,提出了一种基于用户兴趣的结果合成方法,在摘要法计算用户查询与查询结果相关度的基础上引入了词条等级和用户兴趣,实现了元搜索引擎的个性化.通过程序实现此算法,分别与单个搜索引擎以及其他几种结果合成算法比较,证明此算法保证了搜索结果的查全率,又提高了查准率,大大改善了用户检索效果和效率.     

Optimal control of switching systems

This paper considers an optimal control problem for a switching system. For solving this problem we do not make any assumptions about the number of switches nor about the mode sequence, they are determined by the solution of the problem. The switching system is embedded into a larger family of systems and the optimization problem is formulated for the latter. It is shown that the set of trajectories of the switching system is dense in the set of trajectories of the embedded system. The relationship between the two sets of trajectories (1) motivates the shift of focus from the original problem to the more general one and (2) underlies the engineering relevance of the study of the second problem. Sufficient and necessary conditions for optimality are formulated for the second optimization problem. If they exist, bang-bang-type solutions of the embedded optimal control problem are solutions of the original problem. Otherwise, suboptimal solutions are obtained via the Chattering Lemma.     

控制理论中的频率定理:Kalman-Yakubovich引理

介绍了Kalman-Yakubovich引理，重点强调了引理中的频域条件与状态空间条件之间的等价关系，基于这种等价关系，可以直接求得当前控制理论中的几个重要定理，正实引理，有界实引理和Popov判据，还给出了代数Riccati方程有解的频率判据。由于当前LMI法的进展，所以这种等价关系已是频率定理的主要特色，对上述重要定理的推导可以作为频率定理推广应用于其他设计问题时的范例。