Seminars 2009

The fence method is a recently developed strategy for model selection. The idea is to construct a statistical fence to isolate a subgroup of what are called correct models. Once the fence is constructed, the optimal model is selected from those within the fence according to a criterion which can incorporate quantities of practical interest. One advantage of the fence is its flexibility in choosing the measure of lack of fit to address problem of practical interest. In this talk, we show how to derive predictive measures of lack-of-fit to address the main interest in small area estimation, which is estimation of small area means. Simulation results show that the predictive measure makes a significant difference compared with the information criteria and non-predictive fence in situations where a true model does not exist among the candidate models.

This is joint work with Thuan Nguyen of Oregon Health and Science University, and Sunil Rao of Case Western Reserve University.

By using of critical point theory, we deal with a kind nonlinear eigenvalue problem :

$$\left\{\begin{array}{l} -\triangle u-\lambda u= f(x,u)\ \ x\in\Omega\subset \mathbb{R}^N, \\u=0 \ q\hbox{on}\ \partial\Omega \\\int_\Omega|\nabla u|^2-\lambda\int u^2=\alpha \end{array}\right.$$ and obtain some multiple and sign-changing solutions.

A black-box secret sharing scheme (BBSSS) for a given access structure works in exactly the same way over any finite Abelian group, as it only requires black-box access to group operations and to random group elements. In particular, there is no dependence on e.g. the structure of the group or its order. The expansion factor of a BBSSS is the length

 

of a vector of shares (the number of group elements in it) divided by the number of players n. At CRYPTO 2002 Cramer and Fehr proposed a threshold BBSSS with an asymptotically minimal expansion factor THETA(log n). This dramatically improved the previous solution by Desmedt and Frankel from the late 1980s, which had expansion THETA(n). At CRYPTO 2005, Cramer, Fehr and Stam further improved the results, achieving an expansion factor that is absolutely minimal up to an additive term of at most 2, which is an improvement by a constant additive factor. All these results rely on orders in number fields that admit a large enough finite subsets of elements with appropriate number theoretical properties. In this talk we survey these and some related results.

Halevi and Krawczyk proposed a message randomization algorithm called RMX as a front-end tool to the hash-then-sign digital signature schemes such as DSS and RSA in order to free their reliance on the collision resistance property of the hash functions. They have shown that to forge a RMX-hash-then-sign signature scheme, one has to solve a cryptanalytical task which is related to finding second preimages for the hash function. In this article, we will show how to use Dean’s method of finding expandable messages for finding a second preimage in the Merkle-Damgard hash function to existentially forge a signature scheme based on a t-bit RMX-hash function which uses the Davies-Meyer compression functions (e.g., MD4, MD5, SHA family) in $2^{t/2}$ chosen messages plus $2^{t/2+1}$ off-line operations of the compression function and similar amount of memory. This forgery attack also works on the signature schemes that use Davies-Meyer schemes and a variant of RMX published by NIST in its Draft Special Publication (SP) 800-106. We discuss some important applications of our attack.

(Paper will appear in Eurocrypt2009)

A widely shared view is that ubiquitous computing is the next paradigm in information technology. It ?ts that currently 98.8% of all manufactured microprocessors are employed in embedded applications and only 0.2% in traditional computers. The mass deployment of pervasive devices promises many bene?ts such as lower logistic costs, higher process granularity, optimized supply-chains, or location based services among others. On the other hand, many foreseen applications are security sensitive, such as wireless sensor networks for military, ?nancial or automotive applications. Furthermore privacy issues will arise in many pervasive applications. An aggravating factor is that pervasive devices are usually not deployed in a controlled but rather in a hostile environment, i.e. an adversary has physical access to or control over the devices. This adds the whole ?eld of physical attacks to the potential attack scenarios.

Pervasiveness implies mass deployment which in turn implies harsh cost constraints on the used technology. For ASICs (application specific integrated circuits) this means in particular that power, energy, and area requirements (in terms of Gate equivalents, GE) must be kept to a minimum. We will also show that Moore's Law will not relax these constraints but further increase the demand for lightweight solutions.

This talk gives an overview of lightweight cryptography. It covers lightweight block ciphers and lightweight hashing. We start with the design of DESL, a slightly modified lightweight variant of the Data Encryption Standard (DES). Then we look at PRESENT, which is the most compact block cipher for hardware implementations. Subsequently we use PRESENT as the basic building block for lightweight hash functions. Finally this talk is concluded and pointer for open research problems are provided.

Recently, vortex dynamics of Bose-Einstein condensates (BEC) are one of most interesting subjects in Physics. At extremely low temperature, Bose-Einstein condensates can be modelled by the famous Gross-Pitavskii equation(GPE) or coupled Gross-Pitavskii

 equations (GPEs).  We propose a new time-splitting spectral method for the GPE (or GPEs) and study the vortex dynamics of rotating one-component BEC, rotating two-component BEC and spin-1 BEC at a very low temperature. This new numerical method is explicit, unconditionally stable, time reversible, time transverse invariant, and of spectral accuracy in space and second-order accuracy in time. Moreover, it conserves the position density in the discretized level. How to design such a method, detailed numerical study on the efficiency of the method and application of the method to study vortex dynamics will be presented.

This talk will be on two distinct projects I am currently working on. In the first part, we describe an algorithm to compute the "mountain pass" between two given points: a connecting path along which the maximum value is minimized. We describe an algorithm that maintains lower bounds on the optimal value by keeping the two points in separate level set components. This algorithm converges, even in the nonsmooth case, and converges superlinearly locally in the smooth finite-dimensional case. Applications include computational chemistry and partial differential equations.

In the second part (independent of the first part), I will illustrate how recent methods in set-valued and variational analysis of semi-algebraic functions are helping us further our understanding in practical nonsmooth problems in optimization and control. We then present a new result on the structured discontinuity of semi-algebraic set-valued maps and its applications.

The hash function used in cryptography compresses an arbitrary message to a message digest with fixed length. A secure hash function ensures that it is computational infeasible to find two different messages with the same message digest. In this seminar, we give an introduction to hash function design, then we introduce the new hash function JH.

JH uses a new and extremely simple hash structure. With such structure, a hash function can be easily constructed from a bijective function.  The bijective function in JH combines the best features of AES and Serpent, which are the top two block ciphers in the NIST AES competition. For the bijective function used in JH, the substitution- permutation network (SPN) is used to achieve diffusion and confusion.
Two 4-bit-to-4-bit Sboxes are used for confusion, and each round constant bit selects which Sbox is used. A simple Maximum Distance Separable (MDS) code is applied to an eight-dimensional 1024-bit array to achieve efficient diffusion (in the i-th round, the MDS code is applied along the (i mod 8)-th dimension).  Note that AES applies an MDS code to a two-dimensional 128-bit array.  The bijective function in JH can be efficiently implemented in software with the bit-slice approach which is the best feature of Serpent.

JH is strong in security. The simple structure and components of JH allows its security being analyzed easily. The 35.5-round compression function involves 9216 Sboxes, and a differential path involves more than 600 active Sboxes. The large number of active Sboxes ensures that JH is strong against differential attack. JH is efficient on many platforms ranging from hardware to software. The simple components and identical round functions (except for different round constants) allows efficient hardware implementation. The bit-slice implementation of JH gives efficient software performance. The hash speed of JH is about 16.8 cycles/byte on the Core 2 microprocessor running 64-bit operating system, and about 21.3 cycles/byte on the Core 2 microprocessor running 32-bit operating system.

We focus on deblurring and denoising problems. 

For a given blur, we apply a fixed point method to solve the total variation-based image restoration problem.  A new algorithm for the discretized system is presented. Convergence of outer iteration is efficiently improved by adding a linear term on both sides of the system of nonlinear equations. In inner iteration, an algebraic multigrid (AMG) method is applied to solve the linearized systems of equations. We adopt the Krylov subspace method to accelerate the outer nonlinear iteration.  
 

For the blur is unknown, we combine our algorithm for a given blur operator with an alternating minimization implicit iterative scheme to deal with blind deconvolution problem, recover the image and identify the point spread function(PSF). The only assumption needed is to satisfy the practical physical sense.  

This is a joint work with Professor Qianshun Chang and Weicheng Wang.