Xlim - Research Institute

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Mathematics and Computer Sciences

Research projects :

Numeric Symbolic Computation and Optimization

Computer algebra, Algorithms for functional and differential equations, Curves and algebraic systems, Interactions between symbolic and numeric computations, Semi-algebraic optimization, Numerical optimization, Variational analysis, Shape optimization, Automation, Mechatronics.

Information Protection, Cryptography and Coding

Public key Cryptography

We are involved in the design of new public key cryptosystems.Some of them are based on modular arithmetic and have homomorphic properties which are useful in some applications (databases, electronic voting). Others are based on quadratic fields or error correcting codes.

Filtered registers

Linear Feedback Shift Registers (LFSR) are basic tools widely used in the design of stream ciphers. We study the boolean functions used to extract enciphered data from such registers. Feedback with Carry Shift Registers (FCSR) are similar tools but their non-linear structure can be described using 2-adic integers. We have designed several stream ciphers based on FCSR and we continue to improve them. We study the mathematical properties of FCSR and use them to evaluate the security of these stream ciphers.

Error Correcting Codes

Error correcting are used in all communications to correct the errors introduced by the ambiant noise. We study mathematical properties of error correcting codes in order to find better ones. We are also interrested in the use of error correcting codes in public key ciphers and signature.

Applied Arithmetic

Number Theory provides functions which are difficult to compute andare useful in public key cryptography. We study different structures which can provide such functions : binary quadratic forms, elliptic curves, non-abelian groups, combinatoric and word geometry, p-adic numbers, linear recurring sequences.

Realistic Image Synthesis

The "Realistic Image Synthesis" group's main area of expertise concerns realistic rendering techniques for computer graphics. Real-time rendering, animation and visualization (e.g. scientific visualization) are also investigated.

Synthesis, modelling and illumination of 3D textures

Textures are an important element for realistic rendering. Here, two types of texture generation are studied, both using image-based techniques. Photometric textures (e.g. wood, marble, ...) generation is based on spectral analysis of one or more 2D models; we are also interested in geometric textures (e.g. hypertextures).

Material-based models for illumination, texture generation and ageing simulation

The influence of surface defects (e.g. porosity or scratches) is introduced in local illumination computations (BRDF) in computer graphics. Moreover, a full rendering model for metal corrosion is proposed and physical phenomena such as ageing of building materials due to efflorescence are studied. Taking all these phenomena into account also requires to study the relations between BRDF and textures.

Shape modelling and natural phenomena

In order to obtain realistic shapes and animations, it is often necessary to use physically, botanically or biologically-based models. This research theme includes realistic modelling and animation of "natural" objects such as water, wood, algae or fishes, as well as representing climatic phenomena such as fog and rain. We are especially interested in computing interactions between light and rain, in order to obtain visually plausible images at interactive rates. This study is part of a larger project to develop a numerical platform to visualize real time raining scenes for driving simulation applications.

Beam tracing

Beam tracing replaces the infinitesimal rays used in the conventional ray tracing by volumic rays (beams). Beam tracing can be used efficiently for a general antialising in computer graphics as well as the simulation of electromagnetic and acoustic waves propagation for indoor and outdoor environments.

Smart Secure Device

The objective is to strengthen research in security, complementary to the PICC research team and SeFSI transverse program. We are interested in software aspects of security but also the impact of the disruption of hardware components on the software. Our research project is based on the study and improvement of information systems security but also and tools and methods to evaluate their security. Our scope covers in particular smart card and / or TPM (Trusted Platform Module).

Number Theory

Local algebraic theory
Lubin and Oort conjectures, automorphism group of a field of formal series, Nottingham group, ramification, non abelian class field theory.

Global algebraic theory and K-theory
Galois groups, Galois module structure, K-theory of rings of integers, genus formula for wild kernels, K-theory and Iwasawa theory.

Archimedean analytic theory
Asymptotic study of arithmetic functions, distribution of divisors, friable integers.

Ultrametric analytic theory
Frobenius structure of p-adic differential equations, multiplicative semi-normes, continuous endomorphisms of Hadamard algebras.