## Section: Other Grants and Activities

### National Initiatives

#### ANR GECKO Project

Keywords : geometry, algorithm analysis, polynomial matrix, integer matrix.

Participant : G. Villard.

The GECKO project (
*Geometrical Approach to Complexity and Applications* , end of 2005-2008) is funded by ANR and headed by B. Salvy (ALGO project, Inria Rocquencourt). Other teams participating are at the École polytechnique, Université de Nice Sophia-Antipolis, and Université Paul Sabatier in
Toulouse. The project is at the meeting point of numerical analysis, effective methods in algebra, symbolic computation and complexity theory. The aim is to improve significantly solution methods for algebraic or linear differential equations by taking geometry into account.

In Lyon we will concentrate on polynomial and matrix problems (with integer or polynomial entries) including some particular classes of structured matrices.

#### Ministry Grant ACI ``Cryptology''

Keywords : hardware operator for cryptography, encryption, FPGA.

Participants : J.-L. Beuchat, A. Tisserand, G. Villard.

The OPAC project (
*OPérateurs Arithmétiques pour la Cryptographie* , 2002-2005), is a collaboration with the team
*Arithmétique Informatique* of the Lirmm laboratory and the GTA team at Université de Montpellier (see
http://www.lirmm.fr/~bajard/ACI_CRYPTO ). The goal is the development of
hardware operators for cryptographic applications on FPGAs. The project focuses in particular on problems related to finite fields and elliptic curves.

#### Ministry Grant ACI ``Security in Computer Science''

Keywords : digital signature, arithmetic operator, FPGA.

Participants : J.-L. Beuchat, A. Tisserand, G. Villard.

The Ministry Grant ACI ``Security in Computer Science'' funds the OCAM project (
*Opérateurs Cryptographiques et Arithmétique Matérielle* , 2003-2006) in collaboration with the Codes team (Inria Rocquencourt) and the team
*Arithmétique Informatique* of the Lirmm laboratory at Montpellier (see
http://www-rocq.inria.fr/codes/OCAM ). The goal of OCAM is the development of
hardware operators for cryptographic applications based on the algebraic theory of codes. The FPGA implementation of a new digital signature algorithm is used as a first target application (see §
6.1 ).

#### Ministry Grant ACI ``New Interfaces of Mathematics''

Keywords : polynomial approximation, minimax approximation, floating-point arithmetic, polytope, linear programming.

Participants : N. Brisebarre, J.-M. Muller, A. Tisserand, S. Torres.

The GAAP project (
*étude et outils pour la Génération Automatique d'Approximants Polynomiaux efficaces en machine* , 2004-2007) is a collaboration with the LArAl laboratory of Université de Saint-Étienne. The goal is the development of a C library MEPLib aimed at obtaining very good polynomial
approximants under various constraints on the size in bits and the values of the coefficients. The target applications are software and hardware implementations, such as embedded systems for instance.

#### Working group on ``Set Methods for Control Theory'', CNRS GDR MACS

Keywords : set computing, control theory.

Participant : N. Revol.

This working group focuses on the topic of set computing with applications to control theory. The goal of this group is to stimulate exchanges between researchers in computer science and researchers in control theory. It is part of the CNRS GDR MACS (Modélisation, Analyse et Conduite des Systèmes dynamiques). It was headed by S. Lesecq (Lag, INPG Grenoble) and N. Revol.

#### ``Adaptive and Hybrid Algorithms'', Imag-Inria project

Keywords : adaptive algorithm, reliable computation, optimization.

Participants : N. Revol, G. Villard.

The AHA project (
*Adaptive and Hybrid Algorithms* , March 2005-2007) is headed by J.-L. Roch (Laboratoire ID-Imag), and supported by Imag Grenoble and Inria. Our motivation is the conception of algorithms that may adapt themselves automatically to the execution context. Arénaire is involved for building
reliable algorithms (e.g. adaptive precision, general algorithms versus algorithms specific to interval arithmetic, ...). Other partners of the project will focus on parallel developments for problems in optimization and vision. Using the AHA approach our objective is to improve the
performance of softwares such as LinBox (§
5.6 ) and Roxane (§
8.1 ).

#### Roxane Initiative

Keywords : open-software, algebraic computation, numerical computation, efficiency, reliability.

Participants : N. Revol, G. Villard.

Roxane stands for
*Reliable Open Software-Components for Algebraic and Numeric Efficiency* . The goal of this project is to mutualize the efforts of implementation that are done in different research teams. Roxane integrates, in a homogeneous environment, tools to build dedicated and efficient components
for solving real problems, mainly in computer algebra. The promotion of Roxane is done via
http://www-sop.inria.fr/galaad/logiciels/roxane , and schools,
software distribution CDs, etc.