POLSYS - 2012 - Annual activity report

POLSYS

POLSYS - 2012

Project-Team Polsys

Members

Overall Objectives

Introduction
Highlights of the Year

Scientific Foundations

Introduction
Fundamental Algorithms and Structured Systems
Solving Systems over the Reals and Applications.
Low level implementation and Dedicated Algebraic Computation and Linear Algebra.
Solving Systems in Finite Fields, Applications in Cryptology and Algebraic Number Theory.

Application Domains

Cryptology
Engineering sciences

Software

FGb
RAGlib
Epsilon

New Results

The complexity of solving quadratic boolean systems is better than exhaustive search
Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Fields
On the relation between the MXL family of algorithms and Gröbner basis algorithms
On the Complexity of the BKW Algorithm on LWE
On the Complexity of the Arora-Ge algorithm against LWE
On enumeration of polynomial equivalence classes and their application to MPKC
Cryptanalysis of HFE, Multi-HFE and Variants for Odd and Even Characteristic
Solving Polynomial Systems over Finite Fields: Improved Analysis of the Hybrid Approach
Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries
Algebraic Crypanalysis with Side Channels Information
Worst case complexity of the Continued Fraction (CF) algorithm.
Local Generic Position for Root Isolation of Zero-dimensional Triangular Polynomial Systems.
Univariate Real Root Isolation in Multiple Extension Fields
Mixed volume and distance geometry techniques for counting Euclidean embeddings of rigid graphs.
Variant Quantifier Elimination
Global optimization
Gröbner bases and critical points

Bilateral Contracts and Grants with Industry

Oberthur Technologies
Gemalto

Partnerships and Cooperations

National Initiatives
European Initiatives
International Initiatives
International Research Visitors

Dissemination

Scientific Animation
Teaching - Supervision - Juries
Popularization

Bibliography

Publications of the year

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Section: Software

FGb

Participant : Jean-Charles Faugère [contact] .

FGb is a powerful software for computing Groebner bases.It includes the new generation of algorihms for computing Gröbner bases polynomial systems (mainly the F4, F5 and FGLM algorithms). It is implemented in C/C++ (approximately 250000 lines), standalone servers are available on demand. Since 2006, FGb is dynamically linked with Maple software (version 11 and higher) and is part of the official distribution of this software.

See also the web page http://www-polsys.lip6.fr/~jcf/Software/FGb/index.html .

ACM: I.1.2 Algebraic algorithms
Programming language: C/C++

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