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INRIA, Evaluation of Theme Sym B INRIA, Evaluation of Theme Sym B Project-team SPACES∗ November 2006 Project-team title : Solving Problems Through Algebraic Computation and Efficient Soft- ware Scientific leaders : Daniel Lazard (until May 2004), Paul Zimmermann Research centers : INRIA Lorraine/LORIA and INRIA Rocquencourt/LIP6 (until May 2004) Common project-team with : CNRS, University Pierre et Marie Curie (Paris 6) until May 2004, University Henri Poincar´e Nancy 1, University Nancy 2, Institut National Polytechnique de Lorraine 1 Personnel Personnel (March 2002) Misc. INRIA CNRS University Total DR (1) / Professors 1 1 2 CR (2) / Assistant Professors 3 2 2 7 Permanent Engineers (3) Temporary Engineers (4) PhD Students 6 1 7 Post-Doc. 1 1 Total 6 5 2 4 17 External Collaborators 2 2 Visitors (> 1 month) (1) \Senior Research Scientist (Directeur de Recherche)" (2) \Junior Research Scientist (Charg´e de Recherche)" (3) \Civil servant (CNRS, INRIA, ...)" (4) \Associated with a contract (Ing´enieur Expert or Ing´enieur Associ´e)" ∗ Version 1.0, October 2, 2006 1 Personnel (November 2006) Misc. INRIA CNRS University Total DR / Professors 1 1 CR / Assistant Professor 2 1 1 4 Permanent Engineer Temporary Engineer PhD Students 1 1 Post-Doc. 1 1 Total 1 3 1 2 7 External Collaborators 1 1 Visitors (> 1 month) 1 1 Note: two new PhD students should join the group soon, namely Alexander Kruppa, who will work on the Number Field Sieve in the context of the ANR CADO project, and Damien Robert, who will work on extending the SEA (Schoof, Elkies, Atkin) algorithm to curves of genus 2. Changes in staff DR / Professors Misc. INRIA CNRS University total CR / Assistant Professors Arrival 1 1 1 3 Leaving 1 1 Comments : the SPACES project-team was created on 1st June 2002 (decision 3649 from August 27, • 2002) at INRIA Lorraine; from June 2003 (decision 3876 from June 19, 2003) until end of May 2004 (decision • 4335 from October 19, 2004), the project-team was extended on two sites: people at LORIA in Nancy, depending from INRIA Lorraine, and people at LIP6 in Paris, depending from INRIA Rocquencourt. The decision 4335 stopped the SPACES-Paris project-team, whose members created the SALSA team (decision 4814 from January 27, 2006). after the members of the SALSA team left, and the arrival of Pierrick Gaudry, the • members of SPACES-Nancy decided to redesign the scientific objectives, which led to the proposition of a new project-team called CACAO, with head Guillaume Hanrot. The CACAO proposal was first presented at the INRIA Lorraine \comit´e des projets" in December 2004. The reports from the 3 experts (Marc Girault, Dan Zuras, Bart Preneel) arrived in June 2006. The CACAO project-team is expected to be created before the end of 2006 (i.e. two years after the first proposal); the above \Changes in staff" table only takes into account the members of the Spaces • project on the Nancy site, i.e. it does not take into account the members on the Paris site who left the Spaces project to create the SALSA project in May 2004; 2 Pierrick Gaudry (\Charg´e de Recherche" CNRS) joined the project in September • 2005, coming from the TANC project-team. Marion Videau was recruited as Assistant Professor at University Henri Poincar´e • Nancy 1 in September 2006. Current composition of the project-team (November 2006): Paul Zimmermann (project head), Directeur de Recherche, INRIA; • Guillaume Hanrot (project vice-head, head of the future CACAO project-team), Charg´e • de Recherche, INRIA; Pierrick Gaudry, Charg´e de Recherche, CNRS; • Emmanuel Thom´e, Charg´e de Recherche, INRIA; • Marion Videau, Assistant Professor, University Henri Poincar´e Nancy 1; • Nuno Franco, post-doctoral position (6 months per year), • Laurent Fousse, PhD student and \moniteur", University Henri Poincar´e Nancy 1. • Current position of former project-team members (including PhD students during the 2002-2006 period): the members of SPACES-Paris are now members of the SALSA project team; • Patrick P´elissier worked as \Temporary Engineer" in the project-team from Septem- • ber 2003 to August 2005; he is now working for SopraGroup (Colomiers, near Toulouse), a SSII working for Airbus; Vincent Lef`evre (CR INRIA) left the project-team to join the Arenaire project in • September 2006; Bill Allombert was a postdoctoral fellow from September 2002 to August 2003; he is • currently ATER at the University of Montpellier 2; Nicolas Gurel¨ defended his PhD on December 15, 2003; he has recently be hired by • the French ministry of Defence; Jean-Paul Cerri defended his PhD on November 18th, 2005; he is currently \professeur • agr´eg´e" at IUFM d'Epinal;´ Damien Stehl´e defended his PhD on December 2nd, 2005. After a postdoctoral visit • in the Magma Group (Sydney, Australia), he was recruited as \Charg´e de Recherche" CNRS in the Ar´enaire project-team. Last INRIA enlistments Emmanuel Thom´e was recruited as \Charg´e de Recherche" (CR2) at INRIA in Oc- • tober 2003; 3 Other comments : 2 Work progress 2.1 Keywords Cryptology, public-key cryptosystem, Jacobian of algebraic curve, discrete logarithm, fi- nite field, function field sieve, integer factorization, reliable computation, integer arithmetic, floating-point number, complex floating-point number, arbitrary precision, correct rounding, IEEE 754, elementary function, transcendental function, mathematical library, worst case, lattice reduction, 2.2 Context and overall goal of the project The research program of the project-team can be summarized as follows: arithmetics algorithms applications. () () This motto was developed mainly along the arithmetics axis during the evaluation period (2002-2006), and also started to be developed along the algebraic curves and linear algebra and lattices axes. All three axes will be further developed in the next period (2006-2010) [see below]. The main idea of the above motto is the following: to help solving a particular applications, or improving the corresponding efficiency, one needs to develop efficient algorithms. In turn, these algorithms need efficient basic-level operations (arithmetics), and the corresponding implementations. 2.3 Objectives for the evaluation period The original objectives of the Spaces project-team, as presented in October 2000, were (trans- lated from french to english): algebraic solutions: \the goal of this project-team is to make significant progress in • theory and practice on the problem of solving algebraic systems with parameters. [. ]"; real solutions: \Our principal goal to short and medium term is to provide efficient • algorithms to compute at least one point per connected component of a real algebraic variety. [. ]"; arithmetics: \Our goals include of course, as the reader surely understood it, the study • (from the design to the efficient implementation) of algorithms for various arithmetics, either exact or approximated, see a non exhaustive list in section 2.1. [. ] with the hir- ing of Vincent Lef`evre, we aim, in collaboration with the Ar´enaire project-team (INRIA Rh^one-Alpes and ENS Lyon) to efficiently compute the worst cases of elementary func- tions. [. ] recent work from Noam Elkies presented at the ANTS IV conference tend to prove that LLL-based methods should allow approximations of degree 2 or more. [. ] After this study on worst cases of elementary functions, one could imagine | still in collaboration with the Ar´enaire project-team | to design a Newlibm.a library guaranteeing correct rounding of elementary functions (exp; log; sin; cos; : : :)"; 4 hybrid methods: \Our main goal is to continue the effort started several years ago • to design hybrid algorithms with a better efficiency, both theoretically and practically. This concerns both arithmetics themselves (see next section) and their use to solve polynomial systems. [. ]". These objectives have of course evolved with the departure of the members of the new SALSA project-team in June 2004: the SPACES-Nancy team focused on the arithmetics axis, and its applications through • the hybrid methods axis; with the arrival of Emmanuel Thom´e and Pierrick Gaudry, the arithmetics axis was • strengthened on finite fields, and a new axis on algebraic curves was started. The departure of the members of the SALSA project-team stopped of course the on- going collaboration between SPACES-Paris (polynomial systems) and SPACES-Nancy (arith- metics). On the other hand, the departure of the members of the SALSA project-team was a good opportunity to redesign sharper research objectives. This was accomplished in the CACAO research proposal, which has three main axes: algebraic curves over finite fields (elliptic curves, hyperelliptic curves, superelliptic • curves, . ), the corresponding problems (point counting, efficient arithmetic, discrete logarithm), and their application to public-key cryptography; linear algebra and lattices. Here we mean linear algebra problems for huge sparse • matrices over finite fields, as encountered in integer factorization (Number Field Sieve) or discrete logarithm. Lattices are meant in the sense of integer lattices, for which we study efficient reduction algorithms, and their applications; arithmetics: integer arithmetic, finite field arithmetic, floating-point arithmetic, both • in small precision (typically one computer word) and arbitrary precision. The goal here is to design and implement efficient algorithms, that will be useful for the two other research axes. 2.4 Objective Arithmetics: Executive summary 2.4.1 Personnel Laurent Fousse (PhD student), Torbj¨orn Granlund (external collaborator), Guillaume Han- rot, Vincent Lef`evre, Patrick P´elissier (engineer), Damien Stehl´e (PhD student), Paul Zim- mermann. 2.4.2 Project-team positioning The project-team focuses on the two following topics: 5 worst case search: the aim is to develop fast algorithms to search for worst cases of • mathematical functions in the IEEE 754 formats, mainly the double-precision format (53-bit mantissa). This work is done in collaboration with the Arenaire project-team, which is using those worst cases for the design of the crlibm library for correct rounding of elementary functions.
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