Algorithmic number theory dates back to the dawn of mathematics
itself, *cf.* Eratosthenes's sieve to enumerate consecutive prime numbers.
With the
arrival of computers, previously unsolvable problems have come into reach,
which has boosted the development of more or less practical algorithms
for essentially all number theoretic problems. The field is now mature
enough for a more computer science driven approach, taking into account
the theoretical complexities and practical running times of the algorithms.

Concerning the lower level multiprecision arithmetic, folklore has asserted for a long time that asymptotically fast algorithms such as SchÃ¶nhage–Strassen multiplication are impractical; nowadays, however, they are used routinely. On a higher level, symbolic computation provides numerous asymptotically fast algorithms (such as for the simultaneous evaluation of a polynomial in many arguments or linear algebra on sparse matrices), which have only partially been exploited in computational number theory. Moreover, precise complexity analyses do not always exist, nor do sound studies to choose between different algorithms (an exponential algorithm may be preferable to a polynomial one for a large range of inputs); folklore cannot be trusted in a fast moving area such as computer science.

Another problem is the reliability of the computations; many number
theoretic algorithms err with a
small probability, depend on unknown constants or rely on a Riemann
hypothesis. The correctness of their output can either be ensured by a
special design of the algorithm itself (slowing it down) or by an *a
posteriori* verification. Ideally, the algorithm outputs a certificate,
providing an independent *fast* correctness proof. An example is integer
factorisation, where factors are hard to obtain but trivial to
check; primality proofs have initiated sophisticated generalisations.

One of the long term goals of the Lfant project team is to make an inventory of the major number theoretic algorithms, with an emphasis on algebraic number theory and arithmetic geometry, and to carry out complexity analyses. So far, most of these algorithms have been designed and tested over number fields of small degree and scale badly. A complexity analysis should naturally lead to improvements by identifying bottlenecks, systematically redesigning and incorporating modern asymptotically fast methods.

Reliability of the developed algorithms is a second long term goal of our project team. Short of proving the Riemann hypothesis, this could be achieved through the design of specialised, slower algorithms not relying on any unproven assumptions. We would prefer, however, to augment the fastest unproven algorithms with the creation of independently verifiable certificates. Ideally, it should not take longer to check the certificate than to generate it.

All theoretical results are complemented by concrete reference implementations in Pari/Gp, which allow to determine and tune the thresholds where the asymptotic complexity kicks in and help to evaluate practical performances on problem instances provided by the research community. Another important source for algorithmic problems treated by the Lfant project team is modern cryptology. Indeed, the security of all practically relevant public key cryptosystems relies on the difficulty of some number theoretic problem; on the other hand, implementing the systems and finding secure parameters require efficient algorithmic solutions to number theoretic problems.

Modern number theory has been introduced in the second half of the 19th
century by Dedekind, Kummer, Kronecker, Weber and others, motivated by
Fermat's conjecture: There is no non-trivial solution in integers to the
equation

The solution requires to augment the integers by *algebraic
numbers*, that are roots of polynomials in *number
field* consists of the rationals to which have been added finitely
many algebraic numbers together with their sums, differences, products
and quotients. It turns out that actually one generator suffices, and
any number field *algebraic integers*, “numbers without denominators”,
that are roots of a monic polynomial. For instance, *ring of integers* of

Unfortunately, elements in *ideals*, subsets of *principal*, that is,
generated by one element, so that ideals and numbers are essentially
the same. In particular, the unique factorisation of ideals then
implies the unique factorisation of numbers. In general, this is not
the case, and the *class group* *class number*

Using ideals introduces the additional difficulty of having to deal
with *fundamental units*. The *regulator*

One of the main concerns of algorithmic algebraic number theory is to
explicitly compute these invariants (

The *analytic class number formula* links the invariants
*generalised Riemann hypothesis
(GRH)*, which remains unproved even over the rationals, states that
any such

When

Algebraic curves over finite fields are used to build the currently
most competitive public key cryptosystems. Such a curve is given by
a bivariate equation *elliptic curves* of equation
*hyperelliptic curves* of
equation

The cryptosystem is implemented in an associated finite
abelian group, the *Jacobian* *rational function field* with subring *function field* of *coordinate ring*

The size of the Jacobian group, the main security parameter of the
cryptosystem, is given by an *genus*

The security of the cryptosystem requires more precisely that the
*discrete logarithm problem* (DLP) be difficult in the underlying
group; that is, given elements

For any integer *Weil pairing* *Tate-Lichtenbaum pairing*, that is more difficult to define,
but more efficient to implement, has similar properties. From a
constructive point of view, the last few years have seen a wealth of
cryptosystems with attractive novel properties relying on pairings.

For a random curve, the parameter

Complex multiplication provides a link between number fields and
algebraic curves; for a concise introduction in the elliptic curve case,
see Sect. 1.1, for more background material,
. In fact, for most curves *CM field*. The CM field
of an elliptic curve is an imaginary-quadratic field *Hilbert class field*

Algebraically, *Galois* if *Galois group* *abelian* extension is a Galois extension with abelian Galois
group.

Analytically, in the elliptic case *singular value* *modular* function

The same theory can be used to develop algorithms that, given an
arbitrary curve over a finite field, compute its

A generalisation is provided by *ray class fields*; these are
still abelian, but allow for some well-controlled ramification. The tools
for explicitly constructing such class fields are similar to those used
for Hilbert class fields.

Guilhem Castagnos defended his professorial degree (“habilitation à
diriger des recherches”) on the topic of
*Cryptography based on quadratic fields:
cryptanalyses, primitives and protocols*.

Fredrik Johansson won the best paper award at the conference ARITH26 —
26th IEEE Symposium on Computer Arithmetic in Kyoto for his contribution
on dot products and matrix multiplication in arbitrary
precision

*Another Pairing Implementation in PARI*

Keywords: Cryptography - Computational number theory

Scientific Description: Apip , Another Pairing Implementation in PARI, is a library for computing standard and optimised variants of most cryptographic pairings.

The following pairings are available: Weil, Tate, ate and twisted ate, optimised versions (à la Vercauteren–Hess) of ate and twisted ate for selected curve families.

The following methods to compute the Miller part are implemented: standard Miller double-and-add method, standard Miller using a non-adjacent form, Boxall et al. version, Boxall et al. version using a non-adjacent form.

The final exponentiation part can be computed using one of the following variants: naive exponentiation, interleaved method, Avanzi–Mihailescu's method, Kato et al.'s method, Scott et al.'s method.

Part of the library has been included into Pari/Gp proper.

Functional Description: APIP is a library for computing standard and optimised variants of most cryptographic pairings.

Participant: Jérôme Milan

Contact: Andreas Enge

URL: http://

*Abelian Varieties and Isogenies*

Keywords: Computational number theory - Cryptography

Functional Description: AVIsogenies is a Magma package for working with abelian varieties, with a particular emphasis on explicit isogeny computation.

Its prominent feature is the computation of (l,l)-isogenies between Jacobian varieties of genus-two hyperelliptic curves over finite fields of characteristic coprime to l, practical runs have used values of l in the hundreds.

It can also be used to compute endomorphism rings of abelian surfaces, and find complete addition laws on them.

Participants: Damien Robert, Gaëtan Bisson and Romain Cosset

Contact: Damien Robert

Keyword: Arithmetic

Functional Description: The Cm software implements the construction of ring class fields of imaginary quadratic number fields and of elliptic curves with complex multiplication via floating point approximations. It consists of libraries that can be called from within a C program and of executable command line applications.

Release Functional Description: Features - Precisions beyond 300000 bits are now supported by an addition chain of variable length for the -function. Dependencies - The minimal version number of Mpfr has been increased to 3.0.0, that of Mpc to 1.0.0 and that of Pari to 2.7.0.

Participant: Andreas Enge

Contact: Andreas Enge

*Computation of Igusa Class Polynomials*

Keywords: Mathematics - Cryptography - Number theory

Functional Description: Cmh computes Igusa class polynomials, parameterising two-dimensional abelian varieties (or, equivalently, Jacobians of hyperelliptic curves of genus 2) with given complex multiplication.

Participants: Andreas Enge, Emmanuel Thomé and Regis Dupont

Contact: Emmanuel Thomé

Keyword: Number theory

Functional Description: Cubic is a stand-alone program that prints out generating equations for cubic fields of either signature and bounded discriminant. It depends on the Pari library. The algorithm has quasi-linear time complexity in the size of the output.

Participant: Karim Belabas

Contact: Karim Belabas

URL: http://

Keyword: Number theory

Functional Description: Euclid is a program to compute the Euclidean minimum of a number field. It is the practical implementation of the algorithm described in [38] . Some corresponding tables built with the algorithm are also available. Euclid is a stand-alone program depending on the PARI library.

Participants: Jean-Paul Cerri and Pierre Lezowski

Contact: Jean-Paul Cerri

URL: http://

Keywords: Computational geometry - Computational number theory

Functional Description: KleinianGroups is a Magma package that computes fundamental domains of arithmetic Kleinian groups.

Participant: Aurel Page

Contact: Aurel Page

URL: http://

Keyword: Arithmetic

Functional Description: Mpc is a C library for the arithmetic of complex numbers with arbitrarily high precision and correct rounding of the result. It is built upon and follows the same principles as Mpfr. The library is written by Andreas Enge, Philippe Théveny and Paul Zimmermann.

Release Functional Description: Fixed `mpc_pow`, see
http://`#18257`: Switched to libtool 2.4.5.

Participants: Andreas Enge, Mickaël Gastineau, Paul Zimmermann and Philippe Théveny

Contact: Andreas Enge

Keyword: Arithmetic

Functional Description: Mpfrcx is a library for the arithmetic of univariate polynomials over arbitrary precision real (Mpfr ) or complex (Mpc ) numbers, without control on the rounding. For the time being, only the few functions needed to implement the floating point approach to complex multiplication are implemented. On the other hand, these comprise asymptotically fast multiplication routines such as Toom-Cook and the FFT.

Release Functional Description: - new function `product_and_hecke`
- improved memory consumption for unbalanced FFT multiplications

Participant: Andreas Enge

Contact: Andreas Enge

Keyword: Computational number theory

Functional Description: Pari/Gp is a widely used computer algebra system designed for fast computations in number theory (factorisation, algebraic number theory, elliptic curves, modular forms ...), but it also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers, etc., and many transcendental functions.

Participants: Andreas Enge, Hamish Ivey-Law, Henri Cohen and Karim Belabas

Partner: CNRS

Contact: Karim Belabas

Xavier Caruso implemented a new unified framework for dealing with ring extensions and field extensions in SageMath. This code will be integrated soon in the standard distribution.

Fredrik Johansson released a new version, 2.17, of ARB.

ECDSA (Elliptic Curves Digital Signature Algorithm) is a widely
adopted standard for electronic signatures. For instance, it is used in the TLS
(Transport Layer Security) protocol and in many cryptocurrencies such
as Bitcoin. For cryptocurrencies, ECDSA is used in order to sign the
transactions: if Alice wants to give

As a result, if the secret key of Alice is stolen, for example if her computer is compromised, an attacker can stole all her bitcoins. A common solution to this problem is to share the key on multiple devices, for example a laptop and a mobile phone. Both devices must collaborate in order to issue a signature, and if only one device is compromised, no information on the key is leaked. This setting belongs to the area of secure multiparty computation.

There have been recent proposals to construct 2 party variants of ECDSA signatures but constructing efficient protocols proved to be much harder than for other signature schemes. The main reason comes from the fact that the ECDSA signing protocol involves a complex equation compared to other signatures schemes. Lindell recently managed to get an efficient solution using the linearly homomorphic cryptosystem of Paillier. However his solution has some drawbacks, for example the security proof resorts to a non-standard interactive assumption.

By using another approach based on hash proofs systems we obtain a proof that relies on standard assumptions. Moving to concrete constructions, we show how to instantiate our framework using class groups of imaginary quadratic fields. Our implementations show that the practical impact of dropping such interactive assumptions is minimal. Indeed, while for 128-bit security our scheme is marginally slower than Lindell's, for 256-bit security it turns out to be better both in key generation and signing time. Moreover, in terms of communication cost, our implementation significantly reduces both the number of rounds and the transmitted bits without exception.

This paper was presented at the CRYPTO Conference 2019, and is part of the Alambic project.

C. Maire and A. Page updated the preprint *Error-correcting codes based on non-commutative algebras* according to the comments of referees.

In collaboration with Pierre Lezowski, Jean-Paul Cerri has studied in norm-Euclidean properties of totally definite quaternion fields over number fields. Building on their previous work about number fields, they have proved that the Euclidean minimum and the inhomogeneous minimum of orders in such quaternion fields are always equal. Additionally, they are rational under the hypothesis that the base number field is not quadratic. This single remaning open case corresponds to the similar open case remaining for real number fields.

They also have extended Cerri's algorithm for the computation of the upper part of the norm-Euclidean spectrum of a number field to this non-commutative context. This algorithm has allowed to compute the exact value of the norm-Euclidean minimum of orders in totally definite quaternion fields over a quadratic number field. This has provided the first known values of this minimum when the base number field has degree strictly greater than 1.

Members of the team have taken part in an international autumn school
on computational number theory at the Izmir Institute of Technology
(IZTECH) in 2017. Henri Cohen has transformed his two lectures in book
chapters. The text on modular forms
presents the (of course extremely condensed) view of the book
he has coauthored. The chapter on

A complementary approach using modular symbols is used in
by
Karim Belabas, Dominique Bernardi and Bernadette Perrin-Riou to
compute Manin's constant and the modular degree of elliptic curves
defined over

Antonin Riffaut examines in whether there are
relations defined over

E. Milio and D. Robert updated their paper on computing cyclic modular polynomials.

https://

The Alambic project is a research project formed by members of the Inria Project-Team CASCADE of ENS Paris, members of the AriC Inria project-team of ENS Lyon, and members of the CRYPTIS of the university of Limoges. G. Castagnos is an external member of the team of Lyon for this project.

Non-malleability is a security notion for public key cryptographic encryption schemes that ensures that it is infeasible for an adversary to modify ciphertexts into other ciphertexts of messages which are related to the decryption of the first ones. On the other hand, it has been realized that, in specific settings, malleability in cryptographic protocols can actually be a very useful feature. For example, the notion of homomorphic encryption allows specific types of computations to be carried out on ciphertexts and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintexts. The homomorphic property can be used to create secure voting systems, collision-resistant hash functions, private information retrieval schemes, and for fully homomorphic encryption enables widespread use of cloud computing by ensuring the confidentiality of processed data.

The aim of the Alambic project to investigate further theoretical and practical applications of malleability in cryptography. More precisely, this project focuses on three different aspects: secure computation outsourcing and server-aided cryptography, homomorphic encryption and applications and << paradoxical >> applications of malleability.

The

The CLap–CLap ANR project aims at accelerating the expansion of the

draw a conjectural picture of the (still hypothetical)

compute many deformation spaces of Galois representations and make the bridge with deformation spaces of representations of reductive groups,

design new algorithms for computations with Hilbert and Siegel modular forms and their associated Galois representations.

This project will also be the opportunity to contribute to the development of the mathematical software SageMath and to the expansion of computational methodologies.

The CIAO ANR project is a young researcher ANR project led by Damien Robert October 2019.

The aim of the CIAO project is to study the security and improve the efficiency of the SIDH (supersingular isogenies Diffie Helmann) protocol, which is one of the post-quantum cryptographic project submitted to NIST, which passed the first round selection.

The project include all aspects of SIDH, from theoretical ones (computing the endomorphism ring of supersingular elliptic curves, generalisation of SIDH to abelian surfaces) to more practical aspects like arithmetic efficiency and fast implementations, and also extending SIDH to more protocols than just key exchange.

Applications of this project is to improve the security of communications in a context where the currently used cryptosystems are vulnerable to quantum computers. Beyond post-quantum cryptography, isogeny based cryptosystems also allow to construct new interesting cryptographic tools, like Verifiable Delay Functions, used in block chains.

Title: OpenDreamKit

Program: H2020

Duration: January 2016 - December 2019

Coordinator: Nicolas Thiéry

Inria contact: Karim Belabas

Description
http://

OpenDreamKit was a Horizon 2020 European Research Infrastructure project (#676541) that ran for four years, starting from September 2015. It provided substantial funding to the open source computational mathematics ecosystem, and in particular popular tools such as LinBox, MPIR, SageMath, GAP, Pari/GP, LMFDB, Singular, MathHub, and the IPython/Jupyter interactive computing environment.

**International Laboratory for Research in Computer Science and Applied Mathematics**

Associate Team involved in the International Lab:

Title: (Harder Better) FAster STronger cryptography

International Partner (Institution - Laboratory - Researcher): and the PRMAIS project

Université des Sciences et Techniques de Masuku (Gabon) - Tony Ezome

Start year: 2017

See also: http://

The project aims to develop better algorithms for elliptic curve cryptography with prospect of the two challenges ahead: - securing the internet of things - preparing towards quantum computers.

Elliptic curves are currently the fastest public-key cryptosystem (with a key size that can fit on embeded devices) while still through a different mode of operation beeing (possibly) able to resist quantum based computers.

This was the last year of the Fast projet, which was represented at the Journees du Lirimia in Yaounde by Emmanuel Fouotsa.

In total the project funded one EMA and two CIMPA schools, had 14 publications in journals and conferences (with three upcoming preprints), two PhD defense with two upcoming.

The team is used to collaborating with Leiden University through the ALGANT programme for joint PhD supervision.

Eduardo Friedman (U. of Chile), long term collaborator of K. Belabas's and H. Cohen's, is a regular visitor in Bordeaux (about 1 month every year).

Researchers visiting the team to give a talk to the team seminar include David Lubicz (DGA Rennes), Hartmut Monien (Bethe Center for Theoretical Physics, Bonn), Francesco Battestoni (University of Milan), David Roe (MIT, Boston), Maria Dostert (EPFL, Lausanne), and Alice Pellet-Mary (KU Leuven).

Abdoulaye Maiga visited the team for one month in December 2019, and Tony Ezome visited for two weeks in November 2019.

X. Caruso is an editor and one of the founders of the journal
*Annales Henri Lebesgue*.

J.-M. Couveignes is a member of the editorial board (scientific committee)
of the *Publications mathématiques de Besançon* since 2010.

K. Belabas acts on the editorial board of *Journal de Théorie des
Nombres de Bordeaux* since 2005 and of *Archiv der Mathematik* since
2006.

H. Cohen is an editor for the Springer book series
*Algorithms and Computations in Mathematics (ACM)*.

A. Enge is an editor of *Designs, Codes and Cryptography*
since 2004.

F. Johansson, *Computing with precision*, Tech Talk, Google X, Mountain View, CA, USA (January 2019)

K. Belabas is a member of the “conseil scientifique” of the Société Mathématique de France.

Since January 2015, K. Belabas is vice-head of the Math Institute (IMB). He also leads the computer science support service (“cellule informatique”) of IMB and coordinates the participation of the institute in the regional computation cluster PlaFRIM.

He is an elected member of “commission de la recherche” in the academic senate of Bordeaux University.

He was a member of the “Conseil National des Universités” (25th section, pure mathematics) since 2015 until november 2019.

Since January 2017, A. Enge is “délégué scientifique” of the Inria research centre Bordeaux–Sud-Ouest. As such, he is also a designated member of the “commission d'évaluation” of Inria.

He is a member of the administrative council of the Société Arithmétique
de Bordeaux, qui édite le *Journal de théorie des nombres de Bordeaux*
et qui soutient des congrès en théorie des nombres.

J.-P. Cerri is an elected member of the scientific council of the Mathematics Institute of Bordeaux (IMB) and responsible for the bachelor programme in mathematics and informatics.

Master: G. Castagnos, *Cryptanalyse*,
60h, M2, University of Bordeaux, France;

Master: G. Castagnos, *Cryptologie avancée*,
30h, M2, University of Bordeaux, France;

Master: G. Castagnos, *Courbes elliptiques*,
30h, M2, University of Bordeaux, France;

Licence: G. Castagnos, *Arithmétique et Cryptologie*, 24h, L3,
Université de Bordeaux, France

Master : D. Robert, *Courbes elliptiques*,
60h, M2, University of Bordeaux, France;

Master: X. Caruso and J.-M. Couveignes, *Algorithmique arithmétique, introduction à l'algorithmique quantique*,
60h, M2, University of Bordeaux, France;

Master : K. Belabas, *Computer Algebra*,
91h, M2, University of Bordeaux, France;

Master: J.-M. Couveignes, *Modules, espaces quadratiques*,
30h, M1, University of Bordeaux, France;

Licence : J.-P. Cerri, *Arithmétique et Cryptologie*, TD, 36h, L3,
Université de Bordeaux, France

Licence : J.-P. Cerri, *Algèbre linéaire*, TD, 51h, L2, Université
de Bordeaux, France

Licence : J.-P. Cerri, *Topologie*, TD, 35h, L3, Université de
Bordeaux, France

Master : J.-P. Cerri, *Cryptologie*, Cours-TD, 60h, M1, Université
de Bordeaux, France

Licence: J. Kieffer, *Algorithmique Mathématique 2*, 32h,
L3, Université de Bordeaux, France

Master: R. Barbulescu, *Arithmetic algorithms for cryptology*, M2, Master Parisien de Recherche Informatique.

Licence, Master : J.-P. Cerri, 2 TER (L3, M1), 1 Projet (M2), Université de Bordeaux, France

Master : J. Asuncion, *Elliptic curves*, TD, 16h, M1, Universiteit Utrecht (Mastermath), Pays-Bas

Master thesis: Jean-Raphaël Biehler, *Functional encryption*,
supervised by Guilhem Castagnos

Master thesis: Béranger Seguin, *Deformations of Galois representations*,
supervised by Xavier Caruso

Master thesis: William Dallaporta, *Parametrization of ideals
and other algebraic structures by quadratic forms*,
supervised by Karim Belabas

PhD in progress: Ida Tucker, *Design of new advanced cryptosystems from homomorphic building blocks*,
since October 2017, supervised by Guilhem Castagnos and Fabien Laguillaumie

PhD in progress: Abdoulaye Maiga,
*Computing canonical lift of genus 2 hyperelliptic curves*,
University Dakar,
supervised by Djiby Sow, Abdoul Aziz Ciss and D. Robert.

PhD in progress: Jared Asuncion, *Class fields of complex multiplication fields*, since September 2017, supervised by A. Enge and Marco Streng (Universiteit Leiden).

PhD in progress: Elie Eid, *Computing isogenies between elliptic curves and curves of higher genus*,
since September 2018, supervised by Xavier Caruso and Reynald Lercier

PhD in progress: Amaury Durand, *Geometric Gabidulin codes*,
since September 2019, supervised by Xavier Caruso

PhD in progress: Jean Kieffer, *Computing isogenies
between abelian surfaces*, since September 2018, supervised by
Damien Robert and Aurel Page

PhD in progress: Pavel Solomatin
*Topics on $L$-functions*, since October 2014,
supervised by B. de Smit and K. Belabas.

PhD in progress: Anne-Edgar Wilke
*Enumerating integral orbits of prehomogeneous representations*,
since September 2019, supervised by K. Belabas.

PhD in progress: Sudarshan Shinde
*Cryptographic applications of modular curves*
since October 2016, supervised by R. Barbulescu with Pierre-Vincent Koseleff (Sorbonne Université).

X. Caruso has written a report for the doctoral dissertation by
Léo Poyeton, ÉNS de Lyon:
*Extensions de Lie $p$-adiques et $(\varphi ,\Gamma )$-modules*.

X. Caruso has written a report for the doctoral dissertation by
Christopher Doris, University of Bristol:
*Aspects of $p$-adic computation*.

X. Caruso has written a report for the doctoral dissertation by
Joelle Saade, Université de Limoges:
*Méthodes symboliques pour les systèmes différentiels linéaires à singularité irrégulière*.

R. Barbulescu was part of the three members jury of the oral examination in mathematics for math-info the admission examination for ENS de Lyon

D. Robert is a member of the jury of Agregations de Mathematiques. He is also the director of the option “calcul formel” of the Modelisation part of the oral examination.

Alkindi : R. Barbulescu is one of the three organizers of the Alkindi contest, a contest for 13-to-15 year old students which gathers more than 60000 participants from France and Switzerland. D. Robert and the other members invite the winners of the Bordeaux region for a 2 hour visit each year.

from 27/05/2019 to 31/05/2019, X. Caruso supervised a stage at the fablab Coh@bit (at IUT Gradignan) to build some educational material

30/06/2019, X. Caruso: *Ramène pas ta science* on a physical experiment demonstrating that the fastest path between two points is an arc of cycloid

8-10/10/2019, A. Page: *Fête de la Science* at Inria Bordeaux,
activity on cryptography (8 groups of students).

17/10/2019, X. Caruso and A. Page: *Village des 80 ans du CNRS*,
discussion stand "Quizz des idées reçues" on research in mathematics.

19/10/2019, X. Caruso and M.-L. Chabanol: *Village des 80 ans du CNRS* on physical experiment demonstrating that the fastest path between two points is an arc of cycloid

from 07/04/2019 to 14/04/2019, R. Barbulescu was one of two teachers for a math camp in Kinshasa of 150 students https://

from 06/07/2019 to 13/07/2019, R. Barbulescu was the main organiser for a math training camp which gathered the national teams for the International Olympiad of Mathematics of France, Romania and Bulgaria.

5/12/2019, D. Robert: small presentations of cryptography for the student of Ecole Normale Superieure de Lyon.