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Chudnovsky-type algorithms of multiplication in finite fields are well known for their good bilinear complexity. Recently, two advances have been obtained in the study of these algorithms: a strategy to optimize the scalar complexity of the original algorithm and the development of a generic recursive construction over the projective line. The construction of recursive Chudnodvsky-type algorithms over the projective line makes possible an efficient generic strategy to optimize their complexity (number of scalar and bilinear multiplications and additions in the base field). Then, several examples are given. In particular, considering Baum-Shokrollahi’s experiment (1992), this constructive method provides a Chudnovsky-type algorithm of multiplication in F 256 / F 4 \mathbb {F}_{256}/\mathbb {F}_4 with the best known complexity, while being much more efficient than existing optimization methods.

International audience

International audience; The Chudnovsky and Chudnovsky algorithm for the multiplication in extensions of finite fields provides a bilinear complexity which is uniformly linear with respect to the degree of the extension. Recently, Ran-driambololona has generalized the method, allowing asymmetry in the interpolation procedure and leading to new upper bounds on the bilinear complexity. In this article, we first translate this generalization into the language of algebraic function fields. Then, we propose a strategy to effectively construct asymmetric algorithms using places of higher degrees and without derivated evaluation. Finally, we provide examples of three multiplication algorithms along with their Magma implementation: in F 16 13 using only rational places, in F 4 5 using also places of degree two, and in F 2 5 using also places of degree four.

The percentage of disabled persons pursuing their studies up to an engineering level degree is very low in France. At the same time, companies perceive a shortage of computer engineers. In order to fill this injustice and this economic need, Aix-Marseille University and a collective including big companies have joined forces to create an engineering training dedicated to disabled persons. The implementation and management of such training is complex because, on the one hand, the number of actors involved in the project is large and, on the other hand, some actors have to learn to work together. The objective of this article is to formulate a number of recommendations and pitfalls to avoid in order to facilitate, at the pedagogical level, the implementation of similar trainings. The main aim is to enable students to give their best and prevent dropouts. This article also contains a brief feedback on the HUGo training.; Le pourcentage de personnes en situation de handicap poursuivant leurs études jusqu'à un diplôme de niveau I est très faible en France. Parallèlement, les entreprises perçoivent un manque d'ingénieurs informaticiens. Afin de combler cette injustice et ce besoin économique, l'Université d'Aix-Marseille et un collectif comprenant de grandes entreprises se sont associés pour créer une formation d'ingénieurs dédiée aux personnes en situation de handicap. La mise en place et la gestion d'une telle formation sont complexes car d'une part, le nombre d'acteurs impliqués dans le projet est important et d'autre part, certains acteurs doivent apprendre à travailler ensemble. L'objectif de cet article est de formuler un certain nombre de recommandations et de pièges à éviter afin de faciliter, au niveau pédagogique, la mise en place de formations similaires. Il s'agit principalement de permettre aux élèves de tirer le meilleur d'eux mêmes et de prévenir les abandons. Cet article contient également un retour d'expérience succinct concernant la formation HUGo.

International audience; Presented by the Editorial Board The Chudnovsky algorithm for the multiplication in extensions of finite fields provides a bilinear complexity uniformly linear with respect to the degree of the extension. Recently, Randriambololona has generalized the method, allowing asymmetry in the interpolation procedure and leading to new upper bounds on the bilinear complexity. In this note, we describe the construction of this asymmetric method without derived evaluation. To do this, we translate this generalization into the language of algebraic function fields and we give a strategy of construction and implementation.; L'algorithme de multiplication dans les corps finis de Chudnovsky a une complexité bilinéaire uniformément linéaire en le degré de l'extension. Randriambololona a récemment généralisé cette méthode en introduisant l'asymétrie dans la procédure d'interpolation et en obtenant ainsi de nouvelles bornes sur la complexité bilinéaire. Dans cette note, nous décrivons la construction de cette méthode asymétrique sans évaluation dérivée. Pour ce faire, nous traduisons cette généralisation dans le langage des corps de fonctions algébriques, et nous donnons une stratégie de construction et d'implantation.