Normal Elliptic Bases and Torus-Based Cryptography

We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers $n$ and infinitely many values of $q$, we can encode $m$ torus elements, to a small fixed overhead and to $m$ $\phi(n)$-tuples of $F_q$ elements, in quasi-linear time in $\log q$. This improves upon previously known algorithms, which all have a quasi-quadratic complexity. As a result, the cost of the encoding phase is now negligible in Diffie-Hellman cryptographic schemes

Evolution de la criticalité comme indicateur de fatigue pour les alliages à mémoire de forme

In this thesis we put forward a new set of ideas to open the way to experimentally distinguish various stages in the micro-development of fatigue using the framework of the self-organized criticality (SOC). The demonstration is made that the fatigue process belongs to this class of systems and the SOC theory is used to build quantifiers that describe the dissipative regime of the material. The approach, to build these predictors, is based on the study of the multi-scale statistical structure of the intermittent acoustic signal generated by the cyclically loaded sample. The originality of the analysis lies in the interpretation of the statistics in the framework of SOC that enables to draw parallels with a wide range of natural phenomena. The main discoveries of the thesis are that acoustic emissions permit to reveal different dissipative regimes in the fatigue of shape memory alloys and each of these regimes is characterized by a different energy- time structure that is well illustrated through the SOC formalism and the associated power-law distributions. The proofs are also given that the same critical dynamics can hold from the large scale of earthquakes down to the microscopic scale of the sample structure.A travers cette thèse, nous envisageons de distinguer expérimentalement les différents stades intervenant dans le micro-développement de la fatigue à travers le concept de criticalité auto-organisée (SOC). Nous démontrons que le processus d'endommagement par fatigue appartient à cette classe de systèmes et la théorie de la SOC est utilisée pour construire des indicateurs du régime dissipatif du matériau. Ces indicateurs sont construits à partir de l'étude de la structure statistique multi-échelle des signaux acoustiques intermittents générés par le chargement cyclique d'une éprouvette. L'originalité de la démarche tient dans l'interprétation des statistiques à travers le cadre de la SOC qui permet la comparaison avec de nombreux phénomènes naturels. Cette thèse a permis de révéler différents régimes dissipatifs dans la fatigue des alliages à mémoire de formes au moyen d'enregistrements acoustiques et de montrer que chacun de ces régimes est décrit par une structure temps-énergie spécifique illustrée à travers le concept de SOC et les distributions en loi puissance associées. Enfin, une analyse multi-échelle est menée pour souligner qu'une même dynamique critique peut s'appliquer de l'échelle des tremblements de terre à l'échelle microscopique d'une éprouvette

Dysfunction of homeostatic control of dopamine by astrocytes in the developing prefrontal cortex leads to cognitive impairments.

Astrocytes orchestrate neural development by powerfully coordinating synapse formation and function and, as such, may be critically involved in the pathogenesis of neurodevelopmental abnormalities and cognitive deficits commonly observed in psychiatric disorders. Here, we report the identification of a subset of cortical astrocytes that are competent for regulating dopamine (DA) homeostasis during postnatal development of the prefrontal cortex (PFC), allowing for optimal DA-mediated maturation of excitatory circuits. Such control of DA homeostasis occurs through the coordinated activity of astroglial vesicular monoamine transporter 2 (VMAT2) together with organic cation transporter 3 and monoamine oxidase type B, two key proteins for DA uptake and metabolism. Conditional deletion of VMAT2 in astrocytes postnatally produces loss of PFC DA homeostasis, leading to defective synaptic transmission and plasticity as well as impaired executive functions. Our findings show a novel role for PFC astrocytes in the DA modulation of cognitive performances with relevance to psychiatric disorders