GAATI

Laboratoire GAATI

Université de la Polynésie française

Publications

Emmanouil-Marios Athanasakos, Samir M. Perlaza. Leveraging Noisy Observations in Zero-Sum Games. RR-9538, Inria Sophia Antipolis - Méditerranée, Université Côte d'Azur. 2024, pp.24. ⟨hal-04424590⟩

Emmanouil M Athanasakos, Samir M Perlaza. Leveraging Noisy Observations in Zero-Sum Games. 2024. ⟨hal-04432819⟩

Samir M Perlaza, Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, Stefano Rini. Empirical Risk Minimization with Relative Entropy Regularization. IEEE Transactions on Information Theory, In press, ⟨10.1109/TIT.2024.3365728⟩. ⟨hal-03849748v4⟩

Xinying Zou, Samir M. Perlaza, Iñaki Esnaola, Eitan Altman. Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure. AAAI 2024 - Conference on Artificial Intelligence, Feb 2024, Vancouver, Canada. pp.17271-17279, ⟨10.1609/aaai.v38i15.29674⟩. ⟨hal-04353957⟩

Xinying Zou, Samir M Perlaza, Iñaki Esnaola, Eitan Altman, H. Vincent Poor. The Worst-Case Data-Generating Probability Measure in Statistical Learning. IEEE Journal on Selected Areas in Information Theory, 2024, 5, pp.175-189. ⟨10.1109/JSAIT.2024.3383281⟩. ⟨hal-04442591v2⟩

Xiuzhen Ye, Iñaki Esnaola, Samir M Perlaza, Robert F Harrison. An Information Theoretic Metric for Measurement Vulnerability to Data Integrity Attacks on Smart Grids. IET Smart Grid, 2024, pp.1--10. ⟨10.1049/stg2.12163⟩. ⟨hal-03849768⟩

Francisco Daunas, Iñaki Esnaola, Samir M Perlaza, H. Vincent Poor. Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergences. Proceedings of the IEEE International Symposium on Information Theory, Jul 2024, Athens, Greece. ⟨hal-04431558v1⟩

Xinying Zou, Samir M. Perlaza, Iñaki Esnaola, Eitan Altman, H. Vincent Poor. An Exact Characterization of the Generalization Error of Machine Learning Algorithms. RR-9539, INRIA. 2024, pp.80. ⟨hal-04442566v3⟩

Samir M. Perlaza, Xinying Zou, Iñaki Esnaola, Eitan Altman, H. Vincent Poor. An Exact Characterization of the Generalization Error of Machine Learning Algorithms. 2024. ⟨hal-04426500v2⟩

Ke Sun, Samir M. Perlaza, Alain Jean-Marie. 2×2 Zero-Sum Games with Commitments and Noisy Observations. ISIT 2023 - IEEE International Symposium on Information Theory, Jun 2023, Taipei, Taiwan. ⟨10.1109/ISIT54713.2023.10206806⟩. ⟨hal-04091712v2⟩

David Adam, Jean-Luc Chabert. Bhargava’s Exponential Functions and Bernoulli Numbers Associated to the Set of Prime Numbers. Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, Springer International Publishing; Springer International Publishing, pp.9-35, 2023, 978-3-031-28846-3. ⟨10.1007/978-3-031-28847-0_2⟩. ⟨hal-04317005⟩

Samir M. Perlaza, Iñaki Esnaola, Gaetan Bisson, H Vincent Poor. On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation. ISIT 2023 - IEEE International Symposium on Information Theory, Jun 2023, Taipei, Taiwan. ⟨10.1109/ISIT54713.2023.10206506⟩. ⟨hal-04096054v3⟩

Gaetan Bisson. Contributions aux aspects effectifs des variétés abéliennes et à leurs applications. Mathématiques [math]. Université de la Polynésie française, 2023. ⟨tel-04193136⟩

Alexander D. Rahm, Pierre Pratley. Is creeping abandonment of human cancer defences evolutionarily favoured?. Qeios, 2023, ⟨10.32388/T8VD3I.4⟩. ⟨hal-04398999⟩

Francisco Daunas, Iñaki Esnaola, Samir M. Perlaza, H. Vincent Poor. Empirical Risk Minimization with Relative Entropy Regularization Type-II. RR-9508, INRIA, Centre Inria d'Université Côte d'Azur, Sophia Antipolis. 2023. ⟨hal-04110899v2⟩

François Rodier, Florian Caullery, Eric Férard. Distribution of the autocorrelation of random Boolean functions. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences , 2023, 15 (5), pp.995-1009. ⟨10.1007/s12095-023-00653-3⟩. ⟨hal-04317006⟩

Francisco Daunas, Iñaki Esnaola, Samir M Perlaza, H. Vincent Poor. Analysis of the Relative Entropy Asymmetry in the Regularization of Empirical Risk Minimization. (ISIT 2023 - IEEE International Symposium on Information Theory, Jun 2023, Taipei, Taiwan. ⟨10.1109/ISIT54713.2023.10206876⟩. ⟨hal-04097637⟩

Xinying Zou, Samir M. Perlaza, Iñaki Esnaola, Eitan Altman. The Worst-Case Data-Generating Probability Measure. RR-9515, INRIA. 2023. ⟨hal-04181971v2⟩

Francisco Daunas, Iñaki Esnaola, Samir M. Perlaza, H. Vincent Poor. Empirical Risk Minimization with f-Divergence Regularization in Statistical Learning. RR-9521, Inria. 2023. ⟨hal-04258765v3⟩

Ashok Krishnan K. S., Samir M. Perlaza, Eitan Altman. Pricing for Platforms: Games, Equilibria and Cooperation. RR-9510, Inria. 2023. ⟨hal-04132372⟩

Ke Sun, Samir M. Perlaza, Alain Jean-Marie. 2 × 2 Zero-Sum Games with Commitments and Noisy Observations. RR-9505, Inria - Sophia Antipolis. 2023. ⟨hal-03838009v2⟩

Roger Oyono, Nicolas Thériault. Index calculus algorithm for non-planar curves. Finite Fields and Their Applications, 2023, 90, pp.102227. ⟨10.1016/j.ffa.2023.102227⟩. ⟨hal-04138475⟩

Ashok Krishnan K. S., Samir M. Perlaza, Eitan Altman. Pricing Models for Digital Renting Platforms. ASMTA 2023 - International Conference on Analytical & Stochastic Modelling Techniques & Applications, Jun 2023, Florence, France. ⟨10.1007/978-3-031-43185-2_10⟩. ⟨hal-04136929⟩

Xiuzhen Ye, Iñaki Esnaola, Samir M. Perlaza, Robert F Harrison. Stealth Data Injection Attacks with Sparsity Constraints. IEEE Transactions on Smart Grid, 2023, 14 (4), pp.3201 -- 3209. ⟨10.1109/TSG.2023.3238913⟩. ⟨hal-03516567⟩

Sadaf Ul Zuhra, Samir M Perlaza, H. Vincent Poor, Eitan Altman, Mikael Skoglund. Information-Energy Regions in the Finite Block-Length Regime with Finite Channel Inputs. 2022. ⟨hal-03848708⟩

Sadaf Ul Zuhra, Samir M Perlaza, H Vincent Poor, Mikael Skoglund. Information-Energy Trade-offs with EH Non-linearities in the Finite Block-Length Regime with Finite Constellations. ITW 2022 - IEEE Information Theory Workshop, Nov 2022, Mumbai, India. pp.55-60, ⟨10.1109/ITW54588.2022.9965880⟩. ⟨hal-03695522⟩

Sadaf Ul Zuhra, Samir M. Perlaza, H. Vincent Poor, Eitan Altman. Simultaneous Information and Energy Transmission with Finite Constellations. [Research Report] RR-9409, Inria Sophia Antipolis - Méditerranée. 2022, pp.1-37. ⟨hal-03230482v2⟩

Samir M. Perlaza, Iñaki Esnaola, H Vincent Poor. Sensitivity of the Gibbs Algorithm to Data Aggregation in Supervised Machine Learning. [Research Report] RR-9474, Inria. 2022, pp.22. ⟨hal-03703628v3⟩

Gaetan Bisson, Roger Oyono. On the vaccination threshold for Covid-19 in French Polynesia. Pacific Health, 2022, 5, ⟨10.24135/pacifichealth.v5i.59⟩. ⟨hal-03418625⟩

Majed Haddad, Piotr Wiecek, Oussama Habachi, Samir M. Perlaza, Shahid Mehraj Shah. FEAT: Fair Coordinated Iterative Water-Filling Algorithm. MSWIM'22 - 25th International Conference on Modeling, Analysis and Simulation of Wireless and Mobile Systems, Oct 2022, Montreal, Canada. ⟨hal-03773348⟩

Bui Anh Tuan, Alexander D. Rahm, Matthias Wendt. On Farrell-Tate cohomology of GL(3) over rings of quadratic integers. 2022. ⟨hal-02435963v2⟩

Samir M. Perlaza, Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, Stefano Rini. Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis. ISIT 2022 - IEEE International Symposium on Information Theory, Jun 2022, Espoo, Finland. pp.684-689, ⟨10.1109/ISIT50566.2022.9834273⟩. ⟨hal-03561396v2⟩

Adrien Poteaux, Martin Weimann. A quasi-linear irreducibility test in K[[x]][y]. Computational Complexity, 2022, ⟨10.1007/s00037-022-00221-w⟩. ⟨hal-02354929⟩

Sadaf Ul Zuhra, Samir M. Perlaza, H. Vincent Poor, Eitan Altman. Achievable Information-Energy Region in the Finite Block-Length Regime with Finite Constellations. ISIT 2022 - IEEE International Symposium on Information Theory, Jun 2022, Espoo, Finland. pp.2106-2111, ⟨10.1109/ISIT50566.2022.9834694⟩. ⟨hal-03563756⟩

Xiuzhen Ye, Iñaki Esnaola, Samir M. Perlaza, Robert F Harrison. Stealth Data Injection Attacks with Sparsity Constraints. [Research Report] RR-9481, Institut National de Recherche en Informatique et en Automatique (INRIA). 2022. ⟨hal-03781671v2⟩

Samir M. Perlaza, Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, Stefano Rini. Empirical Risk Minimization with Relative Entropy Regularization. [Research Report] RR-9454, Inria. 2022. ⟨hal-03560072v7⟩

Eitan Altman, Mandar Datar, Francesco de Pellegrini, Samir M. Perlaza, Daniel Sadoc Menasché. The Mask Game with Multiple Populations. Dynamic Games and Applications, 2022, 12 (1), pp.147-167. ⟨10.1007/s13235-022-00431-5⟩. ⟨hal-03527522⟩

Rina Paucar R., Claudia Schoemann. A theorem on zero cycles on surfaces. Selecciones Matemáticas, 2022, 9 (01), pp.161-166. ⟨10.17268/sel.mat.2022.01.13⟩. ⟨hal-03835625⟩

Rony Bitan, Ralf Köhl, Claudia Schoemann. The twisted forms of a semisimple group over an Fq-curve. Journal de Théorie des Nombres de Bordeaux, 2021, 33 (1), pp.17-38. ⟨10.5802/jtnb.1150⟩. ⟨hal-03601022⟩

Laia Amorós, Annamaria Iezzi, Kristin Lauter, Chloe Martindale, Jana Sotáková. Explicit Connections Between Supersingular Isogeny Graphs and Bruhat–Tits Trees. Women in Numbers Europe III, 24, Springer, pp.39-73, 2021, Association for Women in Mathematics Series, 978-3-030-77699-2. ⟨10.1007/978-3-030-77700-5_2⟩. ⟨hal-03563867⟩

Sadaf Ul Zuhra, Samir M. Perlaza, Eitan Altman. Simultaneous Information and Energy Transmission with Finite Constellations. ITW 2021 - IEEE Information Theory Workshop, Oct 2021, Kanazawa, Japan. pp.1-6, ⟨10.1109/ITW48936.2021.9611494⟩. ⟨hal-03339165⟩

Adrien Poteaux, Martin Weimann. Computing Puiseux series: a fast divide and conquer algorithm. Annales Henri Lebesgue, 2021, 4, pp.1061--1102. ⟨10.5802/ahl.97⟩. ⟨hal-01578214v3⟩

Izza Mounir, Loick Menvielle, Samir M. Perlaza, Denis Chênevert, Jo-Hanna Planchard, et al.. Psychological Distress and Tobacco Use Among Hospital Workers During COVID-19. Frontiers in Psychiatry, 2021, 12, ⟨10.3389/fpsyt.2021.701810⟩. ⟨hal-03429343⟩

Alexander D. Rahm. AN INTRODUCTION TO TORSION SUBCOMPLEX REDUCTION. Advanced Studies: Euro-Tbilisi Mathematical Journal, 2021, Special issue on Cohomology, Geometry, Explicit Number Theory, 9, p. 105-126. ⟨hal-03112213v2⟩

Gaetan Bisson, Romain Cosset, Damien Robert. AVIsogenies. 2021, ⟨swh:1:dir:05aed8deac96bfb9c122157e4db1d310423c7258;origin=https://hal.archives-ouvertes.fr/hal-03371897;visit=swh:1:snp:57482093ffd15cdb106b284e34b3f7f0813562aa;anchor=swh:1:rev:1f0f6ec99b2c46d1bdf2e1d68aa330d3249f0b1b;path=/⟩. ⟨hal-03371897⟩

David Burns, Rob M. H. de Jeu, Herbert Gangl, Alexander D. Rahm, Dan Yasaki. Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields. Forum of Mathematics, Sigma, 2021, 9 (E40), ⟨10.1017/fms.2021.9⟩. ⟨hal-02550079⟩

Dadja Anade, Jean-Marie Gorce, Philippe Mary, Samir M. Perlaza. Saddlepoint Approximations of Cumulative Distribution Functions of Sums of Random Vectors. [Research Report] RR-9388, Inria Grenoble - Rhône-Alpes. 2021, pp.32. ⟨hal-03143508v3⟩

Samir M. Perlaza. Contributions to Information and Energy Systems. Information Theory [math.IT]. INSA de Lyon; Université Claude Bernard Lyon I, 2021. ⟨tel-03429274⟩

Gaetan Bisson, Stéphane Ballet, Irene Bouw (Dir.). Arithmetic, Geometry, Cryptography and Coding Theory. American Mathematical Society, 770, 2021, Contemporary Mathematics. ⟨hal-03371878⟩

Xiang-Dong Hou, Annamaria Iezzi. An application of the Hasse--Weil bound to rational functions over finite fields. Acta Arithmetica, 2020, 195 (2), pp.207-216. ⟨10.4064/aa190701-5-12⟩. ⟨hal-03601019⟩

Alexander D. Rahm. Statistique pour les Sciences de la Vie et de la Terre. Licence. Polynésie française. 2020. ⟨hal-03139390v2⟩

Arun Gonzales Decano, Nghia Tran, Hawriya Al-Foori, Buthaina Al-Awadi, Leigh Campbell, et al.. Plasmids shape the diverse accessory resistomes of Escherichia coli ST131. Access Microbiology, 2020, ⟨10.1099/acmi.0.000179⟩. ⟨hal-03017581⟩

Laurent Busé, Carlos d'Andrea, Martín Sombra, Martin Weimann. The geometry of the flex locus of a hypersurface. Pacific Journal of Mathematics, 2020, 304 (2), pp.419--437. ⟨10.2140/pjm.2020.304.419⟩. ⟨hal-01779785⟩

Alexander D. Rahm, Noam Solomon, Tara Trauthwein, Barak Weiss. The Distribution of Rational Numbers on Cantor’s Middle Thirds Set. Uniform Distribution Theory, 2020, 15 (2), pp.73-92. ⟨10.2478/udt-2020-0011⟩. ⟨hal-03417923⟩

Adrien Poteaux, Martin Weimann. Computing the equisingularity type of a pseudo-irreducible polynomial. Applicable Algebra in Engineering, Communication and Computing, 2020, 31, pp.435-460. ⟨10.1007/s00200-020-00451-x⟩. ⟨hal-02354930v2⟩

Mohamad Ali Mehrabi, Christophe Doche, Alireza Jolfaei. Elliptic Curve Cryptography Point Multiplication Core for Hardware Security Module. IEEE Transactions on Computers, 2020, 69 (11), pp.1707-1718. ⟨10.1109/TC.2020.3013266⟩. ⟨hal-03601024⟩

Alexander D. Rahm. Bianchi's additional symmetries. Journal of Homotopy and Related Structures, 2020, 15, pp.455-462. ⟨10.1007/s40062-020-00262-4⟩. ⟨hal-02899079⟩

Mohamad Ali Mehrabi, Christophe Doche. Low-Cost, Low-Power FPGA Implementation of ED25519 and CURVE25519 Point Multiplication. Information, 2019, 10 (9), pp.285. ⟨10.3390/info10090285⟩. ⟨hal-03602232⟩

Anh Tuan Bui, Alexander D. Rahm, Matthias Wendt. The Farrell–Tate and Bredon homology for PSL 4 ( Z ) via cell subdivisions. Journal of Pure and Applied Algebra, 2019, 223 (7), pp.2872-2888. ⟨10.1016/j.jpaa.2018.10.002⟩. ⟨hal-03417845⟩

Maryam Sheikhi‐garjan, Mojtaba Bahramian, Christophe Doche. Threshold verifiable multi‐secret sharing based on elliptic curves and Chinese remainder theorem. IET Information Security, 2019, 13 (3), pp.278-284. ⟨10.1049/iet-ifs.2018.5174⟩. ⟨hal-03602233⟩

Martin Weimann. Computing the genus of plane curves with cubic complexity. Conférence Internationale ACA2019, Jul 2019, Montreal, Canada. ⟨hal-02556247⟩

Fabio Perroni, Alexander D. Rahm. On Ruan's Cohomological Crepant Resolution Conjecture for the complexified Bianchi orbifolds. Algebraic and Geometric Topology, 2019, 19, pp.2715-2762. ⟨10.2140/agt.2019.19.2715⟩. ⟨hal-00627034v4⟩

Ethan Berkove, Grant S Lakeland, Alexander D. Rahm, Anh Tuan Bui, Sebastian Schönnenbeck. The mod 2 cohomology rings of congruence subgroups in the Bianchi groups. Journal of Algebraic Combinatorics, 2019, ⟨10.1007/s10801-019-00912-8⟩. ⟨hal-01565065v3⟩

Stéphane Ballet, Alexey Zykin. Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields. Designs, Codes and Cryptography, 2019, 87 (2-3), pp.517-525. ⟨10.1007/s10623-018-0560-8⟩. ⟨hal-02115440⟩

Alexander D. Rahm. Corrigendum to “On a question of Serre” [C. R. Acad. Sci. Paris, Ser. I 350 (2012) 741–744]. Comptes Rendus. Mathématique, 2019, 357 (7), pp.589-590. ⟨10.1016/j.crma.2019.07.008⟩. ⟨hal-03417827⟩

Stéphane Ballet, Jean Chaumine, Julia Pieltant, Matthieu Rambaud, Hugues Randriambololona, et al.. On the tensor rank of multiplication in finite extensions of finite

Adrien Poteaux, Martin Weimann. Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]. 2019. ⟨hal-02137331v2⟩

David Adam. Optimalité pour en problème de Bézivin. Journal de Théorie des Nombres de Bordeaux, 2019, 31 (1), pp.161-177. ⟨10.5802/jtnb.1073⟩. ⟨hal-02548720⟩

Alexander D. Rahm, Panagiotis Tsaknias. GENUINE BIANCHI MODULAR FORMS OF HIGHER LEVEL, AT VARYING WEIGHT AND DISCRIMINANT. Journal de Théorie des Nombres de Bordeaux, 2019, 31 (1), pp.27-48. ⟨10.5802/jtnb.1067⟩. ⟨hal-01478115⟩

David Adam. Polynômes à valeurs entières sur des ensembles invariants par rotation. Journal of Number Theory, 2018, 186, pp.417-438. ⟨10.1016/j.jnt.2017.10.011⟩. ⟨hal-02129534⟩

Sébastien Larrue, Jean-François Butaud, Curtis Daehler, Stéphane Ballet, Julien Chadeyron, et al.. Persistence at the final stage of volcanic island ontogeny: Abiotic predictors explain native plant species richness on 111 remote Pacific atolls. Ecology and Evolution, 2018, ⟨10.1002/ece3.4680⟩. ⟨hal-01934658⟩

Philippe Lebacque, Alexey Zykin. On M-functions associated with modular forms. Moscow Mathematical Journal, 2018, 18 (3), pp.437-472. ⟨10.17323/1609-4514-2018-18-3-437-472⟩. ⟨hal-01475616⟩

Gaetan Bisson, Mehdi Tibouchi. Constructing Permutation Rational Functions from Isogenies. SIAM Journal on Discrete Mathematics, 2018, 32 (3), pp.1741-1749. ⟨10.1137/17M1135736⟩. ⟨hal-02129542⟩

Gaetan Bisson, Dimitar Jetchev. Isogeny Graphs and Endomorphism Rings of Ordinary Abelian Varieties. colloque international “L-functions and algebraic varieties”, Poncelet Scientific Center; Higher School of Economics, Feb 2018, Moscou, Russia. ⟨hal-02129543⟩

Martin Weimann, Denis Simon. Plane curves with minimal discriminant. Journal of Commutative Algebra, 2018, 10 (4), pp.559-598. ⟨10.1216/JCA-2018-10-4-559⟩. ⟨hal-02137328⟩

Arshia Atashpendar, Sarthak Arora, Alexander D. Rahm, Tanja Schilling. Simulation study of the electrical tunneling network conductivity of suspensions of hard spherocylinders. Physical Review E , 2018, 98 (6), ⟨10.1103/PhysRevE.98.062611⟩. ⟨hal-03017594⟩

Bui Anh Tuan, Alexander D. Rahm. Verification of the Quillen conjecture in the rank 2 imaginary quadratic case. Homology, Homotopy and Applications(HHA), 2017, 22 (2), ⟨10.4310/HHA.2020.v22.n2.a17⟩. ⟨hal-02548734⟩

Eric Férard. On the irreducibility of the hyperplane sections of Fermat varieties in ℙ 3 $\mathbb {P}^{3}$ in characteristic 2. II. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences , 2017, 9 (6), pp.749-767. ⟨10.1007/s12095-017-0213-1⟩. ⟨hal-03417811⟩

Martin Weimann. Bivariate Factorization Using a Critical Fiber. Foundations of Computational Mathematics, 2017, 17 (5), pp.1219-1263. ⟨10.1007/s10208-016-9318-8⟩. ⟨hal-01645143⟩

Gaetan Bisson, Marco Streng. On polarised class groups of orders in quartic CM-fields. Mathematical Research Letters, 2017, 24 (2), pp.247-270. ⟨10.4310/MRL.2017.v24.n2.a1⟩. ⟨hal-03371876⟩

Eric Férard. A infinite class of Kasami functions that are not APN infinitely often. Contemporary mathematics, 2017, Contemporary Mathematics, 686, ⟨10.1090/conm/686/13777⟩. ⟨hal-03417866⟩

Ivan Pogildiakov. On the linear bounds on genera of pointless hyperelliptic curves. 2017. ⟨hal-01494793⟩

David Adam, Jean-Luc Chabert. About Number Fields with Pólya Group of Order $$\le $$ ≤ 2. Multiplicative Ideal Theory and Factorization Theory, 170, Springer International Publishing, pp.23-42, 2016, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-319-38855-7_2⟩. ⟨hal-03417781⟩

Jaime Gutierrez, Josef Schicho, Martin Weimann (Dir.). Computer Algebra and Polynomials: Applications of Algebra and Number Theory. Springer International Publishing, 8942, 2015, 978-3-319-15080-2. ⟨10.1007/978-3-319-15081-9⟩. ⟨hal-02137337⟩

Philippe Lebacque, Alexey Zykin. On the number of rational points of Jacobians over finite fields. Acta Arithmetica, 2015, 169 (4), pp.373-384. ⟨10.4064/aa169-4-5⟩. ⟨hal-01689002⟩

Gaetan Bisson. Computing endomorphism rings of abelian varieties of dimension two. Mathematics of Computation, 2015, 84 (294), pp.1977-1989. ⟨10.1090/S0025-5718-2015-02938-X⟩. ⟨hal-03371877⟩

David Adam, Jean-Luc Chabert. On Bhargava's factorials of the set of twin primes in Z and in Fq[T]. International Journal of Number Theory, 2015, 11 (06), pp.1941-1959. ⟨10.1142/S1793042115500840⟩. ⟨hal-01689000⟩

Gerald Bourgeois. Nonsymmetric generic matrix equations. Linear Algebra and its Applications, 2015, 476, pp.159-183. ⟨10.1016/j.laa.2015.03.008⟩. ⟨hal-03417854⟩

David Adam, Michael Welter. Fonctions entières totales en caractéristique finie. Bulletin de la société mathématique de France, 2015, 143 (1), pp.109-124. ⟨10.24033/bsmf.2681⟩. ⟨hal-01689001⟩

Alexey Zykin. Asymptotic properties of zeta functions over finite fields. Finite Fields and Their Applications, 2015, 35, pp.247-283. ⟨10.1016/j.ffa.2015.04.005⟩. ⟨hal-01689003⟩

Christophe Doche. On the Enumeration of Double-Base Chains with Applications to Elliptic Curve Cryptography. Advances in Cryptology – ASIACRYPT 2014, 8874, Springer Berlin Heidelberg, pp.297-316, 2014, Lecture Notes in Computer Science, ⟨10.1007/978-3-662-45611-8_16⟩. ⟨hal-03417789⟩

Florian Luca, Roger Oyono. THE DIOPHANTINE EQUATION Fyn + Fxn+1 = Fxm. Integers, 2014, Annual Volume 2013, 9783110298116. ⟨10.1515/9783110298161.479⟩. ⟨hal-03417919⟩

Gerald Bourgeois. PROPERTY L AND COMMUTING EXPONENTIALS IN DIMENSION AT MOST THREE. Bulletin of the Australian Mathematical Society, 2014, 89 (1), pp.70-78. ⟨10.1017/S0004972713000609⟩. ⟨hal-03417858⟩

Gerald Bourgeois. The Matrix Equation X A - A X = X α g ( X ) over Fields or Rings. Algebra Colloquium, 2014, 2014, pp.1-6. ⟨10.1155/2014/745029⟩. ⟨hal-03417890⟩

Stéphane Ballet, Gaetan Bisson, Roger Oyono, Renate Scheidler, Nicolas Thériault. Special issue on GEOCRYPT 2013. GEOCRYPT 2013, Oct 2013, Punaauia, Tahiti (French Polynesia), France. 8 (4), American Institute of Mathematical Sciences (AIMS), pp.i - ii, 2014, Advances in Mathematics of Communications (AMC), ⟨10.3934/amc.2014.8.4i⟩. ⟨hal-01259563⟩

Eric Férard. On the irreducibility of the hyperplane sections of Fermat varieties in P3 in characteristic 2. Advances in Mathematics of Communications, 2014, 8 (4), pp.497-509. ⟨10.3934/amc.2014.8.497⟩. ⟨hal-01779804⟩

Gérald Bourgeois. Common invariant subspace and commuting matrices. Linear Algebra and its Applications, 2013, 438 (7), pp.3030-3038. ⟨10.1016/j.laa.2012.11.034⟩. ⟨hal-03417853⟩

Roger Oyono, Florian Luca, Aynur Yalciner. L-Functions of elliptic curves and binary recurrences. Bulletin of the Australian Mathematical Society, 2013, 88 (03), pp.509-519. ⟨10.1017/S0004972713000166⟩. ⟨hal-02084932⟩

Gerald Bourgeois. Similar powers of a matrix. Linear and Multilinear Algebra, 2013, 61 (6), pp.699-709. ⟨10.1080/03081087.2012.703190⟩. ⟨hal-03417859⟩

Stéphane Ballet, Jean Chaumine, Julia Pieltant. Shimura modular curves and asymptotic symmetric tensor rank of multiplication in any finite field. Conference on Algebraic Informatics, Sep 2013, Porquerolles Island, France. pp.160-172, ⟨10.1007/978-3-642-40663-8_16⟩. ⟨hal-00828070⟩

Roger Oyono, Nicolas Thériault. Group arithmetic in C 3 , 5 curves. Journal of Symbolic Computation, 2013, 56, pp.1-26. ⟨10.1016/j.jsc.2013.05.008⟩. ⟨hal-02084937⟩

Gérald Bourgeois. About the matrix function X → AX + XA. Linear and Multilinear Algebra, 2013, 62 (7), pp.978-987. ⟨10.1080/03081087.2013.802090⟩. ⟨hal-03417860⟩

Roger Oyono, Florian Luca. The diophantine equation F_N^Y + F_{N+1}^X = F_M^X. Integers : Electronic Journal of Combinatorial Number Theory, 2013, 13, pp.A33. ⟨hal-02084933⟩

Eric Férard, Roger Oyono, François Rodier. Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents. Contemporary mathematics, 2012, Contemporary Math, 574, pp.27-36. ⟨10.1090/conm/574/11423⟩. ⟨hal-01264150⟩

David Adam, Youssef Fares. On two affine-like dynamical systems in a local field. Journal of Number Theory, 2012, 132 (12), pp.2892-2906. ⟨10.1016/j.jnt.2012.05.011⟩. ⟨hal-03417840⟩

David Adam. ABEL ARITHMETIC FUNCTIONS IN FINITE CHARACTERISTIC. International Journal of Number Theory, 2012, 08 (06), pp.1557-1568. ⟨10.1142/S1793042112500959⟩. ⟨hal-03417874⟩

Gerald Bourgeois. Pairs of matrices, one of which commutes with their commutator. Electronic Journal of Linear Algebra, 2011, 22, ⟨10.13001/1081-3810.1460⟩. ⟨hal-03417916⟩

David Adam, Paul-Jean Cahen. Newtonian and Schinzel quadratic fields. Journal of Pure and Applied Algebra, 2011, 215 (8), pp.1902-1918. ⟨10.1016/j.jpaa.2010.11.003⟩. ⟨hal-03417843⟩

David Adam. Polynômes à valeurs entières ainsi que leurs dérivées en caractéristique p. Acta Arithmetica, 2011, 148 (4), pp.351-365. ⟨10.4064/aa148-4-3⟩. ⟨hal-03417928⟩

Gerald Bourgeois. How to solve the matrix equation XA-AX=f(X). Linear Algebra and its Applications, 2011, 434 (3), pp.657-668. ⟨10.1016/j.laa.2010.09.037⟩. ⟨hal-03417851⟩

Stéphane Ballet, Jean Chaumine, Julia Pieltant, Robert Rolland. On the tensor rank of multiplication in finite extensions of finite fields. 2011. ⟨hal-01079416⟩

David Adam. The Gel’fond-Fridman theorem in positive characteristic. Israel Journal of Mathematics, 2011, 185 (1), pp.235-251. ⟨10.1007/s11856-011-0108-3⟩. ⟨hal-03417806⟩

Gérald Bourgeois, Sébastien Orange. Dynamical Systems of Simplices in Dimension Two or Three. Automated Deduction in Geometry, 6301, Springer Berlin Heidelberg, pp.1-21, 2011, Lecture Notes in Computer Science, ⟨10.1007/978-3-642-21046-4_1⟩. ⟨hal-03417786⟩

Florian Luca, Roger Oyono. An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Proceedings of the Japan Academy. Series A. Mathematical Sciences, 2011, 87 (4), ⟨10.3792/pjaa.87.45⟩. ⟨hal-03417925⟩

David Adam. Fonctions à valeurs entières et module de Carlitz. Journal de Théorie des Nombres de Bordeaux, 2010, 22 (2), pp.271-286. ⟨10.5802/jtnb.715⟩. ⟨hal-03417931⟩

Eric Férard, François Rodier. Non linéarité des fonctions booléennes données par des polynômes de degré binaire 3 définies sur F2m avec m pair. Contemporary mathematics, 2010, Contemporary Mathematics, 521, ⟨10.1090/conm/521/10272⟩. ⟨hal-03417862⟩

David Adam, Youssef Fares. Integer-valued Euler–Jackson’s finite differences. Monatshefte für Mathematik, 2010, 161 (1), pp.15-32. ⟨10.1007/s00605-009-0111-5⟩. ⟨hal-03417801⟩

Christophe Ritzenthaler, Roger Oyono. On rationality of the intersection points of a line with a plane quartic. WAIFI 2010: Arithmetic of Finite Fields, 2010, Istanbul, Turkey. pp.224-237, ⟨10.1007/978-3-642-13797-6_16⟩. ⟨hal-01099944⟩

Enrique González-Jiménez, Roger Oyono. Non-hyperelliptic modular curves of genus 3. Journal of Number Theory, 2010, 130 (4), pp.862-878. ⟨10.1016/j.jnt.2009.12.002⟩. ⟨hal-03417839⟩

Alexander D. Rahm, Noam Solomon, Tara Trauthwein, Barak Weiss. The distribution of rational numbers on Cantor's middle thirds set. 2010. ⟨hal-02550072⟩

Gérald Bourgeois, Jean-Charles Faugère. Algebraic Attack on NTRU using Witt Vectors and Gröbner bases. Journal of Mathematical Cryptology, 2010, 3 (3), pp.205--214. ⟨10.1515/jmc.2009.011⟩. ⟨hal-01148133⟩

Gerald Bourgeois. The matrix equation log(XY)=log(X)+log(Y). Linear Algebra and its Applications, 2010, 432 (8), pp.1878-1884. ⟨10.1016/j.laa.2008.12.024⟩. ⟨hal-03417850⟩

David Adam, Jean-Luc Chabert, Youssef Fares. Subsets of ℤ with Simultaneous Orderings. Integers : Electronic Journal of Combinatorial Number Theory, 2010, 10 (4), ⟨10.1515/integ.2010.037⟩. ⟨hal-03417921⟩

Roger Oyono. Non-hyperelliptic modular Jacobians of dimension 3. Mathematics of Computation, 2009, 78 (266), pp.1173-1191. ⟨10.1090/S0025-5718-08-02174-1⟩. ⟨hal-03417861⟩

Gerald Bourgeois. Algebraic systems of matrices and Gröbner basis theory. Linear Algebra and its Applications, 2009, 430 (8-9), pp.2157-2169. ⟨10.1016/j.laa.2008.11.031⟩. ⟨hal-03417849⟩

Stéphane Ballet. On the tensor rank of the multiplication in the finite fields. Journal of Number Theory, 2008, 128 (6), pp.1795-1806. ⟨10.1016/j.jnt.2007.06.010⟩. ⟨hal-03417837⟩

Jean Chaumine. Multiplication in small finite fields using elliptic curves. On Number Theory and its Applications, 2008, 5, pp.343-350. ⟨10.1142/9789812793430_0018⟩. ⟨hal-03417871⟩

Régis Blache, Éric Férard, Hui June Zhu. Hodge-Stickelberger polygons for $L$-functions of exponential sums of $P(x^s)$. Mathematical Research Letters, 2008, 15 (5), pp.1053-1071. ⟨10.4310/MRL.2008.v15.n5.a17⟩. ⟨hal-03417929⟩

Stéphane Ballet. A note on the tensor rank of the multiplication in certain finite fields. On Number Theory and its Applications, 2008, 5, pp.332-342. ⟨10.1142/9789812793430_0017⟩. ⟨hal-03417870⟩

David Adam. Pólya and Newtonian function fields. Manuscripta mathematica, 2008, 126 (2), pp.231-246. ⟨10.1007/s00229-008-0173-z⟩. ⟨hal-03417795⟩

Stéphane Flon, Roger Oyono, Christophe Ritzenthaler. Fast addition on non-hyperelliptic genus 3 curves. On Number Theory and its Applications, 2008, pp.1-28. ⟨10.1142/9789812793430_0001⟩. ⟨hal-03417869⟩

Eric Férard, François Rodier. Nonlinarity of Boolean functions and hyperelliptic curves. 2007. ⟨hal-00145890⟩

Régis Blache, Éric Férard. Newton stratification for polynomials: The open stratum. Journal of Number Theory, 2007, 123 (2), pp.456-472. ⟨10.1016/j.jnt.2006.06.009⟩. ⟨hal-03417835⟩

Régis Blache, Jean-Pierre Cherdieu, Jorge Estrada Sarlabous. Some computational aspects of Jacobians of curves in the family y3=γx5+δ over Fp. Finite Fields and Their Applications, 2007, 13 (2), pp.348-365. ⟨10.1016/j.ffa.2005.09.003⟩. ⟨hal-03417829⟩

R. Granger, F. Hess, R. Oyono, N. Thériault, F. Vercauteren. Ate Pairing on Hyperelliptic Curves. Advances in Cryptology - EUROCRYPT 2007, 4515, Springer Berlin Heidelberg, pp.430-447, 2007, Lecture Notes in Computer Science, ⟨10.1007/978-3-540-72540-4_25⟩. ⟨hal-03417782⟩

Régis Blache. On certain character sums overp -adic rings and theirL -functions. Mathematical News / Mathematische Nachrichten, 2007, 280 (15), pp.1681-1697. ⟨10.1002/mana.200510571⟩. ⟨hal-03417779⟩

Gerald Bourgeois. On commuting exponentials in low dimensions. Linear Algebra and its Applications, 2007, 423 (2-3), pp.277-286. ⟨10.1016/j.laa.2006.12.019⟩. ⟨hal-03417848⟩

François Rodier, Eric Férard. Non linéarité des fonctions booléennes données par des traces de polynômes de degré binaire 3. 2007. ⟨hal-00151591⟩

S. Ballet. An improvement of the construction of the D.V. and G.V. Chudnovsky algorithm for multiplication in finite fields. Theoretical Computer Science, 2006, 352 (1-3), pp.293-305. ⟨10.1016/j.tcs.2005.11.045⟩. ⟨hal-03417855⟩

S. Ballet, D. Le Brigand. On the existence of non-special divisors of degree g and g-1 in algebraic function fields over Fq. Journal of Number Theory, 2006, 116 (2), pp.293-310. ⟨10.1016/j.jnt.2005.04.009⟩. ⟨hal-03417833⟩

Jean Chaumine. Complexité bilinéaire de la multiplication dans des petits corps finis. Comptes Rendus. Mathématique, 2006, 343 (4), pp.265-266. ⟨10.1016/j.crma.2006.06.030⟩. ⟨hal-03417823⟩

Régis Blache. A Stickelberger theorem for p-adic Gauss sums. Acta Arithmetica, 2005, 118 (1), pp.11-26. ⟨10.4064/aa118-1-2⟩. ⟨hal-03417927⟩

S. Ballet, R. Rolland. Multiplication algorithm in a finite field and tensor rank of the multiplication. Journal of Algebra, 2004, 272 (1), pp.173-185. ⟨10.1016/j.jalgebra.2003.09.031⟩. ⟨hal-03417830⟩

Stéphane Ballet, Jean Chaumine. Amélioration des bornes de la complexité bilinéaire de la multiplication dans certains corps finis. Comptes Rendus. Mathématique, 2004, 339 (6), pp.383-385. ⟨10.1016/j.crma.2004.06.011⟩. ⟨hal-03417822⟩

Régis Blache. Exponential sums over lifts of points. Journal of Number Theory, 2004, 105 (2), pp.361-386. ⟨10.1016/j.jnt.2003.10.004⟩. ⟨hal-03417832⟩

Stéphane Ballet, Jean Chaumine. On the Bounds of the Bilinear Complexity of Multiplication in Some Finite Fields. Applicable Algebra in Engineering, Communication and Computing, 2004, 15 (3-4), pp.205-221. ⟨10.1007/s00200-004-0155-7⟩. ⟨hal-03417791⟩

Stéphane Flon, Roger Oyono. Fast Arithmetic on Jacobians of Picard Curves. 2947, Springer Berlin Heidelberg, pp.55-68, 2004, Lecture Notes in Computer Science, ⟨10.1007/978-3-540-24632-9_5⟩. ⟨hal-04085500⟩

Stéphane Ballet. Low increasing tower of algebraic function fields and bilinear complexity of multiplication in any extension of Fq. Finite Fields and Their Applications, 2003, 9 (4), pp.472-478. ⟨10.1016/S1071-5797(03)00026-1⟩. ⟨hal-03417819⟩

Eric Férard. Weight of duals of BCH codes and exponential sums. Finite Fields and Their Applications, 2003, 9 (1), pp.1-19. ⟨10.1016/S1071-5797(02)00016-3⟩. ⟨hal-03417817⟩