Edit Profile (opens in new tab) Lercier, Reynald Co-Author Distance Author ID: lercier.reynald Published as: Lercier, Reynald; Lercier, R. Homepage: https://perso.univ-rennes1.fr/reynald.lercier/ Documents Indexed: 38 Publications since 1995, including 1 Book and 4 Additional arXiv Preprints Co-Authors: 29 Co-Authors with 37 Joint Publications 692 Co-Co-Authors all top 5 Co-Authors 1 single-authored 12 Ritzenthaler, Christophe 8 Joux, Antoine 8 Sijsling, Jeroen 5 Couveignes, Jean-Marc 4 Lorenzo García, Elisa 3 Morain, François 2 Docking, Jordan 2 Lubicz, David 2 Rovetta, Florent 2 van Bommel, Raymond 1 Basson, Romain 1 Caruso, Xavier 1 Dokchitser, Vladimir 1 Dunand, Clément 1 Eid, Élie 1 Ezome, Tony 1 Kammerer, Jean-Gabriel 1 Kılıçer, Pınar 1 Labrande, Hugo 1 Liu, Qing 1 Naccache, David 1 Olive, Marc 1 Renault, Guénaël 1 Rolland, Robert 1 Sirvent, Thomas 1 Smart, Nigel Paul 1 Streng, Marco 1 Thomé, Emmanuel 1 Vercauteren, Frederik all top 5 Serials 4 Mathematics of Computation 1 Israel Journal of Mathematics 1 Acta Arithmetica 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Journal of Number Theory 1 Discrete & Computational Geometry 1 Experimental Mathematics 1 Journal de Théorie des Nombres de Bordeaux 1 Finite Fields and their Applications 1 The Ramanujan Journal 1 LMS Journal of Computation and Mathematics 1 SMF Journée Annuelle 1 Advances in Mathematics of Communications 1 Algebra & Number Theory all top 5 Fields 25 Number theory (11-XX) 22 Algebraic geometry (14-XX) 12 Information and communication theory, circuits (94-XX) 7 Commutative algebra (13-XX) 6 Field theory and polynomials (12-XX) 6 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 31 Publications have been cited 297 times in 191 Documents Cited by ▼ Year ▼ Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects. Zbl 1276.14088 Lercier, Reynald; Ritzenthaler, Christophe 33 2012 The number field sieve in the medium prime case. Zbl 1161.11417 Joux, Antoine; Lercier, Reynald; Smart, Nigel; Vercauteren, Frederik 29 2006 Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the Gaussian integer method. Zbl 1099.11074 Joux, Antoine; Lercier, Reynald 29 2003 Elliptic periods for finite fields. Zbl 1216.11106 Couveignes, Jean-Marc; Lercier, Reynald 19 2009 The function field sieve in the medium prime case. Zbl 1140.94349 Joux, Antoine; Lercier, Reynald 17 2006 Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields. Zbl 1333.14060 Lercier, Reynald; Ritzenthaler, Christophe; Rovetta, Florent; Sijsling, Jeroen 14 2014 Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group. Zbl 1343.14047 Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 13 2016 Plane quartics over \(\mathbb {Q}\) with complex multiplication. Zbl 1409.14051 Kılıçer, Pınar; Labrande, Hugo; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen; Streng, Marco 13 2018 The function field sieve is quite special. Zbl 1057.11069 Joux, Antoine; Lercier, Reynald 12 2002 Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent. Zbl 1344.11049 Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 12 2013 Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time. Zbl 1290.94100 Kammerer, Jean-Gabriel; Lercier, Reynald; Renault, Guénaël 10 2010 Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029 Lercier, Reynald; Morain, François 9 1995 A quasi quadratic time algorithm for hyperelliptic curve point counting. Zbl 1166.11021 Lercier, Reynald; Lubicz, David 8 2006 Computing isogenies in \(\mathbb{F}_{2^n}\). Zbl 0911.11029 Lercier, Reynald 8 1996 On Elkies subgroups of \(\ell\)-torsion points in elliptic curves defined over a finite field. Zbl 1230.11080 Lercier, Reynald; Sirvent, Thomas 8 2008 Covariant algebra of the binary nonic and the binary decimic. Zbl 1366.13006 Lercier, Reynald; Olive, Marc 8 2017 Fast construction of irreducible polynomials over finite fields. Zbl 1287.11141 Couveignes, Jean-Marc; Lercier, Reynald 8 2013 Counting points on elliptic curves over finite fields of small characteristic in quasi quadratic time. Zbl 1035.11067 Lercier, Reynald; Lubicz, David 7 2003 An explicit expression of the Lüroth invariant. Zbl 1360.68915 Basson, Romain; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 5 2013 Reconstructing plane quartics from their invariants. Zbl 1439.13020 Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 5 2020 Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. Zbl 0963.11032 Lercier, R.; Morain, F. 4 2000 Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110 Lercier, R.; Morain, F. 4 1998 “Chinese & Match”, an alternative to Atkin’s “Match and Sort” method used in the SEA algorithm. Zbl 1011.11080 Joux, Antoine; Lercier, Reynald 4 2001 Galois invariant smoothness basis. Zbl 1151.14311 Couveignes, Jean-Marc; Lercier, Reynald 4 2008 Reduction type of smooth plane quartics. Zbl 1494.13006 Lercier, Reynald; Liu, Qing; Lorenzo García, Elisa; Ritzenthaler, Christophe 4 2021 Oracle-assisted static Diffie-Hellman is easier than discrete logarithms. Zbl 1234.94050 Joux, Antoine; Lercier, Reynald; Naccache, David; Thomé, Emmanuel 3 2009 Algorithms to solve the finite field discrete logarithm problem. (Algorithmes pour résoudre le problème du logarithme discret dans les corps finis.) Zbl 1235.11116 Joux, Antoine; Lercier, Reynald 2 2007 The geometry of some parameterizations and encodings. Zbl 1314.14053 Couveignes, Jean-Marc; Lercier, Reynald 2 2014 Elliptic periods and primality proving. Zbl 1310.11118 Ezome, Tony; Lercier, Reynald 1 2013 Distributions of traces of Frobenius for smooth plane curves over finite fields. Zbl 1431.14047 Lercier, Reynald; Ritzenthaler, Christophe; Rovetta, Florent; Sijsling, Jeroen; Smith, Benjamin 1 2019 Stable models of plane quartics with hyperelliptic reduction. Zbl 1519.11035 Lercier, Reynald; Lorenzo García, Elisa; Ritzenthaler, Christophe 1 2021 Reduction type of smooth plane quartics. Zbl 1494.13006 Lercier, Reynald; Liu, Qing; Lorenzo García, Elisa; Ritzenthaler, Christophe 4 2021 Stable models of plane quartics with hyperelliptic reduction. Zbl 1519.11035 Lercier, Reynald; Lorenzo García, Elisa; Ritzenthaler, Christophe 1 2021 Reconstructing plane quartics from their invariants. Zbl 1439.13020 Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 5 2020 Distributions of traces of Frobenius for smooth plane curves over finite fields. Zbl 1431.14047 Lercier, Reynald; Ritzenthaler, Christophe; Rovetta, Florent; Sijsling, Jeroen; Smith, Benjamin 1 2019 Plane quartics over \(\mathbb {Q}\) with complex multiplication. Zbl 1409.14051 Kılıçer, Pınar; Labrande, Hugo; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen; Streng, Marco 13 2018 Covariant algebra of the binary nonic and the binary decimic. Zbl 1366.13006 Lercier, Reynald; Olive, Marc 8 2017 Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group. Zbl 1343.14047 Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 13 2016 Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields. Zbl 1333.14060 Lercier, Reynald; Ritzenthaler, Christophe; Rovetta, Florent; Sijsling, Jeroen 14 2014 The geometry of some parameterizations and encodings. Zbl 1314.14053 Couveignes, Jean-Marc; Lercier, Reynald 2 2014 Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent. Zbl 1344.11049 Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 12 2013 Fast construction of irreducible polynomials over finite fields. Zbl 1287.11141 Couveignes, Jean-Marc; Lercier, Reynald 8 2013 An explicit expression of the Lüroth invariant. Zbl 1360.68915 Basson, Romain; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 5 2013 Elliptic periods and primality proving. Zbl 1310.11118 Ezome, Tony; Lercier, Reynald 1 2013 Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects. Zbl 1276.14088 Lercier, Reynald; Ritzenthaler, Christophe 33 2012 Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time. Zbl 1290.94100 Kammerer, Jean-Gabriel; Lercier, Reynald; Renault, Guénaël 10 2010 Elliptic periods for finite fields. Zbl 1216.11106 Couveignes, Jean-Marc; Lercier, Reynald 19 2009 Oracle-assisted static Diffie-Hellman is easier than discrete logarithms. Zbl 1234.94050 Joux, Antoine; Lercier, Reynald; Naccache, David; Thomé, Emmanuel 3 2009 On Elkies subgroups of \(\ell\)-torsion points in elliptic curves defined over a finite field. Zbl 1230.11080 Lercier, Reynald; Sirvent, Thomas 8 2008 Galois invariant smoothness basis. Zbl 1151.14311 Couveignes, Jean-Marc; Lercier, Reynald 4 2008 Algorithms to solve the finite field discrete logarithm problem. (Algorithmes pour résoudre le problème du logarithme discret dans les corps finis.) Zbl 1235.11116 Joux, Antoine; Lercier, Reynald 2 2007 The number field sieve in the medium prime case. Zbl 1161.11417 Joux, Antoine; Lercier, Reynald; Smart, Nigel; Vercauteren, Frederik 29 2006 The function field sieve in the medium prime case. Zbl 1140.94349 Joux, Antoine; Lercier, Reynald 17 2006 A quasi quadratic time algorithm for hyperelliptic curve point counting. Zbl 1166.11021 Lercier, Reynald; Lubicz, David 8 2006 Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the Gaussian integer method. Zbl 1099.11074 Joux, Antoine; Lercier, Reynald 29 2003 Counting points on elliptic curves over finite fields of small characteristic in quasi quadratic time. Zbl 1035.11067 Lercier, Reynald; Lubicz, David 7 2003 The function field sieve is quite special. Zbl 1057.11069 Joux, Antoine; Lercier, Reynald 12 2002 “Chinese & Match”, an alternative to Atkin’s “Match and Sort” method used in the SEA algorithm. Zbl 1011.11080 Joux, Antoine; Lercier, Reynald 4 2001 Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. Zbl 0963.11032 Lercier, R.; Morain, F. 4 2000 Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110 Lercier, R.; Morain, F. 4 1998 Computing isogenies in \(\mathbb{F}_{2^n}\). Zbl 0911.11029 Lercier, Reynald 8 1996 Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029 Lercier, Reynald; Morain, François 9 1995 all cited Publications top 5 cited Publications all top 5 Cited by 285 Authors 17 Lercier, Reynald 12 Sijsling, Jeroen 11 Ritzenthaler, Christophe 10 Lorenzo García, Elisa 9 Gaudry, Pierrick 8 Barbulescu, Razvan 7 Schost, Éric 7 Thomé, Emmanuel 6 Joux, Antoine 6 Kılıçer, Pınar 6 Morain, François 6 Olive, Marc 6 Pierrot, Cécile 5 Guillevic, Aurore 5 Robert, Damien 4 Ballet, Stéphane 4 Couveignes, Jean-Marc 4 De Feo, Luca 4 Ezome, Tony 4 Lubicz, David 4 Streng, Marco 4 Takagi, Tsuyoshi 4 Tibouchi, Mehdi 3 Badr, Eslam E. 3 Bars Cortina, Francesc 3 Biasse, Jean-François 3 Bonnecaze, Alexis 3 De Micheli, Gabrielle 3 Desmorat, Rodrigue 3 Farashahi, Reza Rezaeian 3 Galbraith, Steven D. 3 Grémy, Laurent 3 Kim, Taechan 3 Kleinjung, Thorsten 3 Kolev, Boris 3 Menezes, Alfred J. 3 Rodríguez-Henríquez, Francisco 3 Rolland, Robert 2 Adj, Gora 2 Atighehchi, Kévin 2 Bartz, Hannes 2 Bouw, Irene I. 2 Carls, Robert 2 Caruso, Xavier 2 Desmorat, Boris 2 Eid, Élie 2 Faugère, Jean-Charles 2 Fouque, Pierre-Alain 2 Gélin, Alexandre 2 Granger, Robert A. 2 Hayasaka, Kenichiro 2 Heninger, Nadia 2 Hidalgo, Rubén Antonio 2 Ionica, Sorina 2 Karemaker, Valentijn 2 Kobayashi, Tetsutaro 2 Kudo, Momonari 2 Lauter, Kristin Estella 2 Lecerf, Grégoire 2 Lombardo, Davide M. 2 Massierer, Maike 2 Moody, Dustin 2 Oliveira, Thomaz 2 Petit, Christophe 2 Puchinger, Sven 2 Rovetta, Florent 2 Sall, Mohamadou 2 Sarkar, Palash 2 Shaska, Tanush 2 Silverberg, Alice 2 Somoza, Anna 2 Sturmfels, Bernd 2 van der Hoeven, Joris 2 Vincent, Christelle 2 Wachter-Zeh, Antonia 2 Zhuang, Jincheng 2 Zimmermann, Paul 1 Abdesselam, Abdelmalek 1 Agostini, Daniele 1 Akleylek, Sedat 1 Al Aswad, Haetham 1 Alcazar, Juan Gerardo 1 Aoki, Kazumaro 1 Arias-de-Reyna, Sara 1 Armana, Cécile 1 Arnault, François 1 Artebani, Michela 1 Asgarli, Shamil 1 Auffray, Nicolas 1 Baaziz, Houria 1 Bazan, Erick Rodriguez 1 Bernstein, Daniel Julius 1 Beshaj, Lubjana 1 Bisson, Gaetan 1 Bluher, Antonia Wilson 1 Bose, Sownak 1 Bostan, Alin 1 Boudjou, Hortense 1 Boudot, Fabrice 1 Braun, Lukas ...and 185 more Authors all top 5 Cited in 62 Serials 23 Mathematics of Computation 10 Journal of Symbolic Computation 10 LMS Journal of Computation and Mathematics 7 Designs, Codes and Cryptography 7 Finite Fields and their Applications 6 Journal of Cryptology 6 Advances in Mathematics of Communications 5 Journal of Algebra 5 Journal of Number Theory 4 International Journal of Number Theory 4 Research in Number Theory 3 Mathematics in Computer Science 2 Acta Arithmetica 2 Archiv der Mathematik 2 Journal of the London Mathematical Society. Second Series 2 Applicable Algebra in Engineering, Communication and Computing 2 Experimental Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 Foundations of Computational Mathematics 2 Journal of Mathematical Cryptology 1 Archive for Rational Mechanics and Analysis 1 Discrete Applied Mathematics 1 International Journal of Engineering Science 1 Nonlinearity 1 Russian Mathematical Surveys 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 Canadian Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Combinatorial Theory. Series A 1 Journal of Computational and Applied Mathematics 1 Journal of the Mathematical Society of Japan 1 Journal of Pure and Applied Algebra 1 Kodai Mathematical Journal 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Osaka Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Theoretical Computer Science 1 Computer Aided Geometric Design 1 Journal of Complexity 1 Discrete & Computational Geometry 1 Journal of the American Mathematical Society 1 SIAM Journal on Discrete Mathematics 1 Journal of Elasticity 1 Computational Complexity 1 Journal of Mathematical Sciences (New York) 1 The Ramanujan Journal 1 Revista Matemática Complutense 1 Journal of Discrete Mathematical Sciences & Cryptography 1 Journal of High Energy Physics 1 Journal of Applied Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of Algebra and its Applications 1 Algebra & Number Theory 1 Foundations and Trends in Communications and Information Theory 1 JSIAM Letters 1 Research in the Mathematical Sciences 1 Prikladnaya Diskretnaya Matematika 1 Matematicheskie Voprosy Kriptografii all top 5 Cited in 20 Fields 118 Number theory (11-XX) 108 Algebraic geometry (14-XX) 67 Information and communication theory, circuits (94-XX) 28 Computer science (68-XX) 15 Commutative algebra (13-XX) 14 Field theory and polynomials (12-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 4 Numerical analysis (65-XX) 4 Mechanics of deformable solids (74-XX) 4 Quantum theory (81-XX) 3 Functions of a complex variable (30-XX) 2 Combinatorics (05-XX) 2 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) Citations by Year