Edit Profile (opens in new tab) Lercier, Reynald Compute Distance To: Compute Author ID: lercier.reynald Published as: Lercier, Reynald; Lercier, R. Documents Indexed: 33 Publications since 1995, including 1 Book Co-Authors: 25 Co-Authors with 32 Joint Publications 561 Co-Co-Authors all top 5 Co-Authors 1 single-authored 9 Ritzenthaler, Christophe 8 Joux, Antoine 7 Sijsling, Jeroen 5 Couveignes, Jean-Marc 3 Morain, François 2 Lubicz, David 2 Rovetta, Florent 1 Basson, Romain 1 Caruso, Xavier 1 Dunand, Clément 1 Eid, Élie 1 Ezome, Tony 1 Kammerer, Jean-Gabriel 1 Kılıçer, Pınar 1 Labrande, Hugo 1 Lorenzo García, Elisa 1 Naccache, David 1 Olive, Marc 1 Renault, Guénaël 1 Rolland, Robert 1 Sirvent, Thomas 1 Smart, Nigel P. 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 22 Number theory (11-XX) 19 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 28 Publications have been cited 223 times in 150 Documents Cited by ▼ Year ▼ Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects. Zbl 1276.14088Lercier, Reynald; Ritzenthaler, Christophe 23 2012 Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the Gaussian integer method. Zbl 1099.11074Joux, Antoine; Lercier, Reynald 23 2003 The number field sieve in the medium prime case. Zbl 1161.11417Joux, Antoine; Lercier, Reynald; Smart, Nigel; Vercauteren, Frederik 21 2006 Elliptic periods for finite fields. Zbl 1216.11106Couveignes, Jean-Marc; Lercier, Reynald 14 2009 The function field sieve in the medium prime case. Zbl 1140.94349Joux, Antoine; Lercier, Reynald 14 2006 The function field sieve is quite special. Zbl 1057.11069Joux, Antoine; Lercier, Reynald 11 2002 Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group. Zbl 1343.14047Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 10 2016 Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time. Zbl 1290.94100Kammerer, Jean-Gabriel; Lercier, Reynald; Renault, Guénaël 8 2010 Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent. Zbl 1344.11049Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 8 2013 Plane quartics over \(\mathbb {Q}\) with complex multiplication. Zbl 1409.14051Kılıçer, Pınar; Labrande, Hugo; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen; Streng, Marco 8 2018 Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields. Zbl 1333.14060Lercier, Reynald; Ritzenthaler, Christophe; Rovetta, Florent; Sijsling, Jeroen 8 2014 A quasi quadratic time algorithm for hyperelliptic curve point counting. Zbl 1166.11021Lercier, Reynald; Lubicz, David 7 2006 Computing isogenies in \(\mathbb{F}_{2^n}\). Zbl 0911.11029Lercier, Reynald 7 1996 On Elkies subgroups of \(\ell\)-torsion points in elliptic curves defined over a finite field. Zbl 1230.11080Lercier, Reynald; Sirvent, Thomas 6 2008 Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029Lercier, Reynald; Morain, François 6 1995 Covariant algebra of the binary nonic and the binary decimic. Zbl 1366.13006Lercier, Reynald; Olive, Marc 6 2017 Counting points on elliptic curves over finite fields of small characteristic in quasi quadratic time. Zbl 1035.11067Lercier, Reynald; Lubicz, David 6 2003 Fast construction of irreducible polynomials over finite fields. Zbl 1287.11141Couveignes, Jean-Marc; Lercier, Reynald 5 2013 An explicit expression of the Lüroth invariant. Zbl 1360.68915Basson, Romain; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 5 2013 Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. Zbl 0963.11032Lercier, R.; Morain, F. 4 2000 Galois invariant smoothness basis. Zbl 1151.14311Couveignes, Jean-Marc; Lercier, Reynald 4 2008 Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110Lercier, R.; Morain, F. 4 1998 “Chinese & Match”, an alternative to Atkin’s “Match and Sort” method used in the SEA algorithm. Zbl 1011.11080Joux, Antoine; Lercier, Reynald 4 2001 Oracle-assisted static Diffie-Hellman is easier than discrete logarithms. Zbl 1234.94050Joux, 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 1235.11116Joux, Antoine; Lercier, Reynald 2 2007 The geometry of some parameterizations and encodings. Zbl 1314.14053Couveignes, Jean-Marc; Lercier, Reynald 2 2014 Reconstructing plane quartics from their invariants. Zbl 1439.13020Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 2 2020 Reduction type of smooth plane quartics. Zbl 07419500Lercier, Reynald; Liu, Qing; Lorenzo García, Elisa; Ritzenthaler, Christophe 2 2021 Reduction type of smooth plane quartics. Zbl 07419500Lercier, Reynald; Liu, Qing; Lorenzo García, Elisa; Ritzenthaler, Christophe 2 2021 Reconstructing plane quartics from their invariants. Zbl 1439.13020Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 2 2020 Plane quartics over \(\mathbb {Q}\) with complex multiplication. Zbl 1409.14051Kılıçer, Pınar; Labrande, Hugo; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen; Streng, Marco 8 2018 Covariant algebra of the binary nonic and the binary decimic. Zbl 1366.13006Lercier, Reynald; Olive, Marc 6 2017 Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group. Zbl 1343.14047Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 10 2016 Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields. Zbl 1333.14060Lercier, Reynald; Ritzenthaler, Christophe; Rovetta, Florent; Sijsling, Jeroen 8 2014 The geometry of some parameterizations and encodings. Zbl 1314.14053Couveignes, Jean-Marc; Lercier, Reynald 2 2014 Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent. Zbl 1344.11049Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 8 2013 Fast construction of irreducible polynomials over finite fields. Zbl 1287.11141Couveignes, Jean-Marc; Lercier, Reynald 5 2013 An explicit expression of the Lüroth invariant. Zbl 1360.68915Basson, Romain; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen 5 2013 Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects. Zbl 1276.14088Lercier, Reynald; Ritzenthaler, Christophe 23 2012 Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time. Zbl 1290.94100Kammerer, Jean-Gabriel; Lercier, Reynald; Renault, Guénaël 8 2010 Elliptic periods for finite fields. Zbl 1216.11106Couveignes, Jean-Marc; Lercier, Reynald 14 2009 Oracle-assisted static Diffie-Hellman is easier than discrete logarithms. Zbl 1234.94050Joux, 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 1230.11080Lercier, Reynald; Sirvent, Thomas 6 2008 Galois invariant smoothness basis. Zbl 1151.14311Couveignes, 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 1235.11116Joux, Antoine; Lercier, Reynald 2 2007 The number field sieve in the medium prime case. Zbl 1161.11417Joux, Antoine; Lercier, Reynald; Smart, Nigel; Vercauteren, Frederik 21 2006 The function field sieve in the medium prime case. Zbl 1140.94349Joux, Antoine; Lercier, Reynald 14 2006 A quasi quadratic time algorithm for hyperelliptic curve point counting. Zbl 1166.11021Lercier, Reynald; Lubicz, David 7 2006 Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the Gaussian integer method. Zbl 1099.11074Joux, Antoine; Lercier, Reynald 23 2003 Counting points on elliptic curves over finite fields of small characteristic in quasi quadratic time. Zbl 1035.11067Lercier, Reynald; Lubicz, David 6 2003 The function field sieve is quite special. Zbl 1057.11069Joux, Antoine; Lercier, Reynald 11 2002 “Chinese & Match”, an alternative to Atkin’s “Match and Sort” method used in the SEA algorithm. Zbl 1011.11080Joux, Antoine; Lercier, Reynald 4 2001 Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. Zbl 0963.11032Lercier, R.; Morain, F. 4 2000 Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110Lercier, R.; Morain, F. 4 1998 Computing isogenies in \(\mathbb{F}_{2^n}\). Zbl 0911.11029Lercier, Reynald 7 1996 Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029Lercier, Reynald; Morain, François 6 1995 all cited Publications top 5 cited Publications all top 5 Cited by 236 Authors 15 Lercier, Reynald 8 Ritzenthaler, Christophe 8 Sijsling, Jeroen 7 Barbulescu, Razvan 7 Lorenzo García, Elisa 6 Schost, Éric 5 Gaudry, Pierrick 5 Joux, Antoine 5 Morain, François 5 Olive, Marc 4 Ballet, Stéphane 4 De Feo, Luca 4 Kılıçer, Pınar 4 Lubicz, David 3 Badr, Eslam E. 3 Bars Cortina, Francesc 3 Biasse, Jean-François 3 Bonnecaze, Alexis 3 Couveignes, Jean-Marc 3 Ezome, Tony 3 Farashahi, Reza Rezaeian 3 Galbraith, Steven D. 3 Guillevic, Aurore 3 Kim, Taechan 3 Kleinjung, Thorsten 3 Menezes, Alfred J. 3 Robert, Damien 3 Rolland, Robert 3 Streng, Marco 3 Thomé, Emmanuel 3 Tibouchi, Mehdi 2 Adj, Gora 2 Atighehchi, Kévin 2 Carls, Robert 2 Desmorat, Rodrigue 2 Faugère, Jean-Charles 2 Fouque, Pierre-Alain 2 Granger, Robert A. 2 Hayasaka, Kenichiro 2 Hidalgo, Rubén Antonio 2 Karemaker, Valentijn 2 Kolev, Boris 2 Lauter, Kristin Estella 2 Lecerf, Grégoire 2 Massierer, Maike 2 Moody, Dustin 2 Oliveira, Thomaz 2 Petit, Christophe 2 Pierrot, Cécile 2 Rodríguez-Henríquez, Francisco 2 Rovetta, Florent 2 Sall, Mohamadou 2 Shaska, Tanush 2 Silverberg, Alice 2 Sturmfels, Bernd 2 Takagi, Tsuyoshi 2 van der Hoeven, Joris 2 Vincent, Christelle 2 Zhuang, Jincheng 1 Abdesselam, Abdelmalek 1 Agostini, Daniele 1 Akleylek, Sedat 1 Alcazar, Juan Gerardo 1 Aoki, Kazumaro 1 Arias-de-Reyna, Sara 1 Armana, Cécile 1 Arnault, François 1 Artebani, Michela 1 Auffray, Nicolas 1 Baaziz, Houria 1 Bernstein, Daniel Julius 1 Beshaj, Lubjana 1 Bisson, Gaetan 1 Bluher, Antonia Wilson 1 Bose, Sownak 1 Bostan, Alin 1 Boudjou, Hortense 1 Braun, Lukas 1 Breiding, Paul 1 Bremner, Murray R. 1 Brieulle, Ludovic 1 Bunyawat, Aunyarat 1 Canales-Martínez, Isaac 1 Caruso, Xavier 1 Çelik, Türkü Özlüm 1 Chatel, Gweltaz 1 Chaumine, Jean 1 Chen, Tien-Ren 1 Cheng, Chen-Mou 1 Cheng, Qi 1 Constantinescu, Nicolae Mircea 1 Cruz-Cortés, Nareli 1 Dang, Thinh H. 1 David, Nicolas 1 Desmorat, Boris 1 Devi, Kiran 1 Dewaghe, Laurent 1 Diarra, Nafissatou 1 Diem, Claus 1 Doliskani, Javad ...and 136 more Authors all top 5 Cited in 56 Serials 21 Mathematics of Computation 10 LMS Journal of Computation and Mathematics 7 Journal of Symbolic Computation 6 Designs, Codes and Cryptography 6 Finite Fields and their Applications 5 Journal of Number Theory 5 Journal of Cryptology 5 Advances in Mathematics of Communications 4 Journal of Algebra 4 International Journal of Number Theory 3 Research in Number Theory 2 Acta Arithmetica 2 Archiv der Mathematik 2 Applicable Algebra in Engineering, Communication and Computing 2 Journal de Théorie des Nombres de Bordeaux 2 Foundations of Computational Mathematics 2 Mathematics in Computer Science 2 Journal of Mathematical Cryptology 1 Archive for Rational Mechanics and Analysis 1 Discrete Applied Mathematics 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 Computational and Applied Mathematics 1 Journal of the Mathematical Society of Japan 1 Journal of Pure and Applied Algebra 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 Experimental Mathematics 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 JSIAM Letters 1 Research in the Mathematical Sciences 1 Prikladnaya Diskretnaya Matematika 1 Matematicheskie Voprosy Kriptografii all top 5 Cited in 19 Fields 99 Number theory (11-XX) 88 Algebraic geometry (14-XX) 51 Information and communication theory, circuits (94-XX) 20 Computer science (68-XX) 14 Field theory and polynomials (12-XX) 13 Commutative algebra (13-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Numerical analysis (65-XX) 3 Functions of a complex variable (30-XX) 3 Mechanics of deformable solids (74-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 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) Citations by Year