Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen Reconstructing plane quartics from their invariants. (English) Zbl 1439.13020 Discrete Comput. Geom. 63, No. 1, 73-113 (2020). Reviewer: Peter Schenzel (Halle) MSC: 13A50 14L24 14H10 14H25 PDF BibTeX XML Cite \textit{R. Lercier} et al., Discrete Comput. Geom. 63, No. 1, 73--113 (2020; Zbl 1439.13020) Full Text: DOI
Lercier, Reynald; Ritzenthaler, Christophe; Rovetta, Florent; Sijsling, Jeroen; Smith, Benjamin Distributions of traces of Frobenius for smooth plane curves over finite fields. (English) Zbl 1431.14047 Exp. Math. 28, No. 1, 39-48 (2019). Reviewer: Fernando Torres (Campinas) MSC: 14Q05 14H10 14H25 14H37 14H45 14H50 PDF BibTeX XML Cite \textit{R. Lercier} et al., Exp. Math. 28, No. 1, 39--48 (2019; Zbl 1431.14047) Full Text: DOI
Kılıçer, Pınar; Labrande, Hugo; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen; Streng, Marco Plane quartics over \(\mathbb {Q}\) with complex multiplication. (English) Zbl 1409.14051 Acta Arith. 185, No. 2, 127-156 (2018). Reviewer: Tony Ezome (Libreville) MSC: 14H25 11G15 11Y40 14H45 14K22 14K25 14Q05 13A50 PDF BibTeX XML Cite \textit{P. Kılıçer} et al., Acta Arith. 185, No. 2, 127--156 (2018; Zbl 1409.14051) Full Text: DOI
Lercier, Reynald; Olive, Marc Covariant algebra of the binary nonic and the binary decimic. (English) Zbl 1366.13006 Bassa, Alp (ed.) et al., Arithmetic, geometry, cryptography and coding theory. 15th international conference on arithmetic, geometry, cryptography, and coding theory (AGCT), CIRM, Luminy, France, May 18–22, 2015. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2810-5/pbk; 978-1-4704-3745-9/ebook). Contemporary Mathematics 686, 65-91 (2017). Reviewer: Ivo M. Michailov (Shumen) MSC: 13A50 13C99 14Q99 PDF BibTeX XML Cite \textit{R. Lercier} and \textit{M. Olive}, Contemp. Math. 686, 65--91 (2017; Zbl 1366.13006) Full Text: DOI arXiv
Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group. (English) Zbl 1343.14047 Math. Comput. 85, No. 300, 2011-2045 (2016). Reviewer: Sungkon Chang (Savannah) MSC: 14Q05 13A50 14H10 14H25 14H37 PDF BibTeX XML Cite \textit{R. Lercier} et al., Math. Comput. 85, No. 300, 2011--2045 (2016; Zbl 1343.14047) Full Text: DOI arXiv
Couveignes, Jean-Marc; Lercier, Reynald The geometry of some parameterizations and encodings. (English) Zbl 1314.14053 Adv. Math. Commun. 8, No. 4, 437-458 (2014). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 14H45 14E20 11G20 12G05 11S20 PDF BibTeX XML Cite \textit{J.-M. Couveignes} and \textit{R. Lercier}, Adv. Math. Commun. 8, No. 4, 437--458 (2014; Zbl 1314.14053) Full Text: DOI arXiv
Lercier, Reynald; Ritzenthaler, Christophe; Rovetta, Florent; Sijsling, Jeroen Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields. (English) Zbl 1333.14060 LMS J. Comput. Math. 17A, Spec. Iss., 128-147 (2014). Reviewer: Fernando Torres (Campinas) MSC: 14Q05 13A50 14H10 14H37 PDF BibTeX XML Cite \textit{R. Lercier} et al., LMS J. Comput. Math. 17A, 128--147 (2014; Zbl 1333.14060) Full Text: DOI arXiv
Basson, Romain; Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen An explicit expression of the Lüroth invariant. (English) Zbl 1360.68915 Kauers, Manuel (ed.), Proceedings of the 38th international symposium on symbolic and algebraic computation, ISSAC 2013, Boston, MA, USA, June 26–29, 2013. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-2059-7). 31-36 (2013). MSC: 68W30 14H50 14Q05 PDF BibTeX XML Cite \textit{R. Basson} et al., in: Proceedings of the 38th international symposium on symbolic and algebraic computation, ISSAC 2013, Boston, MA, USA, June 26--29, 2013. New York, NY: Association for Computing Machinery (ACM). 31--36 (2013; Zbl 1360.68915) Full Text: DOI arXiv
Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent. (English) Zbl 1344.11049 Howe, Everett W. (ed.) et al., ANTS X. Proceedings of the tenth algorithmic number theory symposium, San Diego, CA, USA, July 9–13, 2012. Berkeley, CA: Mathematical Sciences Publishers (MSP) (ISBN 978-1-935107-00-2/hbk; 978-1-935107-01-9/ebook). The Open Book Series 1, 463-486 (2013). MSC: 11G30 14Q05 14H45 PDF BibTeX XML Cite \textit{R. Lercier} et al., Open Book Ser. 1, 463--486 (2013; Zbl 1344.11049) Full Text: arXiv
Couveignes, Jean-Marc; Lercier, Reynald Fast construction of irreducible polynomials over finite fields. (English) Zbl 1287.11141 Isr. J. Math. 194, Part A, 77-105 (2013). MSC: 11Y16 11T06 12E05 68Q25 68W20 68W30 PDF BibTeX XML Cite \textit{J.-M. Couveignes} and \textit{R. Lercier}, Isr. J. Math. 194, Part A, 77--105 (2013; Zbl 1287.11141) Full Text: DOI arXiv
Ezome, Tony; Lercier, Reynald Elliptic periods and primality proving. (English) Zbl 1310.11118 J. Number Theory 133, No. 1, 343-368 (2013). MSC: 11Y11 11Y16 14H52 PDF BibTeX XML Cite \textit{T. Ezome} and \textit{R. Lercier}, J. Number Theory 133, No. 1, 343--368 (2013; Zbl 1310.11118) Full Text: DOI arXiv
Lercier, Reynald; Ritzenthaler, Christophe Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects. (English) Zbl 1276.14088 J. Algebra 372, 595-636 (2012). Reviewer: Enric Nart Viñals (Barcelona) MSC: 14Q05 13A50 14H10 14H37 PDF BibTeX XML Cite \textit{R. Lercier} and \textit{C. Ritzenthaler}, J. Algebra 372, 595--636 (2012; Zbl 1276.14088) Full Text: DOI arXiv
Dunand, Clément; Lercier, Reynald Normal elliptic bases and torus-based cryptography. (English) Zbl 1227.11122 McGuire, Gary (ed.) et al., Finite fields. Theory and applications. Proceedings of the 9th international conference on finite fields and applications, Dublin, Ireland, July 13–17, 2009. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4786-2/pbk). Contemporary Mathematics 518, 137-153 (2010). Reviewer: Robert Fitzgerald (Carbondale) MSC: 11T71 14G50 94A60 PDF BibTeX XML Cite \textit{C. Dunand} and \textit{R. Lercier}, Contemp. Math. 518, 137--153 (2010; Zbl 1227.11122)
Kammerer, Jean-Gabriel; Lercier, Reynald; Renault, Guénaël Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time. (English) Zbl 1290.94100 Joye, Marc (ed.) et al., Pairing-based cryptography – Pairing 2010. 4th international conference, Yamanaka Hot Spring, Japan, December 13–15, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-17454-4/pbk). Lecture Notes in Computer Science 6487, 278-297 (2010). MSC: 94A60 12F10 14G50 PDF BibTeX XML Cite \textit{J.-G. Kammerer} et al., Lect. Notes Comput. Sci. 6487, 278--297 (2010; Zbl 1290.94100) Full Text: DOI
Joux, Antoine; Lercier, Reynald; Naccache, David; Thomé, Emmanuel Oracle-assisted static Diffie-Hellman is easier than discrete logarithms. (English) Zbl 1234.94050 Parker, Matthew G. (ed.), Cryptography and coding. 12th IMA international conference, cryptography and coding 2009, Cirencester, UK, December 15–17, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-10867-9/pbk). Lecture Notes in Computer Science 5921, 351-367 (2009). MSC: 94A60 PDF BibTeX XML Cite \textit{A. Joux} et al., Lect. Notes Comput. Sci. 5921, 351--367 (2009; Zbl 1234.94050) Full Text: DOI
Couveignes, Jean-Marc; Lercier, Reynald Elliptic periods for finite fields. (English) Zbl 1216.11106 Finite Fields Appl. 15, No. 1, 1-22 (2009). MSC: 11T30 12E20 PDF BibTeX XML Cite \textit{J.-M. Couveignes} and \textit{R. Lercier}, Finite Fields Appl. 15, No. 1, 1--22 (2009; Zbl 1216.11106) Full Text: DOI arXiv
Lercier, Reynald; Sirvent, Thomas On Elkies subgroups of \(\ell\)-torsion points in elliptic curves defined over a finite field. (English) Zbl 1230.11080 J. Théor. Nombres Bordx. 20, No. 3, 783-797 (2008). MSC: 11G20 11Y16 PDF BibTeX XML Cite \textit{R. Lercier} and \textit{T. Sirvent}, J. Théor. Nombres Bordx. 20, No. 3, 783--797 (2008; Zbl 1230.11080) Full Text: DOI Numdam EuDML arXiv
Couveignes, Jean-Marc; Lercier, Reynald Galois invariant smoothness basis. (English) Zbl 1151.14311 Chaumine, Jean (ed.) et al., Algebraic geometry and its applications. Dedicated to Gilles Lachaud on his 60th birthday. Proceedings of the first SAGA conference, Papeete, France, May 7–11, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-279-342-3/hbk). Series on Number Theory and Its Applications 5, 142-167 (2008). MSC: 12E20 94A60 PDF BibTeX XML Cite \textit{J.-M. Couveignes} and \textit{R. Lercier}, Ser. Number Theory Appl. 5, 142--167 (2008; Zbl 1151.14311) Full Text: DOI arXiv
Joux, Antoine; Lercier, Reynald Algorithms to solve the finite field discrete logarithm problem. (Algorithmes pour résoudre le problème du logarithme discret dans les corps finis.) (French. English summary) Zbl 1235.11116 Couveignes, Jean-Marc et al., Nouvelle méthodes mathématiques en cryptographie. Paris: Société Mathématique de France. SMF Journée Annuelle 2007, 23-53 (2007). MSC: 11Y16 12E20 68Q25 94A60 PDF BibTeX XML Cite \textit{A. Joux} and \textit{R. Lercier}, SMF Journ. Annu. 2007, 23--53 (2007; Zbl 1235.11116)
Couveignes, Jean-Marc; Lercier, Reynald; Rolland, Robert; Joux, Antoine New mathematical methods in cryptography. (Nouvelle méthodes mathématiques en cryptographie.) (French) Zbl 1202.11003 SMF Journée Annuelle 2007. Paris: Société Mathématique de France. 85 p. (2007). MSC: 11-06 11T71 94A60 00B15 PDF BibTeX XML Cite \textit{J.-M. Couveignes} et al., Nouvelle méthodes mathématiques en cryptographie. Paris: Société Mathématique de France (2007; Zbl 1202.11003) Full Text: Link
Joux, Antoine; Lercier, Reynald The function field sieve in the medium prime case. (English) Zbl 1140.94349 Vaudenay, Serge (ed.), Advances in cryptology – EUROCRYPT 2006. 25th annual international conference on the theory and applications of cryptographic techniques, St. Petersburg, Russia, May 28 – June 1, 2006. Proceedings. Berlin: Springer (ISBN 3-540-34546-9/pbk). Lecture Notes in Computer Science 4004, 254-270 (2006). MSC: 94A60 11T71 11Y16 PDF BibTeX XML Cite \textit{A. Joux} and \textit{R. Lercier}, Lect. Notes Comput. Sci. 4004, 254--270 (2006; Zbl 1140.94349) Full Text: DOI
Joux, Antoine; Lercier, Reynald; Smart, Nigel; Vercauteren, Frederik The number field sieve in the medium prime case. (English) Zbl 1161.11417 Dwork, Cynthia (ed.), Advances in cryptology – CRYPTO 2006. 26th annual international cryptology conference, Santa Barbara, California, USA, August 20–24, 2006. Proceedings. Berlin: Springer (ISBN 3-540-37432-9/pbk). Lecture Notes in Computer Science 4117, 326-344 (2006). MSC: 11Y16 11T71 94A60 PDF BibTeX XML Cite \textit{A. Joux} et al., Lect. Notes Comput. Sci. 4117, 326--344 (2006; Zbl 1161.11417) Full Text: DOI
Lercier, Reynald; Lubicz, David A quasi quadratic time algorithm for hyperelliptic curve point counting. (English) Zbl 1166.11021 Ramanujan J. 12, No. 3, 399-423 (2006). MSC: 11G20 11S40 14G50 PDF BibTeX XML Cite \textit{R. Lercier} and \textit{D. Lubicz}, Ramanujan J. 12, No. 3, 399--423 (2006; Zbl 1166.11021) Full Text: DOI
Lercier, Reynald; Lubicz, David Counting points on elliptic curves over finite fields of small characteristic in quasi quadratic time. (English) Zbl 1035.11067 Biham, Eli (ed.), Advances in cryptology – EUROCRYPT 2003. International conference on the theory and applications of cryptographic techniques, Warsaw, Poland, May 4–8, 2003. Proceedings. Berlin: Springer (ISBN 3-540-14039-5/pbk). Lect. Notes Comput. Sci. 2656, 360-373 (2003). MSC: 11Y16 11G07 14G50 94A60 PDF BibTeX XML Cite \textit{R. Lercier} and \textit{D. Lubicz}, Lect. Notes Comput. Sci. 2656, 360--373 (2003; Zbl 1035.11067) Full Text: Link
Joux, Antoine; Lercier, Reynald Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the Gaussian integer method. (English) Zbl 1099.11074 Math. Comput. 72, No. 242, 953-967 (2003). MSC: 11Y16 11T71 11Y40 68Q25 94A60 PDF BibTeX XML Cite \textit{A. Joux} and \textit{R. Lercier}, Math. Comput. 72, No. 242, 953--967 (2003; Zbl 1099.11074) Full Text: DOI
Joux, Antoine; Lercier, Reynald The function field sieve is quite special. (English) Zbl 1057.11069 Fieker, Claus (ed.) et al., Algorithmic number theory. 5th international symposium, ANTS-V, Sydney, Australia, July 7–12, 2002. Proceedings. Berlin: Springer (ISBN 3-540-43863-7). Lect. Notes Comput. Sci. 2369, 431-445 (2002). MSC: 11Y16 11R58 11Y05 PDF BibTeX XML Cite \textit{A. Joux} and \textit{R. Lercier}, Lect. Notes Comput. Sci. 2369, 431--445 (2002; Zbl 1057.11069) Full Text: Link
Joux, Antoine; Lercier, Reynald “Chinese & Match”, an alternative to Atkin’s “Match and Sort” method used in the SEA algorithm. (English) Zbl 1011.11080 Math. Comput. 70, No. 234, 827-836 (2001). MSC: 11Y16 68W30 PDF BibTeX XML Cite \textit{A. Joux} and \textit{R. Lercier}, Math. Comput. 70, No. 234, 827--836 (2001; Zbl 1011.11080) Full Text: DOI
Lercier, R.; Morain, F. Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. (English) Zbl 0963.11032 Math. Comput. 69, No. 229, 351-370 (2000). Reviewer: Amílcar Pacheco (Rio de Janeiro) MSC: 11G20 11T71 94A60 11Y16 PDF BibTeX XML Cite \textit{R. Lercier} and \textit{F. Morain}, Math. Comput. 69, No. 229, 351--370 (2000; Zbl 0963.11032) Full Text: DOI
Lercier, R.; Morain, F. Algorithms for computing isogenies between elliptic curves. (English) Zbl 0922.11110 Buell, D. A. (ed.) et al., Computational perspectives on number theory. Proceedings of a conference in honor of A. O. L. Atkin, Chicago, IL, USA, September 1995. Providence, RI: American Mathematical Society. AMS/IP Stud. Adv. Math. 7, 77-96 (1998). Reviewer: René Schoof (Roma) MSC: 11Y16 11G20 14Q05 14H52 PDF BibTeX XML Cite \textit{R. Lercier} and \textit{F. Morain}, AMS/IP Stud. Adv. Math. 7, 77--96 (1998; Zbl 0922.11110)
Lercier, Reynald Computing isogenies in \(\mathbb{F}_{2^n}\). (English) Zbl 0911.11029 Cohen, Henri (ed.), Algorithmic number theory. Second international symposium, ANTS-II, Talence, France, May 18-23, 1996. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1122, 197-212 (1996). MSC: 11G20 11Y16 PDF BibTeX XML Cite \textit{R. Lercier}, Lect. Notes Comput. Sci. 1122, 197--212 (1996; Zbl 0911.11029)
Lercier, Reynald; Morain, François Counting the number of points on elliptic curves over finite fields: strategies and performances. (English) Zbl 0903.11029 Guillou, Louis C. (ed.) et al., Advances in cryptology - EUROCRYPT ’95. International conference on the theory and application of cryptographic techniques, Saint-Malo, France, May 21-25, 1995. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 921, 79-94 (1995). MSC: 11Y16 94A60 14H52 68W30 PDF BibTeX XML Cite \textit{R. Lercier} and \textit{F. Morain}, Lect. Notes Comput. Sci. 921, 1--12 (1995; Zbl 0903.11029)