Edit Profile Morain, François Compute Distance To: Compute Author ID: morain.francois Published as: Morain, F.; Morain, François External Links: MGP · Wikidata · GND Documents Indexed: 44 Publications since 1989, including 2 Books all top 5 Co-Authors 16 single-authored 4 Enge, Andreas 3 Gaudry, Pierrick 3 Guillevic, Aurore 3 Lercier, Reynald 3 Thomé, Emmanuel 2 Atkin, Arthur Oliver Lonsdale 2 Hanrot, Guillaume 2 Schost, Éric 1 Aardal, Karen I. 1 Barbulescu, Razvan 1 Bostan, Alin 1 Cavallar, Stefania Hedwig 1 Couveignes, Jean-Marc 1 Dodsons, Bruce 1 Dupont, Régis 1 Duursma, Iwan Maynard 1 Fouquet, Mireille 1 Franke, Jens 1 Gilchrist, Jeff 1 Grémy, Laurent 1 Guillaume, Delalleau 1 Guillerm, Gérard 1 Joux, Antoine 1 Kleinjung, Thorsten 1 Lenstra, Arjen K. 1 Leprévost, Franck 1 Leyland, Paul C. 1 Lioen, Walter M. 1 Marchand, Joël 1 Mihăilescu, Preda 1 Montgomery, Peter L. 1 Muffett, Alec 1 Murphy, Brian M. 1 Olivos, Jorge 1 Putnam, Chris 1 Putnam, Craig 1 Salvy, Bruno 1 Scribot, Charlotte 1 Shallit, Jeffrey O. 1 Smith, Benjamin J. H. 1 te Riele, Herman 1 Williams, Hugh Cowie 1 Wirth, Thomas 1 Zimmermann, Paul all top 5 Serials 7 Mathematics of Computation 2 Acta Arithmetica 2 Journal of Number Theory 2 Journal de Théorie des Nombres de Bordeaux 1 The Mathematical Intelligencer 1 Utilitas Mathematica 1 Journal of Cryptology 1 RAIRO. Informatique Théorique et Applications 1 Applicable Algebra in Engineering, Communication and Computing 1 LMS Journal of Computation and Mathematics 1 Lecture Notes in Computer Science all top 5 Fields 43 Number theory (11-XX) 18 Algebraic geometry (14-XX) 13 Information and communication theory, circuits (94-XX) 5 Computer science (68-XX) 2 Field theory and polynomials (12-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 37 Publications have been cited 297 times in 197 Documents Cited by ▼ Year ▼ Elliptic curves and primality proving. Zbl 0792.11056Atkin, A. O. L.; Morain, F. 59 1993 Isogeny volcanoes and the SEA algorithm. Zbl 1058.11041Fouquet, Mireille; Morain, François 24 2002 Speeding up the computations on an elliptic curve using addition- subtraction chains. Zbl 0724.11068Morain, François; Olivos, Jorge 23 1990 Fast algorithms for computing isogenies between elliptic curves. Zbl 1200.11097Bostan, A.; Morain, F.; Salvy, B.; Schost, É. 21 2008 Building curves with arbitrary small MOV degree over finite prime fields. Zbl 1084.94014Dupont, Régis; Enge, Andreas; Morain, François 12 2005 Speeding up the discrete log computation on curves with automorphisms. Zbl 0968.14034Duursma, I.; Gaudry, P.; Morain, F. 12 1999 Comparing invariants for class fields of imaginary quadratic fields. Zbl 1058.11077Enge, Andreas; Morain, François 11 2002 Computing the number of points on an elliptic curve over a finite field: algorithmic aspects. Zbl 0843.11030Morain, François 11 1995 Finding suitable curves for the elliptic curve method of factorization. Zbl 0815.11063Atkin, A. O. L.; Morain, F. 11 1993 Improving NFS for the discrete logarithm problem in non-prime finite fields. Zbl 1365.94399Barbulescu, Razvan; Gaudry, Pierrick; Guillevic, Aurore; Morain, François 9 2015 Implementing the asymptotically fast version of the elliptic curve primality proving algorithm. Zbl 1127.11084Morain, F. 9 2007 Primality proving using elliptic curves: An update. Zbl 0908.11061Morain, F. 9 1998 Schoof’s algorithm and isogeny cycles. Zbl 0849.14024Couveignes, Jean-Marc; Morain, François 8 1994 Fast decomposition of polynomials with known Galois group. Zbl 1030.11078Enge, Andreas; Morain, François 7 2003 Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums. Zbl 0874.11044Leprévost, F.; Morain, F. 7 1997 Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029Lercier, Reynald; Morain, François 7 1995 Factorization of a 512-bit RSA modulus. Zbl 1082.94511Cavallar, Stefania; Dodsons, Bruce; Lenstra, Arjen K.; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Aardal, Karen; Gilchrist, Jeff; Guillerm, Gérard; Leyland, Paul; Marchand, Joël; Morain, François; Muffett, Alec; Putnam, Chris; Putnam, Craig; Zimmermann, Paul 6 2000 On character sums related to elliptic curves with complex multiplication. Zbl 0841.11042Joux, A.; Morain, F. 6 1995 Computing the cardinality of CM elliptic curves using torsion points. Zbl 1196.11085Morain, François 4 2007 Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110Lercier, R.; Morain, F. 4 1998 Distributed primality proving and the primality of \((2^{3539} +1)/3\). Zbl 0779.11063Morain, François 4 1991 Elliptic curves and primality testing. Zbl 0947.11500Morain, François 4 1990 Generalised Weber functions. Zbl 1319.11039Enge, Andreas; Morain, François 3 2014 Proving the primality of very large numbers with fastECPP. Zbl 1125.11359Franke, Jens; Kleinjung, Thorsten; Morain, François; Wirth, T. 3 2004 Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. Zbl 0963.11032Lercier, R.; Morain, F. 3 2000 Building cyclic elliptic curves modulo large primes. Zbl 0773.14018Morain, François 3 1991 Elliptic curves, primality proving, and some Titanic primes. Zbl 0760.11041Morain, François 3 1991 Solving discrete logarithms on a 170-bit MNT curve by pairing reduction. Zbl 1418.11159Guillevic, Aurore; Morain, François; Thomé, Emmanuel 2 2017 Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using abelian lifts. Zbl 1190.11067Mihailescu, P.; Morain, F.; Schost, É. 2 2007 Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm. Zbl 1356.11091Gaudry, P.; Morain, F. 2 2006 Building pseudoprimes with a large number of prime factors. Zbl 0862.11005Guillaume, D.; Morain, F. 2 1996 Computing discrete logarithms in \(\mathbb F_{p^6}\). Zbl 1384.94066Grémy, Laurent; Guillevic, Aurore; Morain, François; Thomé, Emmanuel 1 2018 Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Zbl 1196.11006Hanrot, Guillaume (ed.); Morain, François (ed.); Thomé, Emmanuel (ed.) 1 2010 Primality in polynomial time (following Adleman, Huang; Agrawal, Kayal, Saxena). Zbl 1097.11059Morain, François 1 2004 Solvability by radicals from an algorithmic point of view. Zbl 1356.12010Hanrot, G.; Morain, F. 1 2001 Isomorphism classes of supersingular elliptic curves of characteristic \(\geq 3\). Zbl 0898.11023Morain, F. 1 1997 Easy numbers for the elliptic curve primality proving algorithm. Zbl 0921.11070Morain, F. 1 1992 Computing discrete logarithms in \(\mathbb F_{p^6}\). Zbl 1384.94066Grémy, Laurent; Guillevic, Aurore; Morain, François; Thomé, Emmanuel 1 2018 Solving discrete logarithms on a 170-bit MNT curve by pairing reduction. Zbl 1418.11159Guillevic, Aurore; Morain, François; Thomé, Emmanuel 2 2017 Improving NFS for the discrete logarithm problem in non-prime finite fields. Zbl 1365.94399Barbulescu, Razvan; Gaudry, Pierrick; Guillevic, Aurore; Morain, François 9 2015 Generalised Weber functions. Zbl 1319.11039Enge, Andreas; Morain, François 3 2014 Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Zbl 1196.11006Hanrot, Guillaume (ed.); Morain, François (ed.); Thomé, Emmanuel (ed.) 1 2010 Fast algorithms for computing isogenies between elliptic curves. Zbl 1200.11097Bostan, A.; Morain, F.; Salvy, B.; Schost, É. 21 2008 Implementing the asymptotically fast version of the elliptic curve primality proving algorithm. Zbl 1127.11084Morain, F. 9 2007 Computing the cardinality of CM elliptic curves using torsion points. Zbl 1196.11085Morain, François 4 2007 Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using abelian lifts. Zbl 1190.11067Mihailescu, P.; Morain, F.; Schost, É. 2 2007 Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm. Zbl 1356.11091Gaudry, P.; Morain, F. 2 2006 Building curves with arbitrary small MOV degree over finite prime fields. Zbl 1084.94014Dupont, Régis; Enge, Andreas; Morain, François 12 2005 Proving the primality of very large numbers with fastECPP. Zbl 1125.11359Franke, Jens; Kleinjung, Thorsten; Morain, François; Wirth, T. 3 2004 Primality in polynomial time (following Adleman, Huang; Agrawal, Kayal, Saxena). Zbl 1097.11059Morain, François 1 2004 Fast decomposition of polynomials with known Galois group. Zbl 1030.11078Enge, Andreas; Morain, François 7 2003 Isogeny volcanoes and the SEA algorithm. Zbl 1058.11041Fouquet, Mireille; Morain, François 24 2002 Comparing invariants for class fields of imaginary quadratic fields. Zbl 1058.11077Enge, Andreas; Morain, François 11 2002 Solvability by radicals from an algorithmic point of view. Zbl 1356.12010Hanrot, G.; Morain, F. 1 2001 Factorization of a 512-bit RSA modulus. Zbl 1082.94511Cavallar, Stefania; Dodsons, Bruce; Lenstra, Arjen K.; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Aardal, Karen; Gilchrist, Jeff; Guillerm, Gérard; Leyland, Paul; Marchand, Joël; Morain, François; Muffett, Alec; Putnam, Chris; Putnam, Craig; Zimmermann, Paul 6 2000 Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. Zbl 0963.11032Lercier, R.; Morain, F. 3 2000 Speeding up the discrete log computation on curves with automorphisms. Zbl 0968.14034Duursma, I.; Gaudry, P.; Morain, F. 12 1999 Primality proving using elliptic curves: An update. Zbl 0908.11061Morain, F. 9 1998 Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110Lercier, R.; Morain, F. 4 1998 Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums. Zbl 0874.11044Leprévost, F.; Morain, F. 7 1997 Isomorphism classes of supersingular elliptic curves of characteristic \(\geq 3\). Zbl 0898.11023Morain, F. 1 1997 Building pseudoprimes with a large number of prime factors. Zbl 0862.11005Guillaume, D.; Morain, F. 2 1996 Computing the number of points on an elliptic curve over a finite field: algorithmic aspects. Zbl 0843.11030Morain, François 11 1995 Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029Lercier, Reynald; Morain, François 7 1995 On character sums related to elliptic curves with complex multiplication. Zbl 0841.11042Joux, A.; Morain, F. 6 1995 Schoof’s algorithm and isogeny cycles. Zbl 0849.14024Couveignes, Jean-Marc; Morain, François 8 1994 Elliptic curves and primality proving. Zbl 0792.11056Atkin, A. O. L.; Morain, F. 59 1993 Finding suitable curves for the elliptic curve method of factorization. Zbl 0815.11063Atkin, A. O. L.; Morain, F. 11 1993 Easy numbers for the elliptic curve primality proving algorithm. Zbl 0921.11070Morain, F. 1 1992 Distributed primality proving and the primality of \((2^{3539} +1)/3\). Zbl 0779.11063Morain, François 4 1991 Building cyclic elliptic curves modulo large primes. Zbl 0773.14018Morain, François 3 1991 Elliptic curves, primality proving, and some Titanic primes. Zbl 0760.11041Morain, François 3 1991 Speeding up the computations on an elliptic curve using addition- subtraction chains. Zbl 0724.11068Morain, François; Olivos, Jorge 23 1990 Elliptic curves and primality testing. Zbl 0947.11500Morain, François 4 1990 all cited Publications top 5 cited Publications all top 5 Cited by 297 Authors 11 Morain, François 8 Sutherland, Andrew V. 7 Enge, Andreas 7 Miret, Josep M. 6 Heuberger, Clemens 6 Silverberg, Alice 5 Lercier, Reynald 5 Valls, Magda 4 Galbraith, Steven D. 4 Moody, Dustin 4 Moreno, Ramiro 4 Rubin, Karl Cooper 4 Sadornil, Daniel 4 Schost, Éric 4 Thomé, Emmanuel 3 Barbulescu, Razvan 3 Bernstein, Daniel Julius 3 Bisson, Gaetan 3 Bröker, Reinier 3 De Feo, Luca 3 Joux, Antoine 3 Kleinjung, Thorsten 3 Konstantinou, Elisavet 3 Lange, Tanja 3 Lauter, Kristin Estella 3 Robert, Damien 3 Tena Ayuso, Juan Gabriel 3 Weng, Annegret 2 Atkin, Arthur Oliver Lonsdale 2 Brent, Richard Peirce 2 Cheon, Jung Hee 2 Chiesa, Alessandro 2 Couveignes, Jean-Marc 2 Dujella, Andrej 2 Dupont, Régis 2 Duquesne, Sylvain 2 Ezome, Tony 2 Gaudry, Pierrick 2 Granger, Robert A. 2 Grantham, Jon 2 Guillevic, Aurore 2 Hong, Jin 2 Ionica, Sorina 2 Kim, Minkyu 2 Kim, Taechan 2 Kontogeorgis, Aristides I. 2 Lee, Eunjeong 2 Lee, Hyangsook 2 Lenstra, Arjen K. 2 Lenstra, Hendrik W. jun. 2 Leprévost, Franck 2 Menezes, Alfred J. 2 Mihăilescu, Preda 2 Milio, Enea 2 Muir, James A. 2 Nakazawa, Naoya 2 Park, Cheol Min 2 Prodinger, Helmut 2 Rio, Anna 2 Salvy, Bruno 2 Saouter, Yannick 2 Satoh, Takakazu 2 Schertz, Reinhard 2 Scott, Michael L. 2 Streng, Marco 2 Sun, Zhihong 2 Valera, Javier 2 Yao, David D. W. 2 Zhang, Fangguo 1 Abarzúa, Rodrigo 1 Abatzoglou, Alexander 1 Abdelaziz, Y. 1 Abelard, Simon 1 Adj, Gora 1 Ahmadi, Omran 1 Alaca, Şaban 1 Baaziz, Houria 1 Balasubramaniam, Pagavathigounder 1 Bank, Efrat 1 Barreto, Paulo S. L. M. 1 Ben-Sasson, Eli 1 Bertin, Marie-Jose 1 Binegar, Skye 1 Birkner, Peter 1 Bluher, Antonia Wilson 1 Boneh, Dan 1 Bos, Joppe W. 1 Bosma, Wieb 1 Bostan, Alin 1 Brezing, Friederike 1 Brlek, Srečko 1 Brooks, Ernest Hunter 1 Bruinier, Jan Hendrik 1 Camacho-Navarro, Catalina 1 Casteran, Pierre 1 Castro, Douglas A. 1 Charles, Denis Xavier 1 Chatterji, Samaresh 1 Chen, Binglong 1 Chen, Tien-Ren ...and 197 more Authors all top 5 Cited in 59 Serials 46 Mathematics of Computation 17 Journal of Number Theory 9 Designs, Codes and Cryptography 8 Journal of Cryptology 8 Journal de Théorie des Nombres de Bordeaux 6 Applied Mathematics and Computation 6 Finite Fields and their Applications 6 LMS Journal of Computation and Mathematics 5 Theoretical Computer Science 4 Computers & Mathematics with Applications 3 Applicable Algebra in Engineering, Communication and Computing 3 Experimental Mathematics 3 International Journal of Number Theory 3 Mathematics in Computer Science 2 Bulletin of the Australian Mathematical Society 2 Discrete Applied Mathematics 2 Periodica Mathematica Hungarica 2 Journal of Symbolic Computation 2 Journal of Complexity 2 Bulletin of the American Mathematical Society. New Series 2 Computational Complexity 2 The Ramanujan Journal 2 Foundations of Computational Mathematics 2 Journal of Physics A: Mathematical and Theoretical 2 Advances in Mathematics of Communications 1 Rocky Mountain Journal of Mathematics 1 Acta Arithmetica 1 Advances in Mathematics 1 Duke Mathematical Journal 1 Information Sciences 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Pure and Applied Algebra 1 Mathematische Annalen 1 Mathematics and Computers in Simulation 1 Osaka Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Tokyo Journal of Mathematics 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Algorithmica 1 Applied Mathematics Letters 1 SIAM Journal on Discrete Mathematics 1 International Journal of Foundations of Computer Science 1 International Journal of Computer Mathematics 1 RAIRO. Informatique Théorique et Applications 1 Cybernetics and Systems Analysis 1 Journal of Mathematical Sciences (New York) 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Journal of Integer Sequences 1 Journal of High Energy Physics 1 Journal of Mathematical Cryptology 1 Involve 1 Acta Universitatis Sapientiae. Informatica 1 Afrika Matematika 1 JSIAM Letters 1 Open Mathematics 1 Research in Number Theory 1 SIAM Journal on Applied Algebra and Geometry all top 5 Cited in 19 Fields 167 Number theory (11-XX) 88 Algebraic geometry (14-XX) 65 Information and communication theory, circuits (94-XX) 26 Computer science (68-XX) 8 Combinatorics (05-XX) 5 Field theory and polynomials (12-XX) 4 Special functions (33-XX) 4 Numerical analysis (65-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Manifolds and cell complexes (57-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.