Edit Profile (opens in new tab) Morain, François Co-Author Distance Author ID: morain.francois Published as: Morain, François; Morain, F. External Links: MGP · Wikidata · GND · IdRef · theses.fr Documents Indexed: 52 Publications since 1989, including 1 Book and 6 Additional arXiv Preprints 1 Contribution as Editor · 1 Further Contribution Software Indexed: 2 Packages Co-Authors: 43 Co-Authors with 30 Joint Publications 1,118 Co-Co-Authors all top 5 Co-Authors 22 single-authored 4 Enge, Andreas 4 Gaudry, Pierrick 4 Guillevic, Aurore 3 Lercier, Reynald 3 Thomé, Emmanuel 2 Atkin, Arthur Oliver Lonsdale 2 Barbulescu, Razvan 2 Hanrot, Guillaume 2 Schost, Éric 2 Smith, Benjamin Andrew 1 Aardal, Karen I. 1 Augot, Daniel 1 Bardos, Claude Williams 1 Bostan, Alin 1 Cavallar, Stefania Hedwig 1 Charpentier, Éric 1 Couveignes, Jean-Marc 1 David, Guy 1 Dodsons, Bruce 1 Dupont, Régis 1 Duursma, Iwan Maynard 1 Fontaine, Jean-Marc 1 Fouquet, Mireille 1 Franke, Jens 1 Gilchrist, Jeff 1 Girard, Jean-Yves 1 Godefroy, Gilles 1 Grémy, Laurent 1 Guillerm, Gérard 1 Habsieger, Laurent 1 Hindry, Marc 1 Joux, Antoine 1 Karoubi, Max 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 Lawrence 1 Muffett, Alec 1 Nikol’skiĭ, Nikolaĭ Kapitonovich 1 Olivos, Jorge 1 Putnam, Chris 1 Putnam, Craig 1 Raynaud, Michel 1 Renault, Guénaël 1 Salvy, Bruno 1 Scribot, Charlotte 1 Shallit, Jeffrey Outlaw 1 te Riele, Herman 1 Tenenbaum, Gérald 1 Waldschmidt, Michel 1 Williams, Hugh Cowie 1 Zimmermann, Paul all top 5 Serials 7 Mathematics of Computation 2 Acta Arithmetica 2 Journal of Number Theory 2 Applicable Algebra in Engineering, Communication and Computing 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 LMS Journal of Computation and Mathematics 1 Lecture Notes in Computer Science 1 Research in Number Theory 1 Le Sel et le Fer all top 5 Fields 45 Number theory (11-XX) 18 Algebraic geometry (14-XX) 13 Information and communication theory, circuits (94-XX) 6 Computer science (68-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Field theory and polynomials (12-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 41 Publications have been cited 451 times in 301 Documents Cited by ▼ Year ▼ Elliptic curves and primality proving. Zbl 0792.11056 Atkin, A. O. L.; Morain, F. 86 1993 Isogeny volcanoes and the SEA algorithm. Zbl 1058.11041 Fouquet, Mireille; Morain, François 41 2002 Fast algorithms for computing isogenies between elliptic curves. Zbl 1200.11097 Bostan, A.; Morain, F.; Salvy, B.; Schost, É. 38 2008 Speeding up the computations on an elliptic curve using addition- subtraction chains. Zbl 0724.11068 Morain, François; Olivos, Jorge 33 1990 Improving NFS for the discrete logarithm problem in non-prime finite fields. Zbl 1365.94399 Barbulescu, Razvan; Gaudry, Pierrick; Guillevic, Aurore; Morain, François 24 2015 Computing the number of points on an elliptic curve over a finite field: algorithmic aspects. (Calcul du nombre de points sur une courbe elliptique dans un corps fini: aspects algorithmiques.) Zbl 0843.11030 Morain, François 17 1995 Speeding up the discrete log computation on curves with automorphisms. Zbl 0968.14034 Duursma, I.; Gaudry, P.; Morain, F. 17 1999 Finding suitable curves for the elliptic curve method of factorization. Zbl 0815.11063 Atkin, A. O. L.; Morain, F. 15 1993 Implementing the asymptotically fast version of the elliptic curve primality proving algorithm. Zbl 1127.11084 Morain, F. 14 2007 Building curves with arbitrary small MOV degree over finite prime fields. Zbl 1084.94014 Dupont, Régis; Enge, Andreas; Morain, François 14 2005 Comparing invariants for class fields of imaginary quadratic fields. Zbl 1058.11077 Enge, Andreas; Morain, François 14 2002 Schoof’s algorithm and isogeny cycles. Zbl 0849.14024 Couveignes, Jean-Marc; Morain, François 12 1994 Primality proving using elliptic curves: An update. Zbl 0908.11061 Morain, F. 10 1998 Fast decomposition of polynomials with known Galois group. Zbl 1030.11078 Enge, Andreas; Morain, François 9 2003 Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums. (Revêtements de courbes elliptiques à multiplication complexe par des courbes hyperelliptiques et sommes de caractères.) Zbl 0874.11044 Leprévost, F.; Morain, F. 8 1997 Factorization of a 512-bit RSA modulus. Zbl 1082.94511 Cavallar, 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 8 2000 On character sums related to elliptic curves with complex multiplication. (Sur les sommes de caractères liées aux courbes elliptiques à multiplication complexe.) Zbl 0841.11042 Joux, A.; Morain, F. 7 1995 Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029 Lercier, Reynald; Morain, François 7 1995 Generalised Weber functions. Zbl 1319.11039 Enge, Andreas; Morain, François 7 2014 Computing discrete logarithms in \(\mathbb F_{p^6}\). Zbl 1384.94066 Grémy, Laurent; Guillevic, Aurore; Morain, François; Thomé, Emmanuel 5 2018 Computing the cardinality of CM elliptic curves using torsion points. Zbl 1196.11085 Morain, François 5 2007 Distributed primality proving and the primality of \((2^{3539} +1)/3\). Zbl 0779.11063 Morain, François 4 1991 Building cyclic elliptic curves modulo large primes. Zbl 0773.14018 Morain, François 4 1991 Elliptic curves and primality testing. (Courbes elliptiques et tests de primalité.) Zbl 0947.11500 Morain, François 4 1990 Proving the primality of very large numbers with fastECPP. Zbl 1125.11359 Franke, Jens; Kleinjung, Thorsten; Morain, François; Wirth, T. 4 2004 Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110 Lercier, R.; Morain, F. 4 1998 Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. Zbl 0963.11032 Lercier, R.; Morain, F. 4 2000 Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using abelian lifts. Zbl 1190.11067 Mihailescu, P.; Morain, F.; Schost, É. 4 2007 Elliptic curves, primality proving, and some Titanic primes. Zbl 0760.11041 Morain, François 3 1991 Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm. Zbl 1356.11091 Gaudry, P.; Morain, F. 3 2006 Solving discrete logarithms on a 170-bit MNT curve by pairing reduction. Zbl 1418.11159 Guillevic, Aurore; Morain, François; Thomé, Emmanuel 3 2017 Building pseudoprimes with a large number of prime factors. Zbl 0862.11005 Guillaume, D.; Morain, F. 2 1996 Isomorphism classes of supersingular elliptic curves of characteristic \(\geq 3\). (Classes d’isomorphismes des courbes elliptiques supersingulières en caractéristique \(\geq 3\).) Zbl 0898.11023 Morain, F. 2 1997 Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Zbl 1196.11006 2 2010 Easy numbers for the elliptic curve primality proving algorithm. Zbl 0921.11070 Morain, F. 1 1992 Modular equations for some \(\eta \)-products. Zbl 1286.11050 Morain, François 1 2013 Solvability by radicals from an algorithmic point of view. Zbl 1356.12010 Hanrot, G.; Morain, F. 1 2001 Atkin’s test: News from the front. Zbl 0734.68053 Morain, François 1 1990 Primality in polynomial time (following Adleman, Huang; Agrawal, Kayal, Saxena). (La primalité en temps polynomial (d’après Adleman, Huang; Agrawal, Kayal, Saxena).) Zbl 1097.11059 Morain, François 1 2004 Modular curves over number fields and ECM. Zbl 1499.11216 Morain, F. 1 2022 Deterministic factoring with oracles. Zbl 1535.11173 Morain, François; Renault, Guénaël; Smith, Benjamin 1 2023 Deterministic factoring with oracles. Zbl 1535.11173 Morain, François; Renault, Guénaël; Smith, Benjamin 1 2023 Modular curves over number fields and ECM. Zbl 1499.11216 Morain, F. 1 2022 Computing discrete logarithms in \(\mathbb F_{p^6}\). Zbl 1384.94066 Grémy, Laurent; Guillevic, Aurore; Morain, François; Thomé, Emmanuel 5 2018 Solving discrete logarithms on a 170-bit MNT curve by pairing reduction. Zbl 1418.11159 Guillevic, Aurore; Morain, François; Thomé, Emmanuel 3 2017 Improving NFS for the discrete logarithm problem in non-prime finite fields. Zbl 1365.94399 Barbulescu, Razvan; Gaudry, Pierrick; Guillevic, Aurore; Morain, François 24 2015 Generalised Weber functions. Zbl 1319.11039 Enge, Andreas; Morain, François 7 2014 Modular equations for some \(\eta \)-products. Zbl 1286.11050 Morain, François 1 2013 Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Zbl 1196.11006 2 2010 Fast algorithms for computing isogenies between elliptic curves. Zbl 1200.11097 Bostan, A.; Morain, F.; Salvy, B.; Schost, É. 38 2008 Implementing the asymptotically fast version of the elliptic curve primality proving algorithm. Zbl 1127.11084 Morain, F. 14 2007 Computing the cardinality of CM elliptic curves using torsion points. Zbl 1196.11085 Morain, François 5 2007 Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using abelian lifts. Zbl 1190.11067 Mihailescu, P.; Morain, F.; Schost, É. 4 2007 Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm. Zbl 1356.11091 Gaudry, P.; Morain, F. 3 2006 Building curves with arbitrary small MOV degree over finite prime fields. Zbl 1084.94014 Dupont, Régis; Enge, Andreas; Morain, François 14 2005 Proving the primality of very large numbers with fastECPP. Zbl 1125.11359 Franke, Jens; Kleinjung, Thorsten; Morain, François; Wirth, T. 4 2004 Primality in polynomial time (following Adleman, Huang; Agrawal, Kayal, Saxena). (La primalité en temps polynomial (d’après Adleman, Huang; Agrawal, Kayal, Saxena).) Zbl 1097.11059 Morain, François 1 2004 Fast decomposition of polynomials with known Galois group. Zbl 1030.11078 Enge, Andreas; Morain, François 9 2003 Isogeny volcanoes and the SEA algorithm. Zbl 1058.11041 Fouquet, Mireille; Morain, François 41 2002 Comparing invariants for class fields of imaginary quadratic fields. Zbl 1058.11077 Enge, Andreas; Morain, François 14 2002 Solvability by radicals from an algorithmic point of view. Zbl 1356.12010 Hanrot, G.; Morain, F. 1 2001 Factorization of a 512-bit RSA modulus. Zbl 1082.94511 Cavallar, 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 8 2000 Computing isogenies between elliptic curves over \(F_{p^n}\) using Couveignes’s algorithm. Zbl 0963.11032 Lercier, R.; Morain, F. 4 2000 Speeding up the discrete log computation on curves with automorphisms. Zbl 0968.14034 Duursma, I.; Gaudry, P.; Morain, F. 17 1999 Primality proving using elliptic curves: An update. Zbl 0908.11061 Morain, F. 10 1998 Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110 Lercier, R.; Morain, F. 4 1998 Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums. (Revêtements de courbes elliptiques à multiplication complexe par des courbes hyperelliptiques et sommes de caractères.) Zbl 0874.11044 Leprévost, F.; Morain, F. 8 1997 Isomorphism classes of supersingular elliptic curves of characteristic \(\geq 3\). (Classes d’isomorphismes des courbes elliptiques supersingulières en caractéristique \(\geq 3\).) Zbl 0898.11023 Morain, F. 2 1997 Building pseudoprimes with a large number of prime factors. Zbl 0862.11005 Guillaume, D.; Morain, F. 2 1996 Computing the number of points on an elliptic curve over a finite field: algorithmic aspects. (Calcul du nombre de points sur une courbe elliptique dans un corps fini: aspects algorithmiques.) Zbl 0843.11030 Morain, François 17 1995 On character sums related to elliptic curves with complex multiplication. (Sur les sommes de caractères liées aux courbes elliptiques à multiplication complexe.) Zbl 0841.11042 Joux, A.; Morain, F. 7 1995 Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029 Lercier, Reynald; Morain, François 7 1995 Schoof’s algorithm and isogeny cycles. Zbl 0849.14024 Couveignes, Jean-Marc; Morain, François 12 1994 Elliptic curves and primality proving. Zbl 0792.11056 Atkin, A. O. L.; Morain, F. 86 1993 Finding suitable curves for the elliptic curve method of factorization. Zbl 0815.11063 Atkin, A. O. L.; Morain, F. 15 1993 Easy numbers for the elliptic curve primality proving algorithm. Zbl 0921.11070 Morain, F. 1 1992 Distributed primality proving and the primality of \((2^{3539} +1)/3\). Zbl 0779.11063 Morain, François 4 1991 Building cyclic elliptic curves modulo large primes. Zbl 0773.14018 Morain, François 4 1991 Elliptic curves, primality proving, and some Titanic primes. Zbl 0760.11041 Morain, François 3 1991 Speeding up the computations on an elliptic curve using addition- subtraction chains. Zbl 0724.11068 Morain, François; Olivos, Jorge 33 1990 Elliptic curves and primality testing. (Courbes elliptiques et tests de primalité.) Zbl 0947.11500 Morain, François 4 1990 Atkin’s test: News from the front. Zbl 0734.68053 Morain, François 1 1990 all cited Publications top 5 cited Publications all top 5 Cited by 438 Authors 16 Morain, François 9 Enge, Andreas 9 Sutherland, Andrew V. 7 De Feo, Luca 7 Miret, Josep M. 7 Thomé, Emmanuel 6 Gaudry, Pierrick 6 Heuberger, Clemens 6 Lauter, Kristin Estella 6 Lercier, Reynald 6 Robert, Damien 5 Barbulescu, Razvan 5 Bröker, Reinier 5 Guillevic, Aurore 5 Moody, Dustin 5 Schost, Éric 5 Silverberg, Alice 5 Valls, Magda 4 Galbraith, Steven D. 4 Jao, David 4 Kleinjung, Thorsten 4 Lenstra, Arjen K. 4 Moreno, Ramiro 4 Pierrot, Cécile 4 Rubin, Karl Cooper 4 Sadornil, Daniel 3 Bernstein, Daniel Julius 3 Bisson, Gaetan 3 De Micheli, Gabrielle 3 Dujella, Andrej 3 Duquesne, Sylvain 3 Joux, Antoine 3 Joye, Marc 3 Konstantinou, Elisavet 3 Lange, Tanja 3 Masson, Simon 3 Mihăilescu, Preda 3 Sanso, Antonio 3 Scott, Michael 3 Smith, Benjamin Andrew 3 Sotáková, Jana 3 Streng, Marco 3 Tena Ayuso, Juan Gabriel 3 Weng, Annegret 3 Yasuda, Masaya 2 Abdelaziz, Y. 2 Arpin, Sarah 2 Atkin, Arthur Oliver Lonsdale 2 Brent, Richard Peirce 2 Castryck, Wouter 2 Charles, Denis Xavier 2 Cheon, Jung Hee 2 Chiesa, Alessandro 2 Costello, Craig 2 Couveignes, Jean-Marc 2 Dajani, Karma 2 Dupont, Régis 2 Eid, Élie 2 Eisenträger, Kirsten 2 El Housni, Youssef 2 Eriksen, Jonathan Komada 2 Ezome, Tony 2 Fouotsa, Emmanuel 2 Granger, Robert A. 2 Grantham, Jon 2 Grémy, Laurent 2 Hakuta, Keisuke 2 Hong, Jin 2 Ionica, Sorina 2 Jetchev, Dimitar P. 2 Jorgenson, Jay Alan 2 Kalle, Charlene 2 Karabina, Koray 2 Kieffer, Jean 2 Kim, Minkyu 2 Kim, Taechan 2 Kochergin, Vadim Vasil’evich 2 Kontogeorgis, Aristides I. 2 Lee, Eunjeong 2 Lee, Hyangsook 2 Lenstra, Hendrik W. jun. 2 Leprévost, Franck 2 Lv, Chang 2 Maillard, Jean-Marie 2 McGuire, Gary 2 Menezes, Alfred J. 2 Milio, Enea 2 Monroe, Laura 2 Muir, James A. 2 Naehrig, Michael 2 Nakazawa, Naoya 2 Nikolaev, Mikhaĭl V. 2 Ozdemir, Enver 2 Panny, Lorenz 2 Park, Cheol Min 2 Prodinger, Helmut 2 Rassias, Michael Th. 2 Rio, Anna 2 Salvy, Bruno 2 Saouter, Yannick ...and 338 more Authors all top 5 Cited in 80 Serials 47 Mathematics of Computation 18 Journal of Number Theory 15 Designs, Codes and Cryptography 12 Journal of Cryptology 9 Journal de Théorie des Nombres de Bordeaux 8 Finite Fields and their Applications 6 Applied Mathematics and Computation 6 LMS Journal of Computation and Mathematics 6 Journal of Mathematical Cryptology 5 Theoretical Computer Science 4 Computers & Mathematics with Applications 4 Experimental Mathematics 4 International Journal of Number Theory 4 Journal of Physics A: Mathematical and Theoretical 3 Bulletin of the Australian Mathematical Society 3 Journal of Symbolic Computation 3 Applicable Algebra in Engineering, Communication and Computing 3 The Ramanujan Journal 3 Mathematics in Computer Science 3 Research in Number Theory 3 Prikladnaya Diskretnaya Matematika 2 Discrete Applied Mathematics 2 Periodica Mathematica Hungarica 2 Mathematische Annalen 2 Journal of Complexity 2 Bulletin of the American Mathematical Society. New Series 2 Computational Complexity 2 Journal of Discrete Mathematical Sciences & Cryptography 2 Foundations of Computational Mathematics 2 Involve 2 Matematicheskie Voprosy Kriptografii 1 Matimyás Matematika 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nonlinearity 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 Algebra 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Mathematics and Computers in Simulation 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Tokyo Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 Bulletin of the Korean Mathematical Society 1 Acta Applicandae Mathematicae 1 Algorithmica 1 Applied Mathematics Letters 1 SIAM Journal on Discrete Mathematics 1 Japan Journal of Industrial and Applied 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 Tatra Mountains Mathematical Publications 1 Journal of Mathematical Sciences (New York) 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Journal of Integer Sequences 1 Interdisciplinary Information Sciences (IIS) 1 Fundamenta Informaticae 1 Journal of High Energy Physics 1 Lobachevskii Journal of Mathematics 1 Moscow Mathematical Journal 1 Journal of Systems Science and Complexity 1 Advances in Mathematics of Communications 1 Algebra & Number Theory 1 Acta Universitatis Sapientiae. Informatica 1 Afrika Matematika 1 JSIAM Letters 1 Open Mathematics 1 SIAM Journal on Applied Algebra and Geometry 1 Moroccan Journal of Algebra and Geometry with Applications all top 5 Cited in 22 Fields 239 Number theory (11-XX) 125 Algebraic geometry (14-XX) 116 Information and communication theory, circuits (94-XX) 42 Computer science (68-XX) 10 Combinatorics (05-XX) 8 Field theory and polynomials (12-XX) 7 Quantum theory (81-XX) 6 Special functions (33-XX) 6 Numerical analysis (65-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Manifolds and cell complexes (57-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 \(K\)-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-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.