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Author ID: morain.francois Recent zbMATH articles by "Morain, François"
Published as: Morain, François; Morain, F.
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Publications by Year

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 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

Citations by Year

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