Publications de/of F. Morain
Habilitation
Morain, F.
Courbes elliptiques, arithmétique et corps finis.
Mémoire d'habilitation, Université Paris 6, 1997.
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Thèse/thesis
Morain, F.
Courbes elliptiques et tests de primalité.
Thèse, Université Claude Bernard-Lyon I, Sept. 1990.
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- Chapitre 2: On Cornacchia's algorithm, F. Morain et J.-L. Nicolas. Il est recommandé de consulter également l'article de Nitaj sur le même sujet (Exposition. Math., 1995, vol. 13, pp. 358--365).
- Chapitre 3.1: Construction of Hilbert class fields of imaginary quadratic fields and dihedral equations modulo p.
- Chapitre 3.2: Solving equations of small degree modulo large primes.
- Chapitre 4: Speeding up the computations on an elliptic curve using addition-subtraction chains, F. Morain et J. Olivos, paru dans RAIRO Inform. Théor. Appl., 1990, 24, 6, p. 531-543.
- Chapitre 5: Using a programmable gate array in modular arithmetic.
- Chapitre 6: Atkin's test: news from the front, paru dans les Proceedings d'EUROCRYPT '89, Lecture Notes in Comput. Sci. 434.
- Chapitre 7: Elliptic curves, primality proving and some Titanic primes, paru dans les comptes-rendus des Journées Arithmétiques 1989, Astéristque vol 198--199-200.
- Chapitre 8: Distributed Primality Proving and the primality of (2^3539+1)/3, paru dans les Proceedings d'EUROCRYPT '90, Lecture Notes in Comput. Sci. 473.
Livre/Book
Morain, F., and Nicolas, J.
Mathématiques / Informatique - 14 problèmes
corrigés.
Enseignement Supérieur et Informatique. Vuibert, 1995.
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Articles
2008
- Bostan, A., Morain, F., Salvy, B., and Schost, É.
Fast algorithms for computing isogenies between elliptic curves.
Math. Comp. 77, 263 (2008), 1755-1778.
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2007
- Mihailescu, P., Morain, F., and Schost, É.
Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm
using Abelian lifts.
In ISSAC '07: Proceedings of the 2007 international symposium on
Symbolic and algebraic computation (New York, NY, USA, 2007), ACM Press,
pp. 285-292.
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- Morain, F.
Computing the cardinality of CM elliptic curves using torsion
points.
J. Théor. Nombres Bordeaux 19, 3 (2007), 663-681.
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- Morain, F.
Implementing the asymptotically fast version of the elliptic curve
primality proving algorithm.
Math. Comp. 76 (2007), 493-505.
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2006
- Gaudry, P., and Morain, F.
Fast algorithms for computing the eigenvalue in the
Schoof-Elkies-Atkin algorithm.
In ISSAC '06: Proceedings of the 2006 international symposium on
Symbolic and algebraic computation (New York, NY, USA, 2006), ACM Press,
pp. 109-115.
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- Morain, F.
Encyclopédie de l'informatique et des systèmes
d'information (sous la direction de J. Akoka et I. Comyn-Wattiau).
Vuibert, 2006, ch. Algorithmes algébriques.
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2005
- Dupont, R., Enge, A., and Morain, F.
Building curves with arbitrary small MOV degree over finite prime
fields.
J. of Cryptology 18, 2 (2005), 79-89.
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- Morain, F.
Encyclopedia of cryptography and security.
Springer, 2005, ch. Elliptic curves for primality proving.
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2004
- Franke, J., Kleinjung, T., Morain, F., and Wirth, T.
Proving the primality of very large numbers with fastecpp.
In Algorithmic Number Theory (2004), D. Buell, Ed., vol. 3076
of Lecture Notes in Comput. Sci., Springer-Verlag, pp. 194-207.
6th International Symposium, ANTS-VI, Burlington, VT, USA, June 2004,
Proceedings.
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- Morain, F.
La primalité en temps polynomial [d'après Adleman, Huang ;
Agrawal, Kayal, Saxena].
Astérisque (2004), Exp. No. 917, ix, 205-230.
Séminaire Bourbaki. Vol. 2002/2003.
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2003
- Enge, A., and Morain, F.
Fast decomposition of polynomials with known Galois group.
In Applied Algebra, Algebraic Algorithms and Error-Correcting
Codes (2003), M. Fossorier, T. Høholdt, and A. Poli, Eds., vol. 2643 of
Lecture Notes in Comput. Sci., Springer-Verlag, pp. 254-264.
15th International Symposium, AAECC-15, Toulouse, France, May 2003,
Proceedings.
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2002
- Enge, A., and Morain, F.
Comparing invariants for class fields of imaginary quadratic fields.
In Algorithmic Number Theory (2002), C. Fieker and D. R.
Kohel, Eds., vol. 2369 of Lecture Notes in Comput. Sci.,
Springer-Verlag, pp. 252-266.
5th International Symposium, ANTS-V, Sydney, Australia, July 2002,
Proceedings.
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- Fouquet, M., and Morain, F.
Isogeny volcanoes and the SEA algorithm.
In Algorihmic Number Theory (2002), C. Fieker and D. R.
Kohel, Eds., vol. 2369 of Lecture Notes in Comput. Sci.,
Springer-Verlag, pp. 276-291.
5th International Symposium, ANTS-V, Sydney, Australia, July 2002,
Proceedings.
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- Morain, F.
L'art du secret.
Dossier hors-série. Pour la Science, juillet/octobre 2002, ch. La
factorisation d'entiers, pp. 62-64.
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2001
- Hanrot, G., and Morain, F.
Solvability by radicals from a practical algorithmic point of view.
Nov. 2001.
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- Hanrot, G., and Morain, F.
Solvability by radicals from an algorithmic point of view.
In Symbolic and algebraic computation (2001), B. Mourrain,
Ed., ACM, pp. 175-182.
Proceedings ISSAC'2001, London, Ontario.
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2000
- Cavallar, S., Dodson, B., Lenstra, A. K., Lioen, W., Montgomery, P. L.,
Murphy, B., te Riele, H., Aardal, K., Gilchrist, J., Guillerm, G., Leyland,
P., Marchand, J., Morain, F., Muffett, A., Putnam, C., Putnam, C., and
Zimmermann, P.
Factorization of a 512-bit RSA modulus.
In Advances in Cryptology - EUROCRYPT 2000 (2000),
B. Preneel, Ed., vol. 1807 of Lecture Notes in Comput. Sci.,
Springer-Verlag, pp. 1-18.
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- Lercier, R., and Morain, F.
Computing isogenies between elliptic curves over Fp^n using
Couveignes's algorithm.
Math. Comp. 69, 229 (Jan. 2000), 351-370.
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1999
- Duursma, I., Gaudry, P., and Morain, F.
Speeding up the discrete log computation on curves with
automorphisms.
In Advances in Cryptology - ASIACRYPT '99 (1999), K. Y. Lam,
E. Okamoto, and C. Xing, Eds., vol. 1716 of Lecture Notes in Comput.
Sci., Springer-Verlag, pp. 103-121.
International Conference on the Theory and Applications of Cryptology
and Information Security, Singapore, November 1999, Proceedings.
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1998
- Lercier, R., and Morain, F.
Algorithms for computing isogenies between elliptic curves.
In Computational Perspectives on Number Theory: Proceedings of a
Conference in Honor of A. O. L. Atkin (1998), D. A. Buell and J. T.
Teitelbaum, Eds., vol. 7 of AMS/IP Studies in Advanced Mathematics,
American Mathematical Society, International Press, pp. 77-96.
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- Morain, F.
La machine des frères Carissan.
Pour la Science 243 (Jan. 1998), 10-11.
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- Morain, F.
Primality proving using elliptic curves: an update.
In Algorithmic Number Theory (1998), J. P. Buhler, Ed.,
vol. 1423 of Lecture Notes in Comput. Sci., Springer-Verlag,
pp. 111-127.
Third International Symposium, ANTS-III, Portland, Oregon, june 1998,
Proceedings.
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1997
- Leprévost, F., and Morain, F.
Revêtements de courbes elliptiques à multiplication complexe
par des courbes hyperelliptiques et sommes de caractères.
J. Number Theory 64 (1997), 165-182.
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- Morain, F.
Classes d'isomorphismes des courbes elliptiques supersingulières en
caractéristique >= 3.
Utilitas Math. 52 (Dec. 1997), 241-253.
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- Morain, F.
Courbes elliptiques, arithmétique et corps finis.
Mémoire d'habilitation, Université Paris 6, 1997.
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1996
- Couveignes, J.-M., Dewaghe, L., and Morain, F.
Isogeny cycles and the Schoof-Elkies-Atkin algorithm.
Research Report LIX/RR/96/03, LIX, Apr. 1996.
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- Guillaume, D., and Morain, F.
Building pseudoprimes with a large number of prime factors.
Appl. Algebra Engrg. Comm. Comput. 7, 4 (1996), 263-277.
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- Morain, F., Shallit, J., and Williams, H. C.
La machine à congruences.
La revue du Musée des Arts et Métiers 14 (Mar. 1996),
14-19.
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1995
- Joux, A., and Morain, F.
Sur les sommes de caractères liées aux courbes elliptiques
à multiplication complexe.
J. Number Theory 55, 1 (Nov. 1995), 108-128.
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- Lercier, R., and Morain, F.
Counting the number of points on elliptic curves over finite fields:
strategies and performances.
In Advances in Cryptology - EUROCRYPT '95 (1995), L. C.
Guillou and J.-J. Quisquater, Eds., vol. 921 of Lecture Notes in Comput.
Sci., pp. 79-94.
International Conference on the Theory and Application of
Cryptographic Techniques, Saint-Malo, France, May 1995, Proceedings.
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- Morain, F.
Calcul du nombre de points sur une courbe elliptique dans un corps
fini : aspects algorithmiques.
J. Théor. Nombres Bordeaux 7 (1995), 255-282.
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- Morain, F., and Nicolas, J.
Mathématiques / Informatique - 14 problèmes
corrigés.
Enseignement Supérieur et Informatique. Vuibert, 1995.
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- Shallit, J., Williams, H. C., and Morain, F.
Discovery of a lost factoring machine.
Math. Intelligencer 17, 3 (1995), 41-47.
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1994
- Couveignes, J.-M., and Morain, F.
Schoof's algorithm and isogeny cycles.
In Algorithmic Number Theory (1994), L. Adleman and M.-D.
Huang, Eds., vol. 877 of Lecture Notes in Comput. Sci.,
Springer-Verlag, pp. 43-58.
1st Algorithmic Number Theory Symposium - Cornell University, May
6-9, 1994.
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1993
- Atkin, A. O. L., and Morain, F.
Elliptic curves and primality proving.
Math. Comp. 61, 203 (July 1993), 29-68.
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- Atkin, A. O. L., and Morain, F.
Finding suitable curves for the elliptic curve method of
factorization.
Math. Comp. 60, 201 (Jan. 1993), 399-405.
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- Morain, F.
Pseudoprimes: a survey of recent results.
In Eurocode 1992 (1993), P. Camion, P. Charpin, and
S. Harari, Eds., CISM Courses and Lectures, Springer, pp. 207-215.
Udine, nov 1992.
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1992
- Keller, W., and Morain, F.
The complete factorization of some large Mersenne composites.
Abstracts of the AMS 13, 5 (Oct. 1992), 506.
92T-11-163.
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- Morain, F.
Easy numbers for the Elliptic Curve Primality Proving
algorithm.
In ISSAC '92 (New York, 1992), P. S. Wang, Ed., ACM Press,
pp. 263-268.
Proceedings, July 27-29, Berkeley.
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- Morain, F.
Elliptic curves, primality proving and some Titanic primes.
In Journées Arithmétiques 1989 (1992),
vol. 198-199-200 of Astérisque, SMF, pp. 245-251.
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- Morain, F.
Enjeux et avancées de la théorie algorithmique des nombres.
Rapport de Recherche LIX/RR/92/03, Laboratoire d'Informatique de
l'Ecole Polytechnique (LIX), 1992.
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- Morain, F.
Prime values of partition numbers and the primality of p(1840926).
Rapport de Recherche LIX/92/RR/11, Laboratoire d'Informatique de
l'Ecole Polytechnique (LIX), 1992.
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1991
- Morain, F.
Building cyclic elliptic curves modulo large primes.
In Advances in Cryptology - EUROCRYPT '91 (1991), D.
Davies, Ed., vol. 547 of Lecture Notes in Comput. Sci.,
Springer-Verlag, pp. 328-336.
Proceedings of the Workshop on the Theory and Application of
Cryptographic Techniques, Brighton, United Kingdom, April 8-11, 1991.
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- Morain, F.
Distributed primality proving and the primality of (23539+1)/3.
In Advances in Cryptology - EUROCRYPT '90 (1991), I. B.
Damgård, Ed., vol. 473 of Lecture Notes in Comput. Sci.,
Springer-Verlag, pp. 110-123.
Proceedings of the Workshop on the Theory and Application of
Cryptographic Techniques, Aarhus, Denmark, May 21-24, 1990.
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- Morain, F.
A la chasse aux papillons.
Quadrature, 10 (1991), 33-34.
Septembre-Octobre.
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1990
- Morain, F.
Atkin's test: news from the front.
In Advances in Cryptology - EUROCRYPT '89 (1990), J.-J.
Quisquater, Ed., vol. 434 of Lecture Notes in Comput. Sci.,
Springer-Verlag, pp. 626-635.
Proc. Eurocrypt '89, Houthalen, April 10-13.
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- Morain, F.
Comment calculer an.
Quadrature, 6 (1990), 60-61.
Novembre-Octobre.
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- Morain, F.
Courbes elliptiques et tests de primalité.
Thèse, Université Claude Bernard-Lyon I, Sept. 1990.
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- Morain, F.
Les plus grands nombres premiers connus.
Quadrature, 3 (Apr. 1990), 49-50.
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- Morain, F.
Qui factorisera F9 ?
Quadrature, 4 (1990), 31-32.
Mai-Juin.
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- Morain, F., and Olivos, J.
Speeding up the computations on an elliptic curve using
addition-subtraction chains.
RAIRO Inform. Théor. Appl. 24, 6 (1990), 531-543.
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1989
- Hervé, J.-C., Morain, F., Salesin, D., Serpette, B., Vuillemin, J., and
Zimmermann, P.
Bignum: A portable and efficient package for arbitrary precision
arithmetic.
Rapport de Recherche 1016, INRIA, Apr. 1989.
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- Morain, F.
On the lcm of the differences of eight primes.
Math. Comp. 52, 185 (Jan. 1989), 225-229.
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1988
- Morain, F.
Implementation of the Atkin-Goldwasser-Kilian primality testing
algorithm.
Rapport de Recherche 911, INRIA, Oct. 1988.
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- Morain, F.
La factorisation de F11 est achevée.
Pour la Science, 132 (Oct. 1988).
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