Publications of François Morain
- Primality proving
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Implementation of the
Atkin-Goldwasser-Kilian primality testing algorithm, F. Morain,
INRIA Research Report 911, october 1988. Abstract
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Courbes elliptiques et tests de primalité
Thèse, Université de Lyon I, 20 septembre 1990. It contains several chapters, some of which are:
- Chapter 2: On Cornacchia's algorithm, F. Morain and J.-L. Nicolas. I suggest you also read Nitaj's article on the same topic (Exposition. Math., 1995, vol. 13, pp. 358--365).
- Chapter 3.1: Construction of Hilbert class fields of imaginary quadratic fields and dihedral equations modulo p.
- Chapter 3.2: Solving equations of small degree modulo large primes.
- Chapter 4: Speeding up the computations on an elliptic curve using addition-subtraction chains, F. Morain et J. Olivos, published in RAIRO Inform. Théor. Appl., 1990, 24, 6, p. 531-543.
- Chapter 5: Using a programmable gate array in modular arithmetic.
- Chapter 6: Atkin's test: news from the front, published in the Proceedings of EUROCRYPT '89, Lecture Notes in Comput. Sci. 434.
- Chapter 7: Elliptic curves, primality proving and some Titanic primes, published in the comptes-rendus des Journées Arithmétiques 1989, Astéristque vol 198--199-200.
- Chapter 8: Distributed Primality Proving and the primality of (2^3539+1)/3, published in the Proceedings d'EUROCRYPT '90, Lecture Notes in Comput. Sci. 473.
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Elliptic curves and primality proving, A. O. L. Atkin and F. Morain, Math. Comp. 61, 203, july 1993, pp. 29-68. Abstract.
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Easy numbers for the Elliptic Curve Primality Proving Algorithm, F. Morain, in Paul S. Wang, editor, ISSAC '92, pages 263--268, New York, 1992. ACM Press. Proceedings, July 27--29, Berkeley. Résumé.
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Prime values of partition
numbers and the primality of p(1840926), F. Morain, LIX Research
Report LIX/RR/92/11.
Abstract.
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Primality proving using elliptic curves: an update, F. Morain, 1998, Proc. of ANTS-III, Lecture Notes in Comput. Sci. 1423.
- Complex multiplication
- Pseudoprimes
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Pseudoprimes: a survey of recent results, F. Morain, Proc. EUROCODE 1992, P. Camion, P. Charpin and S. Harari (eds), CISM Courses and Lectures, vol. 339, pp. 207-215, Springer-Verlag. Abstract.
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Building pseudoprimes with a large number of prime factors , D. Guillaume and F. Morain, AAECC, vol. 7, n. 4, 1996, pp. 263--277. Abstract.
- Elliptic curves over finite fields
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Schoof's algorithm and isogeny cycles , J.-M. Couveignes and F. Morain, appeared in Proc. ANTS-I, Lecture Notes in Computer Science 877, 1994, pp. 43-58. Abstract.
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Isogeny cycles and the Schoof-Elkies-Atkin algorithm,
J.-M. Couveignes, L. Dewaghe and F. Morain, Rapport de recherche
LIX/RR/96/03, submitted for publication.
.ps,
.pdf,
Abstract .
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Counting the number of points of on elliptic curves over finite fields: strategies and performances , R. Lercier and F. Morain, appeared in Proc. Eurocrypt '95, Lecture Notes in Computer Science 921, Springer, 1995, pp. 79-94. Abstract.
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Calcul du nombre de points sur une courbe elliptique dans un corps fini : aspects algorithmiques , F. Morain, appeared in J. Théor. Nombres Bordeaux, 7, 1995, p. 255--282.
ps.gz, pdf
Abstract.
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Counting points on elliptic curves over F(p^n) using Couveignes's algorithm , R. Lercier and F. Morain, preprint (version 95/09/08). Abstract.
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Counting points on elliptic curves over F(p^n) using Couveignes's algorithm , R. Lercier and F. Morain, submitted version (version 96/01/25). Abstract.
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Classes d'isomorphismes des courbes elliptiques supersingulières en caractéristique >= 3, F. Morain, submitted version. Abstract.
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Algorithms for computing isogenies between elliptic curves., R. Lercier and F. Morain, preprint. Abstract.
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Isogeny computations and point counting on elliptic curves., F. Morain, slides of a talk given at ECC'98, Waterloo, september 1998.
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Isogeny volcanoes and the SEA algorithm., M. Fouquet and F. Morain, submitted.
- Algebraic curves and cryptology:
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Speeding up the discrete
log computation on curves with automorphisms, I. Duursma,
P. Gaudry and F. Morain, LIX Research Report LIX/RR/99/03.
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Speeding up the discrete log computation on curves with automorphisms, I. Duursma, P. Gaudry and F. Morain, slides of the MPKC conference, Toronto, june 1999.
- Building robust (hyper)elliptic cryptosystems, F. Morain, slides for the MACG'2000 workshop.
- Character sums
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Évaluation des
sommes de caractères, A. Joux and F. Morain, LIX Research
Report LIX/RR/93/11, final version in J. Number Theory.,
vol. 55, n. 1, 1995, pp. 108--128. Abstract.
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Revêtements de courbes
elliptiques à multiplication complexe par des courbes
hyperelliptiques et sommes de caractères, F. Leprevost and
F. Morain, LIX Research Report LIX/RR/94/07, final version in
J. Number Theory., vol. 64, 1997, pp. 165--182.
Abstract.
- Solving equations by radicals
- Surveys
- Miscellaneous
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Building cyclic elliptic curves modulo large primes, F. Morain, appeared in Proc. Eurocrypt '91, Lecture Notes in Computer Science 547, Springer, 1991, pp. 328-336. Abstract.
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Enjeux et avancées de la
théorie algorithmique des nombres, F. Morain, LIX Research
report LIX/RR/92/03. Abstract.
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Finding suitable curves for the elliptic curve method of factorization, A. O. L. Atkin and F. Morain, Math. Comp., 60, 201, january 1993, pp. 399-405. Abstract.
- Informal notes