The number of points on an elliptic curve modulo a prime. Email on the Number Theory Mailing List, 1988. ,
The number of points on an elliptic curve modulo a prime. Mail to the number theory mailing list available at http ://www.lix.polytechnique.fr/Labo, 1991. ,
Irreducibles and the composed product for polynomials over a finite field, Discrete Mathematics, vol.65, issue.2, pp.115-139, 1987. ,
DOI : 10.1016/0012-365X(87)90135-X
Algorithmes Efficaces en Calcul Formel. published by the Authors Cette version est la prépublication de l'ouvrage du même nom à paraître dans la collection https ://hal.archives-ouvertes The Magma algebra system I : The user language Lattices of Compatibly Embedded Finite Fields, Bes14] Sébastien Besnier. Courbes elliptiques et isogénies : implantation dans Sage, pp.235-265351, 1997. ,
URL : https://hal.archives-ouvertes.fr/hal-01431717
Fast computation of special resultants, Journal of Symbolic Computation, vol.41, issue.1, pp.1-29, 2006. ,
DOI : 10.1016/j.jsc.2005.07.001
URL : https://hal.archives-ouvertes.fr/inria-00000960
Fast algorithms for manipulating formal power series, BLS12] Reinier Bröker, Kristin Lauter, and Andrew V. Sutherland. Modular polynomials via isogeny volcanoes. Mathematics of Computation, pp.581-595, 1978. ,
Fast algorithms for computing isogenies between elliptic curves Mathematics of Computation, Brö08] Reinier Bröker. A p-adic algorithm to compute the Hilbert class polynomial . Mathematics of Computation, pp.1755-17782417, 2008. ,
DOI : 10.1090/s0025-5718-08-02066-8
Computing the endomorphism ring of an ordinary elliptic curve over a finite field, Journal of Number Theory, vol.131, issue.5, pp.815-831, 2011. ,
DOI : 10.1016/j.jnt.2009.11.003
URL : https://hal.archives-ouvertes.fr/inria-00383155
Enumeration of rational points on elliptic curves over finite fields, 1991. ,
Cryptographic Hash Functions from Expander Graphs, Journal of Cryptology, vol.4, issue.2, 2009. ,
DOI : 10.1007/978-1-4757-1920-8
URL : http://csrc.nist.gov/groups/ST/hash/documents/LAUTER_HashJuly27.pdf
On Fast Multiplication of Polynomials over Arbitrary Algebras, Acta Informatica, vol.28, issue.7, pp.693-701, 1991. ,
Isogeny cycles and the Schoof-Elkies-Atkin algorithm, Research Report LIX/RR/96/03, LIX, p.96, 1996. ,
A Course in Computational Algebraic Number Theory, 1996. ,
DOI : 10.1007/978-3-662-02945-9
Quelques calculs en théorie des nombres, 1994. ,
Computing l-Isogenies Using the p-Torsion ,
Isomorphisms between Artin-Schreier towers, Mathematics of Computation, vol.69, issue.232, pp.1625-1631, 2000. ,
Hard Homogeneous Spaces, IACR Cryptology ePrint Archive, p.291, 2006. ,
Primes of the form x 2 + ny 2, 1989. ,
Matrix multiplication via arithmetic progressions, Journal of Symbolic Computation, vol.9, issue.3, pp.251-280, 1990. ,
DOI : 10.1016/S0747-7171(08)80013-2
URL : https://doi.org/10.1016/s0747-7171(08)80013-2
Fast Algorithms for Towers of Finite Fields and Isogenies. (Algorithmes Rapides pour les Tours de Corps Finis et les Isogénies, 2010. ,
URL : https://hal.archives-ouvertes.fr/tel-00547034
Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic, Journal of Number Theory, vol.131, issue.5, pp.873-893, 2011. ,
DOI : 10.1016/j.jnt.2010.07.003
URL : https://hal.archives-ouvertes.fr/hal-00505798
Fast Algorithms for l-adic Towers over Finite Fields, International Symposium on Symbolic and Algebraic Computation, ISSAC'13, pp.165-172, 2013. ,
Fast arithmetic for the algebraic closure of finite fields, International Symposium on Symbolic and Algebraic Computation, pp.122-129, 2014. ,
Explicit isogenies in quadratic time in any characteristic, LMS Journal of Computation and Mathematics, vol.273, issue.A, pp.267-282, 2016. ,
DOI : 10.1007/s00145-004-0328-3
URL : https://hal.archives-ouvertes.fr/hal-01320940
Towards quantumresistant cryptosystems from supersingular elliptic curve isogenies, Journal of Mathematical Cryptology, vol.8, issue.3, pp.209-247, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00652846
Fast arithmetics in Artin???Schreier towers over finite fields, Journal of Symbolic Computation, vol.47, issue.7, pp.771-792, 2012. ,
DOI : 10.1016/j.jsc.2011.12.008
URL : https://hal.archives-ouvertes.fr/hal-00505799
Taking roots over high extensions of finite fields, Mathematics of Computation, vol.83, issue.285, p.2014 ,
DOI : 10.1090/S0025-5718-2013-02715-9
URL : http://www.csd.uwo.ca/%7Eeschost/publications/sqrt-paper.pdf
Computing in degree 2 k extensions of finite fields of odd characteristic. Designs, Codes and Cryptography, pp.559-569, 2015. ,
Elliptic and modular curves over finite
fields and related computational issues, AMS IP STUDIES IN ADVANCED MATHEMATICS, vol.7, pp.21-76, 1998. ,
DOI : 10.1090/amsip/007/03
Fast Decomposition of Polynomials with Known Galois Group, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 15th International Symposium, AAECC-15 Proceedings, volume 2643 of Lecture Notes in Computer Science, pp.254-264, 2003. ,
DOI : 10.1007/3-540-44828-4_27
Computing modular polynomials in quasi-linear time, Mathematics of Computation, vol.78, issue.267, pp.1809-1824, 2009. ,
DOI : 10.1090/S0025-5718-09-02199-1
URL : https://hal.archives-ouvertes.fr/inria-00143084
Isogeny Volcanoes and the SEA Algorithm, Lecture Notes in Computer Science, vol.2369, pp.276-291, 2002. ,
DOI : 10.1007/3-540-45455-1_23
URL : ftp://lix.polytechnique.fr/pub/submissions/morain/Preprints/LIX:RR:00:05:volcanoes.ps.Z
Anneau d'endomorphismes et cardinalité des courbes elliptiques, 2001. ,
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms, Advances in Cryptology?CRYPTO 2001, pp.190-200, 2001. ,
DOI : 10.1007/3-540-44647-8_11
URL : http://www.cacr.math.uwaterloo.ca/techreports/2000/corr2000-53.ps
The hasse invariant andp-division points of an elliptic curve, Archiv der Mathematik, vol.145, issue.1, pp.148-158, 1976. ,
DOI : 10.1007/BF01224654
Amélioration de l'algorithme de Couveignes à l'aide de la structure de 2-Sylow. Master's thesis ,
Pairing the Volcano, Lecture Notes in Computer Science, vol.6197, pp.201-218, 2010. ,
DOI : 10.1007/978-3-642-14518-6_18
URL : https://hal.archives-ouvertes.fr/hal-01323886
Algorithmique des couplages et cryptographie, 2010. ,
Elliptic curve cryptosystems, Mathematics of Computation, vol.48, issue.177, pp.203-209, 1987. ,
DOI : 10.1090/S0025-5718-1987-0866109-5
URL : http://www.ams.org/mcom/1987-48-177/S0025-5718-1987-0866109-5/S0025-5718-1987-0866109-5.pdf
Hyperelliptic cryptosystems, Journal of Cryptology, vol.2, issue.4, pp.139-150, 1989. ,
DOI : 10.2140/pjm.1988.131.157
Endomorphism rings of elliptic curves over finite fields, 1996. ,
Complex Multiplication Structure of Elliptic Curves, Journal of Number Theory, vol.56, issue.2, pp.227-241, 1996. ,
Computing Isogenies in F 2 n, Algorithmic Number Theory, Second International Symposium Proceedings, volume 1122 of Lecture Notes in Computer Science, pp.197-212, 1996. ,
DOI : 10.1007/3-540-61581-4_55
Algorithmique des courbes elliptiques dans les corps finis, 1997. ,
URL : https://hal.archives-ouvertes.fr/tel-01101949
On Elkies subgroups of \ell -torsion points in elliptic curves defined over a finite field, Journal de Th??orie des Nombres de Bordeaux, vol.20, issue.3, pp.783-797, 2008. ,
DOI : 10.5802/jtnb.650
Four-Dimensional Gallant???Lambert???Vanstone Scalar Multiplication, Journal of Cryptology, vol.77, issue.262, pp.248-283, 2014. ,
DOI : 10.1007/s13389-011-0017-8
URL : https://eprint.iacr.org/2011/608.pdf
On p-Adic Differential Equations with Separation of Variables, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '16, pp.319-323, 2016. ,
DOI : 10.1007/3-540-56939-1
URL : https://hal.archives-ouvertes.fr/hal-01265226
La méthode des graphes. Exemples et applications, Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata), pp.217-242, 1986. ,
Use of Elliptic Curves in Cryptography Advances in Cryptology -CRYPTO '85, Proceedings, pp.417-426, 1985. ,
Determining the 2-Sylow subgroup of an elliptic curve over a finite field, Mathematics of computation, vol.74, issue.249, pp.411-427, 2005. ,
An algorithm to compute volcanoes of 2-isogenies of elliptic curves over finite fields, Applied Mathematics and Computation, vol.176, issue.2, pp.739-750, 2006. ,
Computing the height of volcanoes of l-isogenies of elliptic curves over finite fields, Applied Mathematics and Computation, vol.196, issue.1, pp.67-76, 2008. ,
Analysis of the GHS Weil descent attack on the ECDLP over characteristic two finite fields of composite degree, Progress in Cryptology?INDOCRYPT 2001, pp.195-213, 2001. ,
Ramanujan graphs and Hecke operators, Bulletin of the American Mathematical Society, vol.23, issue.1, pp.127-137, 1990. ,
Ramanujan graphs, AMS IP STUDIES IN AD- VANCED MATHEMATICS, vol.7, pp.159-178, 1995. ,
Public-Key Cryptosystem Based on Isogenies. IACR Cryptology ePrint Archive A Note on Elliptic Curves Over Finite Fields, Mathematics of Computation, vol.49, issue.179, pp.145301-304, 1987. ,
Fast multiplication of polynomials over fields of characteristic 2, Acta Informatica, vol.7, issue.4, pp.395-398, 1977. ,
DOI : 10.1007/BF00289470
Elliptic curves over finite fields and the computation of square roots mod p. Mathematics of computation, pp.483-494, 1985. ,
Counting points on elliptic curves over finite fields, Journal de Théorie des Nombres de Bordeaux, pp.219-254, 1995. ,
DOI : 10.5802/jtnb.142
URL : http://www.emath.fr/Maths/Jtnb/SAUVE/almira.math.u-bordeaux.fr/jtnb/1995-1/schoof.ps
[Sho93] Victor Shoup. Fast Construction of Irreducible Polynomials over Finite Fields, Proceedings of the Fourth Annual ACM/SIGACT-SIAM Symposium on Discrete Algorithms, pp.25-27, 1977. ,
The arithmetic of elliptic curves, 1986. ,
Fast multiplication of large numbers, Computing, vol.150, issue.3-4, pp.281-292, 1971. ,
DOI : 10.1007/BF02242355
On the Distribution of Atkin and Elkies Primes, Foundations of Computational Mathematics, vol.14, issue.2, pp.285-297, 2014. ,
Computing Hilbert class polynomials with the Chinese remainder theorem, Mathematics of Computation, vol.80, issue.273, pp.501-538, 2011. ,
An Elliptic Curve Trapdoor System, Journal of Cryptology, vol.19, issue.1, pp.115-133, 2006. ,
DOI : 10.1007/s00145-004-0328-3
Isogénies entre courbes elliptiques Comptes Rendus hebdomadaires de l'Académie des Sciences de Paris Série AB, pp.238-241, 1971. ,
Elliptic curves : number theory and cryptography, 2008. ,
Multiplying matrices faster than coppersmith-winograd, Proceedings of the 44th symposium on Theory of Computing, STOC '12, pp.887-898, 2012. ,
DOI : 10.1145/2213977.2214056
URL : http://www.eecs.berkeley.edu/~virgi/matrixmult-f.pdf