A. O. Atkin, The number of points on an elliptic curve modulo a prime (II) Available at http://listserv, 1992.

I. Blake, G. Seroussi, and N. Smart, Elliptic curves in cryptography, 1999.
DOI : 10.1017/CBO9781107360211

A. Bostan, F. Morain, B. Salvy, and . Schost, Fast algorithms for computing isogenies between elliptic curves, Mathematics of Computation, vol.77, issue.263, 2006.
DOI : 10.1090/S0025-5718-08-02066-8

URL : https://hal.archives-ouvertes.fr/inria-00091441

R. P. Brent and H. T. Kung, Fast Algorithms for Manipulating Formal Power Series, Journal of the ACM, vol.25, issue.4, pp.581-595, 1978.
DOI : 10.1145/322092.322099

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

D. G. Cantor and E. Kaltofen, On fast multiplication of polynomials over arbitrary algebras, Acta Informatica, vol.7, issue.7, pp.693-701, 1991.
DOI : 10.1007/BF01178683

D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, Proceedings of the nineteenth annual ACM conference on Theory of computing , STOC '87, pp.251-280, 1990.
DOI : 10.1145/28395.28396

URL : http://dx.doi.org/10.1016/s0747-7171(08)80013-2

J. Couveignes, L. Dewaghe, and F. Morain, Isogeny cycles and the Schoof-Elkies-Atkin algorithm, 1996.

J. Couveignes and F. Morain, Schoof's algorithm and isogeny cycles, Algorithmic Number Theory 1st Algorithmic Number Theory Symposium -Cornell University, pp.43-58, 1994.
DOI : 10.1007/3-540-58691-1_42

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

L. Dewaghe, Remarks on the Schoof-Elkies-Atkin algorithm, Mathematics of Computation, vol.67, issue.223, pp.1247-1252, 1998.
DOI : 10.1090/S0025-5718-98-00962-4

N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A. O. L. Atkin, pp.21-76, 1998.
DOI : 10.1090/amsip/007/03

A. Enge, Computing modular polynomials in quasi-linear time, Mathematics of Computation, vol.78, issue.267, 2006.
DOI : 10.1090/S0025-5718-09-02199-1

URL : https://hal.archives-ouvertes.fr/inria-00143084

J. Gathen and J. Gerhard, Modern Computer Algebra, 1999.

J. Gathen and V. Shoup, Computing Frobenius maps and factoring polynomials, computational complexity, vol.10, issue.2, pp.187-224, 1992.
DOI : 10.1007/BF01272074

P. Gaudry and F. Morain, Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm, Proceedings of the 2006 international symposium on Symbolic and algebraic computation , ISSAC '06, pp.109-115, 2006.
DOI : 10.1145/1145768.1145791

URL : https://hal.archives-ouvertes.fr/inria-00001009

E. Kaltofen and V. Shoup, Subquadratic-time factoring of polynomials over finite fields, Mathematics of Computation, vol.67, issue.223, pp.1179-1197, 1998.
DOI : 10.1090/S0025-5718-98-00944-2

S. Lang, Elliptic Functions, Springer GTM, vol.112, 1986.

H. W. Lenstra, Galois theory and primality testing, Orders and their applications, pp.1-21, 1985.
DOI : 10.1007/978-1-4899-6699-5_24

URL : https://openaccess.leidenuniv.nl/bitstream/handle/1887/3818/346_071.pdf?sequence=1

M. Maurer and V. Müller, Finding the Eigenvalue in Elkies' Algorithm, Experimental Mathematics, vol.273, issue.170, pp.275-285, 2001.
DOI : 10.1080/10586458.2001.10504448

P. Mih?-ailescu, Cyclotomy primality proofs and their certificates, Mathematica Goettingensis, 2006.

P. Mih?-ailescu, Elliptic curve Gauss sums and counting points, Mathematica Goettingensis, 2006.

F. Morain, Calcul du nombre de points sur une courbe elliptique dans un corps fini : aspects algorithmiques, Journal de Th??orie des Nombres de Bordeaux, vol.7, issue.1, pp.255-282, 1995.
DOI : 10.5802/jtnb.143

C. Pascal and . Schost, Change of order for bivariate triangular sets, Proceedings of the 2006 international symposium on Symbolic and algebraic computation , ISSAC '06, pp.277-284, 2006.
DOI : 10.1145/1145768.1145814

F. Rouillier, Solving Zero-Dimensional Systems Through the Rational Univariate Representation, Applicable Algebra in Engineering, Communication and Computing, vol.9, issue.5, pp.433-461, 1999.
DOI : 10.1007/s002000050114

URL : https://hal.archives-ouvertes.fr/inria-00073264

A. Schönhage and V. Strassen, Fast multiplication of large numbers, Computing, vol.150, issue.3-4, pp.281-292, 1971.
DOI : 10.1007/BF02242355

R. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Math. Comp, vol.44, issue.170, pp.483-494, 1985.

R. Schoof, Counting points on elliptic curves over finite fields, Journal de Th??orie des Nombres de Bordeaux, vol.7, issue.1, pp.219-254, 1995.
DOI : 10.5802/jtnb.142

V. Shoup, Fast Construction of Irreducible Polynomials over Finite Fields, Journal of Symbolic Computation, vol.17, issue.5, pp.371-391, 1994.
DOI : 10.1006/jsco.1994.1025

V. Shoup, A New Polynomial Factorization Algorithm and its Implementation, Journal of Symbolic Computation, vol.20, issue.4, pp.363-397, 1995.
DOI : 10.1006/jsco.1995.1055

V. Shoup, Efficient computation of minimal polynomials in algebraic extensions of finite fields, Proceedings of the 1999 international symposium on Symbolic and algebraic computation , ISSAC '99, pp.53-58, 1999.
DOI : 10.1145/309831.309859