S. Abelard, P. Gaudry, and P. Spaenlehauer, Improved complexity bounds for counting points on hyperelliptic curves, To appear in Foundations of Computational Mathematics, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01613530

M. Leonard, M. Adleman, and . Huang, Counting points on curves and Abelian varieties over finite fields, Journal of Symbolic Computation, vol.32, issue.3, pp.171-189, 2001.

S. Ballentine, A. Guillevic, E. L. García, C. Martindale, M. Massierer et al., Isogenies for Point Counting on Genus Two Hyperelliptic Curves with Maximal Real Multiplication, Algebraic Geometry for Coding Theory and Cryptography, pp.63-94, 2017.
DOI : 10.4153/CJM-1991-061-x

URL : https://hal.archives-ouvertes.fr/hal-01421031

C. Birkenhake and H. Lange, Complex Abelian varieties, 2013.
DOI : 10.1007/978-3-662-06307-1

A. Bostan, G. Lecerf, B. Salvy, É. Schost, and B. Wiebelt, Complexity issues in bivariate polynomial factorization, Proceedings of the 2004 international symposium on Symbolic and algebraic computation , ISSAC '04, pp.42-49, 2004.
DOI : 10.1145/1005285.1005294

URL : https://hal.archives-ouvertes.fr/hal-00186759

I. Boyer, Variétés abéliennes et jacobiennes de courbes hyperelliptiques, en particulier à multiplication réelle ou complexe, 2014.

G. David and . Cantor, On the analogue of the division polynomials for hyperelliptic curves, Journal fur die reine und angewandte Mathematik, pp.91-146, 1994.

R. Carls and D. Lubicz, A p-Adic Quasi-Quadratic Time Point Counting Algorithm, International Mathematics Research Notices, vol.2, issue.4, pp.698-735, 2009.
DOI : 10.5802/jtnb.142

URL : https://hal.archives-ouvertes.fr/hal-00383103

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

J. S. Ellenberg, Endomorphism Algebras of Jacobians, Advances in Mathematics, vol.162, issue.2, pp.243-271, 2001.
DOI : 10.1006/aima.2001.1994

URL : https://doi.org/10.1006/aima.2001.1994

G. Frey and M. Müller, Arithmetic of Modular Curves and Applications, Algorithmic Algebra and Number Theory, pp.11-48, 1999.
DOI : 10.1007/978-3-642-59932-3_2

P. Gaudry, D. Kohel, and B. Smith, Counting Points on Genus 2 Curves with Real Multiplication, ASIACRYPT 2011, pp.504-519, 2011.
DOI : 10.1007/978-3-642-25385-0_27

URL : https://hal.archives-ouvertes.fr/inria-00598029

P. Gaudry and É. Schost, A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii???s Algorithm, ANTS-VI, pp.208-222, 2004.
DOI : 10.1007/978-3-540-24847-7_15

P. Gaudry and É. Schost, Genus 2 point counting over prime fields, Journal of Symbolic Computation, vol.47, issue.4, pp.368-400, 2012.
DOI : 10.1016/j.jsc.2011.09.003

URL : https://hal.archives-ouvertes.fr/inria-00542650

C. Michael and . Harrison, An extension of Kedlaya's algorithm for hyperelliptic curves, Journal of Symbolic Computation, vol.47, issue.1, pp.89-101, 2012.

D. Harvey, Counting points on hyperelliptic curves in average polynomial time, Annals of Mathematics, vol.179, issue.2, pp.783-803, 2014.
DOI : 10.4007/annals.2014.179.2.7

URL : http://arxiv.org/pdf/1210.8239.pdf

D. Harvey and A. V. Sutherland, Computing Hasse???Witt matrices of hyperelliptic curves in average polynomial time, II, Frobenius distributions: Lang-Trotter and Sato-Tate conjectures, pp.127-148, 2016.
DOI : 10.1090/conm/663/13352

URL : http://arxiv.org/pdf/1410.5222

M. Huang and D. Ierardi, Counting Points on Curves over Finite Fields, Journal of Symbolic Computation, vol.25, issue.1, pp.1-21, 1998.
DOI : 10.1006/jsco.1997.0164

URL : https://doi.org/10.1006/jsco.1997.0164

S. Kiran and . Kedlaya, Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, Journal of the Ramanujan mathematical society, vol.16, issue.4, pp.323-338, 2001.

S. Kiran, A. V. Kedlaya, and . Sutherland, Computing L-series of hyperelliptic curves, ANTS-VIII, pp.312-326, 2008.

R. David, B. A. Kohel, and . Smith, Efficiently computable endomorphisms for hyperelliptic curves, ANTS VII, pp.495-509, 2006.

J. Mestre, Familles de courbes hyperelliptiques ?? multiplications r??elles, Arithmetic algebraic geometry, pp.193-208, 1991.
DOI : 10.1007/978-1-4612-0457-2_9

J. Pila, Frobenius maps of abelian varieties and finding roots of unity in finite fields, Mathematics of Computation, vol.55, issue.192, pp.745-763, 1990.
DOI : 10.1090/S0025-5718-1990-1035941-X

T. Satoh, The canonical lift of an ordinary elliptic curve over a finite field and its point counting, Journal of the Ramanujan mathematical society, vol.15, issue.4, pp.247-270, 2000.

R. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Mathematics of Computation, vol.44, issue.170, pp.483-494, 1985.
DOI : 10.2307/2007968

G. Shimura, Introduction to the arithmetic theory of automorphic functions, 1971.

A. Sutherland, A generic approach to searching for Jacobians, Mathematics of Computation, vol.78, issue.265, pp.485-507, 2009.
DOI : 10.1090/S0025-5718-08-02143-1

URL : http://www.ams.org/mcom/2009-78-265/S0025-5718-08-02143-1/S0025-5718-08-02143-1.pdf

W. Tautz, J. Top, and A. Verberkmoes, Explicit hyperelliptic curves with real multiplication and permutation polynomials, Journal canadien de math??matiques, vol.43, issue.5, pp.1055-1064, 1991.
DOI : 10.4153/CJM-1991-061-x

. Paul-van-wamelen, Proving that a genus 2 curve has complex multiplication, Mathematics of Computation, vol.68, issue.228, pp.1663-1677, 1999.
DOI : 10.1090/S0025-5718-99-01101-1

J. Von, Z. Gathen, and J. Gerhard, Modern computer algebra, 2013.

R. Zippel, Effective polynomial computation Université de Lorraine, CNRS, Inria Email address: simon.abelard@loria.fr Email address: pierrick, 1993.
DOI : 10.1007/978-1-4615-3188-3