E. Bach, Explicit bounds for primality testing and related problems, Mathematics of Computation, vol.55, issue.191, pp.55-355, 1990.
DOI : 10.1090/S0025-5718-1990-1023756-8

J. Belding, R. Bröker, A. Enge, and K. Lauter, Computing Hilbert Class Polynomials, pp.282-295, 2009.
DOI : 10.1007/978-3-540-79456-1_19

URL : https://hal.archives-ouvertes.fr/inria-00246115

G. Bisson, Endomorphism rings in cryptography, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00609211

G. Bisson, R. Cosset, and D. Robert, AVIsogenies, a library for computing isogenies between abelian varieties, 2012.

R. Bröker, D. Gruenewald, and K. Lauter, Explicit CM theory for level 2-structures on abelian surfaces, Algebra & Number Theory, vol.5, issue.4, pp.495-528, 2011.
DOI : 10.2140/ant.2011.5.495

J. H. Bruinier and T. Yang, CM-values of Hilbert modular functions, Inventiones mathematicae, vol.163, issue.2, pp.229-288, 2006.
DOI : 10.1007/s00222-005-0459-7

G. Cardona and J. Quer, Field of moduli and field of definition for curves of genus 2, Computational Aspects of Algebraic Curves, pp.71-83, 2006.
DOI : 10.1142/9789812701640_0006

R. Carls, D. Kohel, and D. Lubicz, Higher-dimensional 3-adic CM construction, Journal of Algebra, vol.319, issue.3, pp.971-1006, 2008.
DOI : 10.1016/j.jalgebra.2007.11.016

URL : https://hal.archives-ouvertes.fr/hal-00383119

R. Carls and D. Lubicz, A p-Adic Quasi-Quadratic Time Point Counting Algorithm, International Mathematics Research Notices, issue.4, pp.698-735, 2009.
DOI : 10.1093/imrn/rnn143

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

R. Cosset and D. Robert, Computing (, )-isogenies in polynomial time on Jacobians of genus 2 curves, Cryptology ePrint Archive, Report, vol.143, 2011.

J. Couveignes, Linearizing torsion classes in the Picard group of algebraic curves over finite fields, Journal of Algebra, vol.321, issue.8, pp.2085-2118, 2009.
DOI : 10.1016/j.jalgebra.2008.09.032

URL : https://hal.archives-ouvertes.fr/hal-00630403

K. Dickman, On the frequency of numbers containing prime factors of a certain relative magnitude, Ark. Mat. Astr. Fys, vol.22, issue.10, pp.1-14, 1930.

K. Eisenträger and K. Lauter, A CRT algorithm for constructing genus 2 curves over finite fields, in Rodier and Vladut [32], preprint version at arXiv:math, pp.405305-161

A. Enge and A. V. Sutherland, Class Invariants by the CRT Method, Hanrot et al. [22], pp.142-156, 2012.
DOI : 10.1007/978-3-642-14518-6_14

URL : https://hal.archives-ouvertes.fr/inria-00448729

D. Freeman and K. Lauter, Computing endomorphism rings of Jacobians of genus 2 curves over finite fields, Algebraic Geometry and Its Applications, pp.29-66, 2010.
DOI : 10.1142/9789812793430_0002

A. Fröhlich, Algebraic number fields: L-functions and Galois properties, pp.437486-55, 1977.

P. Gaudry, T. Houtmann, D. Kohel, C. Ritzenthaler, and A. Weng, The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography, pp.114-129, 2009.
DOI : 10.1007/11935230_8

URL : https://hal.archives-ouvertes.fr/inria-00103435

Z. Eyal, K. E. Goren, and . Lauter, Genus 2 curves with complex multiplication, Int. Math. Res. Not. IMRN, issue.5, pp.1068-1142, 2012.

H. Grundman, J. Johnson-leung, K. Lauter, A. Salerno, B. Viray et al., Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory, Cojocaru et al. [11], pp.35-60
DOI : 10.1090/fic/060/03

J. C. Lagarias and A. M. Odlyzko, Effective versions of the Chebotarev density theorem, Fröhlich [18], pp.409-464

K. Lauter and B. Viray, An arithmetic intersection formula for denominators of Igusa class polynomials, American Journal of Mathematics, vol.137, issue.2, 2012.
DOI : 10.1353/ajm.2015.0010

K. Lauter and T. Yang, Computing genus 2 curves from invariants on the Hilbert moduli space, Journal of Number Theory, vol.131, issue.5, pp.936-958, 2011.
DOI : 10.1016/j.jnt.2010.05.012

H. W. Lenstra, J. Jr, C. Pila, and . Pomerance, A Hyperelliptic Smoothness Test, II, Proc. London Math. Soc. (3), pp.105-146, 2002.
DOI : 10.1112/plms/84.1.105

D. Lubicz and D. Robert, Computing isogenies between abelian varieties, Compositio Mathematica, vol.2, issue.05, 2010.
DOI : 10.1515/crll.1837.16.221

URL : https://hal.archives-ouvertes.fr/hal-00446062

J. Mestre, Construction de courbes de genre 2 ?? partir de leurs modules, Mora and Traverso [30], pp.313-334
DOI : 10.1007/978-1-4612-0441-1_21

T. Shaska, Computational aspects of algebraic curves, Lecture Notes Series on Computing Pte. Ltd, vol.13, 2005.

G. Shimura, Abelian varieties with complex multiplication and modular functions, Princeton Mathematical Series, vol.4699, p.149244911076, 1998.
DOI : 10.1515/9781400883943

A. Spallek, Kurven vom Geschlecht 2 und ihre Anwendung in Public-Key- Kryptosystemen, 1994.

C. Theodorus and . Streng, Complex multiplication of abelian surfaces, 2010.

V. Andrew and . Sutherland, Computing Hilbert class polynomials with the Chinese remainder theorem, Math. Comp, vol.80, issue.273, pp.501-538, 2011.

. Paul-van-wamelen, Examples of genus two CM curves defined over the rationals, Mathematics of Computation, vol.68, issue.225, pp.307-320, 1999.
DOI : 10.1090/S0025-5718-99-01020-0

A. Weng, Constructing hyperelliptic curves of genus 2 suitable for cryptography, Mathematics of Computation, vol.72, issue.241, pp.435-45814029, 2003.
DOI : 10.1090/S0025-5718-02-01422-9

T. Yang, An arithmetic intersection formula on Hilbert modular surfaces, 2012a:11078) [42] , Arithmetic intersection on a Hilbert modular surface and the Faltings height, pp.1275-1309, 2010.
DOI : 10.1353/ajm.2010.0002