The number of points on an elliptic curve modulo a prime. manuscript, Chicago IL, 1988. ,
Complex abelian varieties, 2004. ,
DOI : 10.1007/978-3-662-06307-1
Computing the endomorphism ring of an ordinary elliptic curve over a finite field, Journal of Number Theory, vol.131, issue.5, 2009. ,
DOI : 10.1016/j.jnt.2009.11.003
URL : https://hal.archives-ouvertes.fr/inria-00383155
Identity-Based Encryption from the Weil Pairing, SIAM Journal on Computing, vol.32, issue.3, pp.586-615, 2003. ,
DOI : 10.1137/S0097539701398521
Short signatures from the Weil pairing, Journal of Cryptology, vol.17, issue.4, pp.297-319, 2004. ,
Explicit CM-theory in dimension 2, 2009. ,
Modular polynomials via isogeny volcanoes, Mathematics of Computation, vol.81, issue.278, 2009. ,
DOI : 10.1090/S0025-5718-2011-02508-1
Moyenne arithmético-géométrique, suites de Borchardt et applications, 2006. ,
An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves, Journal of Cryptology, vol.68, issue.226, pp.24-41, 2010. ,
DOI : 10.1007/s00145-010-9057-y
URL : https://hal.archives-ouvertes.fr/inria-00135324
Computing modular correspondences for abelian varieties, Journal of Algebra, vol.343, issue.1, 2009. ,
DOI : 10.1016/j.jalgebra.2011.06.031
Isogeny Volcanoes and the SEA Algorithm, Algorithmic number theory, pp.276-291, 2002. ,
DOI : 10.1007/3-540-45455-1_23
Fast genus 2 arithmetic based on Theta functions, Journal of Mathematical Cryptology, vol.1, issue.3, pp.243-265, 2007. ,
DOI : 10.1515/JMC.2007.012
URL : https://hal.archives-ouvertes.fr/inria-00000625
Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem, Journal of Symbolic Computation, vol.44, issue.12, pp.1690-1702, 2009. ,
DOI : 10.1016/j.jsc.2008.08.005
URL : https://hal.archives-ouvertes.fr/inria-00337631
Attribute-based encryption for fine-grained access control of encrypted data, Proceedings of the 13th ACM conference on Computer and communications security , CCS '06, p.98, 2006. ,
DOI : 10.1145/1180405.1180418
A one round protocol for tripartite Diffie?Hellman, Journal of Cryptology, vol.17, issue.4, pp.263-276, 2004. ,
DOI : 10.1007/s00145-004-0312-y
Linear Systems on Abelian Varieties, American Journal of Mathematics, vol.111, issue.1, pp.65-94, 1989. ,
DOI : 10.2307/2374480
Elliptic curve cryptosystems Mathematics of computation, pp.203-209, 1987. ,
Theta Relations and Projective Normality of Abelian Varieties, American Journal of Mathematics, vol.98, issue.4, pp.865-889, 1976. ,
DOI : 10.2307/2374034
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
Efficient pairing computation with theta functions Algorithmic Number Theory, 9th International Symposium, 2010. ,
DOI : 10.1007/978-3-642-14518-6_21
URL : https://hal.archives-ouvertes.fr/hal-00528944/document
Reducing elliptic curve logarithms to logarithms in a finite field, Proceedings of the twenty-third annual ACM symposium on Theory of computing, p.89, 1991. ,
Construction de courbes de genre 2 ?? partir de leurs modules, Effective methods in algebraic geometry, pp.313-334, 1991. ,
DOI : 10.1007/978-1-4612-0441-1_21
On the equations defining abelian varieties. I, Inventiones Mathematicae, vol.111, issue.4, pp.287-354, 1966. ,
DOI : 10.1007/BF01389737
On the equations defining abelian varieties. II, Inventiones Mathematicae, vol.3, issue.2, pp.75-135, 1967. ,
DOI : 10.1007/BF01389741
On the equations defining abelian varieties. III, Inventiones Mathematicae, vol.80, issue.3, pp.215-244, 1967. ,
DOI : 10.1007/BF01425401
Tata lectures on theta I, volume 28 of Progress in Mathematics, With the assistance of C. Musili, M. Nori, E. Previato and M. Stillman, 1983. ,
Tata lectures on theta II Jacobian theta functions and differential equations, Progress in Mathematics Birkhäuser Boston Inc, vol.43, 1984. ,
DOI : 10.1007/978-0-8176-4579-3
Essai sur une méthode générale pour déterminer la valeur des intégrales ultraelliptiques , fondée sur des transformations remarquables de ces transcendantes, C. R. Acad. Sci. Paris, vol.2, pp.622-627, 1836. ,
De transformatione Integralium Abelianorum primiordinis commentation, J. reine angew. Math, vol.16, pp.221-341, 1837. ,
DOI : 10.1515/crll.1837.16.221
Theta functions and applications in cryptography, 2010. ,
Fuzzy Identity-Based Encryption, Advances in Cryptology? EUROCRYPT 2005, pp.457-473, 2005. ,
DOI : 10.1007/11426639_27
Elliptic curves over finite fields and the computation of square roots mod p, Mathematics of computation, vol.44, issue.170, pp.483-494, 1985. ,
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
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.4044
Isogenies and the discrete logarithm problem in jacobians of genus 3 hyperelliptic curves, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00537860
Computing Hilbert class polynomials with the Chinese remainder theorem, Mathematics of Computation, vol.80, issue.273, 2009. ,
DOI : 10.1090/S0025-5718-2010-02373-7
Equations for the Jacobian of a hyperelliptic curve, Transactions of the American Mathematical Society, vol.350, issue.08, pp.3083-3106, 1999. ,
DOI : 10.1090/S0002-9947-98-02056-X
Self-blindable credential certificates from the Weil pairing Advances in Cryptology?ASIACRYPT, pp.533-551, 2001. ,