L. Babai, On Lov??sz??? lattice reduction and the nearest lattice point problem, Combinatorica, vol.357, issue.1, pp.1-13, 1986.
DOI : 10.1007/BF02579403

P. R. Bending, Curves of genus 2 with ? 2 multiplication, 1998.

J. W. Bos, C. Costello, H. Hisil, and K. Lauter, High-Performance Scalar Multiplication Using 8-Dimensional GLV/GLS Decomposition, Cryptographic Hardware and Embedded Systems -CHES 2013, pp.331-348, 2013.
DOI : 10.1007/978-3-642-40349-1_19

A. Brumer, The rank of J0(N ), Asterisque, vol.228, pp.41-68, 1995.

M. Ciet, F. Sica, and J. Quisquater, Analysis of the Gallant?Lambert?Vanstone method based on efficient endomorphisms: Elliptic and hyperelliptic curves, Selected Areas in Cryptography: SAC 2002 Lecture Notes in Comput. Sci, pp.2595-2616, 2003.

S. D. Galbraith, Mathematics of public key cryptography, 2012.
DOI : 10.1017/CBO9781139012843

S. D. Galbraith, X. Lin, and M. Scott, Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves, J. Crypt, vol.47, pp.24-27, 2011.
DOI : 10.1007/3-540-48892-8_15

R. P. Gallant, R. J. Lambert, and S. A. Vanstone, Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms, Advances in Cryptology: CRYPTO 2001, pp.2139-190, 2001.
DOI : 10.1007/3-540-44647-8_11

P. Gaudry, D. R. Kohel, and B. Smith, Counting Points on Genus 2 Curves with Real Multiplication, Advances in Cryptology: ASI- ACRYPT 2011, pp.7073-504, 2011.
DOI : 10.1007/978-3-642-25385-0_27

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

A. Guillevic and S. Ionica, Four-Dimensional GLV via the Weil Restriction, p.311, 2013.
DOI : 10.1007/978-3-642-42033-7_5

URL : https://hal.archives-ouvertes.fr/hal-00864966

K. Hashimoto, On Brumer's family of {RM}-curves of genus two, Tohoku Mathematical Journal, vol.52, issue.4, pp.52-56, 2000.
DOI : 10.2748/tmj/1178207751

H. Hisil, K. Wong, G. Carter, and E. Dawson, Twisted Edwards curves revisited Advances in Cryptology: ASIACRYPT, Lecture Notes in Comput. Sci, pp.5350-326, 2008.

M. Kaib, The Gauss lattice basis reduction algorithm succeeds with any norm Fundamentals of Computation Theory, Lecture Notes in Comput . Sci, pp.529-275, 1991.

D. R. Kohel and B. Smith, Efficiently computable endomorphisms for hyperelliptic curves Algorithmic number theory: ANTS-VII, Lecture Notes in Comput. Sci, pp.4076-495, 2006.

H. W. Lenstra and J. , Complex Multiplication Structure of Elliptic Curves, Journal of Number Theory, vol.56, issue.2, pp.56-58, 1996.
DOI : 10.1006/jnth.1996.0015

P. Longa and F. Sica, Four-dimensional Gallant?Lambert?Vanstone scalar multiplication, Advances in Cryptology ? ASIACRYPT 2012, pp.7658-718, 2012.
DOI : 10.1007/978-3-642-34961-4_43

URL : http://arxiv.org/abs/1106.5149

J. Mestre, Familles de courbes hyperelliptiquesàhyperelliptiques`hyperelliptiquesà multiplications réelles, Progr. Math, vol.89, pp.313-334, 1991.
DOI : 10.1007/978-1-4612-0457-2_9

J. Mestre, Une g??n??ralisation d???une construction de Richelot, Journal of Algebraic Geometry, vol.22, issue.3, pp.575-580, 2013.
DOI : 10.1090/S1056-3911-2012-00589-X

P. L. Montgomery, Speeding the Pollard and elliptic curve methods of factorization, Mathematics of Computation, vol.48, issue.177, pp.48-177, 1987.
DOI : 10.1090/S0025-5718-1987-0866113-7

G. C. Pohlig and M. E. Hellman, An improved algorithm for computing logarithms over<tex>GF(p)</tex>and its cryptographic significance (Corresp.), IEEE Transactions on Information Theory, vol.24, issue.1, pp.106-110, 1978.
DOI : 10.1109/TIT.1978.1055817

H. Ruck, Abelian surfaces and jacobian varieties over finite fields, Compositio Math, pp.76-79, 1990.

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

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

B. Smith, Families of fast elliptic curves from Q-curves
URL : https://hal.archives-ouvertes.fr/hal-00825287

H. P. Swinnerton-dyer, A Brief Guide to Algebraic Number Theory. LMS Student Texts 50, 2001.

K. Takashima, A New Type of Fast Endomorphisms on Jacobians of Hyperelliptic Curves and Their Cryptographic Application, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.89, issue.1, pp.1-124, 2006.
DOI : 10.1093/ietfec/e89-a.1.124

W. Tautz, J. Top, and A. Verberkmoes, Explicit hyperelliptic curves with real multiplication and permutation polynomials " . Can, J. Math, pp.43-48, 1991.
DOI : 10.4153/cjm-1991-061-x

J. Wilson, Curves of genus 2 with real multiplication by a square root of 5, 1998.

J. Vélu, Isogénies entre courbes elliptiques, C. R. Math. Acad. Sci. Paris, vol.273, pp.238-241, 1971.

Z. Zhou, Z. Hu, M. Xu, and W. Song, Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves, Information Processing Letters, vol.110, issue.22, pp.110-132, 2010.
DOI : 10.1016/j.ipl.2010.08.014