L. M. Adleman, J. Demarrais, and M. Huang, A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields, ANTS-I, pp.28-40, 1994.
DOI : 10.1007/3-540-58691-1_39

S. Arita, Weil Descent of Elliptic Curves over Finite Fields of Characteristic Three, Advances in Cryptolgy ? ASIACRYPT, pp.248-258, 2000.
DOI : 10.1007/3-540-44448-3_19

J. Couveignes, Algebraic groups and discrete logarithm, Public-key cryptography and computational number theory, pp.17-27, 2001.
DOI : 10.1515/9783110881035.17

D. Cox, J. Little, and D. Shea, Ideals, varieties, and algorithms. Undergraduate Texts in Mathematics, 1997.

C. Diem, The GHS-attack in odd characteristic, J. Ramanujan Math. Soc, vol.18, pp.1-32, 2003.

C. Diem, An Index Calculus Algorithm for Plane Curves of Small Degree, ANTS-VII, pp.543-557, 2006.
DOI : 10.1007/11792086_38

C. Diem and E. Thomé, Index Calculus in Class Groups of Non-hyperelliptic Curves of Genus Three, Journal of Cryptology, vol.38, issue.192, 2007.
DOI : 10.1007/s00145-007-9014-6

URL : https://hal.archives-ouvertes.fr/inria-00107290

D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Mathematics, vol.150

A. Enge and P. Gaudry, A general framework for subexponential discrete logarithm algorithms, Acta Arithmetica, vol.102, issue.1, pp.83-103, 2002.
DOI : 10.4064/aa102-1-6

URL : https://hal.archives-ouvertes.fr/inria-00512717

A. Enge and P. Gaudry, An L (1/3???+?????) Algorithm for the Discrete Logarithm Problem for Low Degree Curves, Advances in Cryptology ? EUROCRYPT 2007, pp.379-393, 2007.
DOI : 10.1007/978-3-540-72540-4_22

URL : https://hal.archives-ouvertes.fr/inria-00135324

J. Faugère, A new efficient algorithm for computing Gr??bner bases (F4), Journal of Pure and Applied Algebra, vol.139, issue.1-3, pp.61-88, 1999.
DOI : 10.1016/S0022-4049(99)00005-5

J. Faugère, A new efficient algorithm for computing Gröbner bases without reduction to zero (F5), pp.75-83, 2002.

E. V. Flynn, The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field, Mathematical Proceedings of the Cambridge Philosophical Society, vol.1, issue.03, pp.425-441, 1990.
DOI : 10.1007/BF01389737

S. Galbraith and N. Smart, A Cryptographic Application of Weil Descent, Cryptography and Coding, pp.191-200, 1999.
DOI : 10.1007/3-540-46665-7_23

S. Gao, Factoring multivariate polynomials via partial differential equations, Mathematics of Computation, vol.72, issue.242, pp.801-822, 2003.
DOI : 10.1090/S0025-5718-02-01428-X

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.4344

P. Gaudry, An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves, Advances in Cryptology ? EUROCRYPT, pp.19-34, 2000.
DOI : 10.1007/3-540-45539-6_2

URL : https://hal.archives-ouvertes.fr/inria-00512401

P. Gaudry, F. Hess, and N. Smart, Constructive and destructive facets of Weil descent on elliptic curves, Journal of Cryptology, vol.44, issue.1, pp.19-46, 2002.
DOI : 10.1007/s00145-001-0011-x

URL : https://hal.archives-ouvertes.fr/inria-00512763

P. Gaudry, E. Thomé, N. Thériault, and C. Diem, A double large prime variation for small genus hyperelliptic index calculus, Mathematics of Computation, vol.76, issue.257, pp.475-492, 2007.
DOI : 10.1090/S0025-5718-06-01900-4

URL : https://hal.archives-ouvertes.fr/inria-00077334

R. Granger and F. Vercauteren, On the Discrete Logarithm Problem on Algebraic Tori, Advances in Cryptology ? CRYPTO 2005, pp.66-85, 2005.
DOI : 10.1007/11535218_5

F. Hess, The GHS Attack Revisited, Advances in Cryptology ? EUROCRYPT 2003, pp.374-387, 2003.
DOI : 10.1007/3-540-39200-9_23

F. Heß, Computing relations in divisor class groups of algebraic curves over finite fields, 2004.

M. Huang, K. Kueh, and K. Tan, Lifting Elliptic Curves and Solving the Elliptic Curve Discrete Logarithm Problem, Lecture Notes in Comput. Sci, vol.877, pp.377-384, 2000.
DOI : 10.1007/10722028_22

M. Jacobson, N. Koblitz, J. Silverman, A. Stein, and E. Teske, Analysis of the Xedni calculus attack, Designs, Codes and Cryptography, vol.20, issue.1, pp.41-64, 2000.
DOI : 10.1023/A:1008312401197

N. Koblitz, Elliptic curve cryptosystems, Mathematics of Computation, vol.48, issue.177, pp.203-209, 1987.
DOI : 10.1090/S0025-5718-1987-0866109-5

M. Maurer, A. Menezes, and E. Teske, Abstract, LMS Journal of Computation and Mathematics, vol.15, pp.127-174, 2002.
DOI : 10.1109/18.259647

A. Menezes, T. Okamoto, and S. A. Vanstone, Reducing elliptic curve logarithms to logarithms in a finite field, IEEE Transactions on Information Theory, vol.39, issue.5, pp.1639-1646, 1993.
DOI : 10.1109/18.259647

A. Menezes and M. Qu, Analysis of the Weil Descent Attack of Gaudry, Hess and Smart, Topics in Cryptology ? CT-RSA 2001, pp.308-318, 2001.
DOI : 10.1007/3-540-45353-9_23

A. Menezes, Y. Wu, and R. Zuccherato, An elementary introduction to hyperelliptic curves, Algebraic aspects of cryptography, pp.155-178, 1997.

V. Miller, Use of Elliptic Curves in Cryptography, Advances in Cryptology ? CRYPTO '86, pp.417-426, 1987.
DOI : 10.1007/3-540-39799-X_31

K. Nagao, Decomposed attack for the jacobian of a hyperelliptic curve over an extension field. Cryptology ePrint Archive, Report, vol.112, 2007.

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

J. Pila, Counting points on curves over families in polynomial time, 2005.

J. M. Pollard, Monte Carlo methods for index computation mod p, Math. Comp, vol.32, issue.143, pp.918-924, 1978.

T. Satoh and K. Araki, Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves, Comment. Math. Helv, vol.47, issue.1, pp.81-92, 1998.

I. Semaev, Summation polynomials and the discrete logarithm problem on elliptic curves, p.31, 2004.

I. A. Semaev, Evaluation of discrete logarithms in a group of $p$-torsion points of an elliptic curve in characteristic $p$, Mathematics of Computation of the American Mathematical Society, vol.67, issue.221, pp.353-356, 1998.
DOI : 10.1090/S0025-5718-98-00887-4

J. Silverman, The Xedni calculus and the elliptic curve discrete logarithm problem, Designs, Codes and Cryptography, vol.20, issue.1, pp.5-40, 2000.
DOI : 10.1023/A:1008319518035

N. Smart, The Discrete Logarithm Problem on Elliptic Curves of Trace One, Journal of Cryptology, vol.12, issue.3, pp.193-196, 1999.
DOI : 10.1007/s001459900052

N. Thériault, Index Calculus Attack for Hyperelliptic Curves of Small Genus, Advances in Cryptology ? ASIACRYPT 2003, pp.75-92, 2003.
DOI : 10.1007/978-3-540-40061-5_5

P. C. Van-oorschot and M. J. Wiener, Parallel Collision Search with Cryptanalytic Applications, Journal of Cryptology, vol.12, issue.1, pp.1-28, 1999.
DOI : 10.1007/PL00003816