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, Lecture Notes in Comput. Sci, vol.877, pp.28-40, 1994.
DOI : 10.1007/3-540-58691-1_39

A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The design and analysis of computer algorithms, 1974.

D. G. Cantor, Computing in the Jacobian of a hyperelliptic curve, Mathematics of Computation, vol.48, issue.177, pp.95-101, 1987.
DOI : 10.1090/S0025-5718-1987-0866101-0

F. Chung and L. Lu, The Diameter of Sparse Random Graphs, Advances in Applied Mathematics, vol.26, issue.4, pp.257-279, 2001.
DOI : 10.1006/aama.2001.0720

D. Coppersmith, Solving Homogeneous Linear Equations Over GF(2) via Block Wiedemann Algorithm, Mathematics of Computation, vol.62, issue.205, pp.333-350, 1994.
DOI : 10.2307/2153413

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

C. Diem, Index calculus in class groups of plane curves of small degree, Cryptology ePrint Archive, Report, vol.119, 2005.

A. Enge, Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time, Mathematics of Computation, vol.71, issue.238, pp.729-742, 2002.
DOI : 10.1090/S0025-5718-01-01363-1

A. Enge and P. Gaudry, A general framework for subexponential discrete logarithm algorithms, Acta Arith, pp.83-103, 2002.

P. Flajolet, D. Knuth, and B. Pittel, The first cycles in an evolving graph, Discrete Math, pp.167-215, 1989.

P. Gaudry, An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves, Proceedings Index calculus for abelian varieties and the elliptic curve discrete logarithm problem, Cryptology ePrint Archive, pp.19-34073, 2000.
DOI : 10.1007/3-540-45539-6_2

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

F. Heß, Computing Riemann???Roch Spaces in Algebraic Function Fields and Related Topics, Journal of Symbolic Computation, vol.33, issue.4, pp.425-445, 2002.
DOI : 10.1006/jsco.2001.0513

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

N. Koblitz, Hyperelliptic cryptosystems, Journal of Cryptology, vol.2, issue.4, pp.139-150, 1989.
DOI : 10.1007/BF02252872

A. K. Lenstra and M. S. Manasse, Factoring with two large primes, Mathematics of Computation, vol.63, issue.208, pp.785-798, 1994.
DOI : 10.1090/S0025-5718-1994-1250773-9

P. Leyland, A. K. Lenstra, B. Dodson, A. Muffett, S. S. Wagstaff et al., MPQS with Three Large Primes, Proceedings, pp.448-462, 2002.
DOI : 10.1007/3-540-45455-1_35

URL : http://infoscience.epfl.ch/record/164535

A. Menezes, Y. Wu, and R. Zuccherato, An elementary introduction to hyperelliptic curves, Appendix to Algebraic aspects of cryptography, pp.155-178, 1998.

V. Müller, A. Stein, and C. Thiel, Computing discrete logarithms in real quadratic congruence function fields of large genus, Mathematics of Computation, vol.68, issue.226, pp.807-822, 1999.
DOI : 10.1090/S0025-5718-99-01040-6

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

S. Pohlig and M. 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

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

E. Thomé, Subquadratic Computation of Vector Generating Polynomials and Improvement of the Block Wiedemann Algorithm, Algorithmes de calcul de logarithme discret dans les corps finis, pp.757-775, 2002.
DOI : 10.1006/jsco.2002.0533

E. Volcheck, Computing in the jacobian of a plane algebraic curve, ANTS-I (L. Adleman and M

T. Wollinger, J. Pelzl, and C. Paar, Cantor versus Harley: optimization and analysis of explicit formulae for hyperelliptic curve cryptosystems, IEEE Transactions on Computers, vol.54, issue.7, 2004.
DOI : 10.1109/TC.2005.109

I. Lorraine, SPACES ? 615 rue du Jardin botanique ? 54602 Villers-L` es-Nancy Cedex ? France (3) University of Waterloo, Department of Combinatorics and Optimization ? Waterloo, Ontario ? N2L 3G1 ? Canada (4) Faculty for Mathematics and Informatics, pp.10-11

L. Unité-de-recherche-inria-lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4

I. Unité-de-recherche and . Rennes, IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex (France) Unité de recherche, 2004.

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