R. D. Accola, Two theorems on Riemann surfaces with noncyclic automorphism groups, Proc. Amer, pp.598-602, 1970.

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 nite elds, 1st Algorithmic Number Theory Symposium -Cornell University, 1994.

J. Buhler and N. Koblitz, Lattice basis reduction, Jacobi sums and hyperelliptic cryptosystems, Bulletin of the Australian Mathematical Society, vol.877, issue.01, pp.147-154, 1998.
DOI : 10.1112/jlms/s2-10.4.457

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

J. Chao, N. Matsuda, J. Sato, and S. Tsujii, EEcient construction of secure hyperelliptic discrete logarithm problems of large genera, Proc. Symposium on Cryptography and Information Security, 1997.

Y. J. Chen, On the elliptic curve discrete logarithm problem, 1999.

J. H. Cheon, D. H. Lee, and S. G. Hahn, Elliptic curve discrete logarithms and Wieferich primes, 1998.

I. Duursma and K. Sakurai, EEcient algorithms for the jacobian variety of hyperelliptic curves y 2 = x p x + 1 over a nite eld of odd characteristic p, Proceedings of the "International Conference on Coding Theory, Cryptography and Related Areas, 1998.

P. Flajolet and A. M. Odlyzko, Random mapping statistics Advances in Cryptology, Proc. Eurocrypt '89, 1990.

G. Frey and H. R. Uck, A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves, Math. Comp, vol.62, issue.206, pp.865-874, 1994.

S. D. Galbraith, S. Paulus, and N. P. Smart, Arithmetic on superelliptic curves, Mathematics of Computation, vol.71, issue.237, 1999.
DOI : 10.1090/S0025-5718-00-01297-7

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.1706

R. Gallant, R. Lambert, and S. Vanstone, Improving the parallelized Pollard lambda search on anomalous binary curves, Mathematics of Computation, vol.69, issue.232, 1998.
DOI : 10.1090/S0025-5718-99-01119-9

P. Gaudry, A variant of the Adleman-DeMarrais-Huang algorithm and its application to small genera, Research Report LIX/RR, vol.99, 1999.

M. J. Jacobson, N. Koblitz, J. H. Silverman, A. Stein, and E. Teske, Analysis of the Xedni calculus attack, 1999.

E. Kani and M. Rosen, Idempotent relations and factors of Jacobians, Mathematische Annalen, vol.12, issue.2, pp.307-327, 1989.
DOI : 10.1007/BF01442878

H. J. Kim, J. Cheon, and S. Hahn, Elliptic logarithm over a nite eld and the lifting to Q, 1998.

N. Koblitz, A course in number theory and cryptography, Graduate Texts in Mathematics. Springer{Verlag, vol.114, 1987.

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

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

N. Koblitz, A family of jacobians suitable for discrete log cryptosystems Advances in Cryptology { CRYPTO '88, 94{99. Springer{Verlag Proceedings of a conference on the theory and application of cryptography held at the University of California, 1988.

N. Koblitz, CM-Curves with Good Cryptographic Properties, Lecture Notes in Comput. Sci, vol.576, pp.279-287, 1992.
DOI : 10.1007/3-540-46766-1_22

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.6778

H. W. Lenstra and J. , Factoring Integers with Elliptic Curves, The Annals of Mathematics, vol.126, issue.3, pp.649-673, 1987.
DOI : 10.2307/1971363

R. Lercier, Finding good random elliptic curves for cryptosystems deened over F2n Advances in Cryptology { EUROCRYPT '97, International Conference on the Theory and Application of Cryptographic Techniques, 1997.

R. Lercier and F. Morain, Counting the number of points on elliptic curves over nite elds: strategies and performances, Advances in Cryptology { EUROCRYPT '95 79{94, 1995. International Conference on the Theory and Application of Cryptographic Techniques, 1995.

A. Menezes, T. Okamoto, and S. A. Vanstone, Reducing elliptic curves logarithms to logarithms in a nite eld, IEEE Trans. Inform. Theory, issue.5, pp.391639-1646, 1993.

A. J. Menezes, Elliptic curve public key cryptosystems, 1993.
DOI : 10.1007/978-1-4615-3198-2

V. Miller, Use of elliptic curves in cryptography Advances in Cryptology { CRYPTO, Proceedings, Santa Barbara (USA), 1986.

J. S. Milne, Jacobian Varieties, Arithmetic Geometry, pp.167-212, 1986.
DOI : 10.1007/978-1-4613-8655-1_7

V. M. Uller, Fast multiplication on elliptic curves over small elds of characteristic two, J. of Cryptology, vol.11, issue.4, pp.219-234, 1998.

D. Mumford, Tata lectures on theta II, 1984.
DOI : 10.1007/978-0-8176-4578-6

S. Nakajima, p-ranks and automorphism groups of algebraic curves, Trans. Amer. Math. Soc, vol.303, issue.2, pp.595-607, 1987.

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

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

J. Quisquater and J. Delescaille, How easy is collision search? Application to DES, Advances in Cryptology Proc. Eurocrypt '89, 1990.
DOI : 10.1007/3-540-46885-4_43

P. Roquette, Absch???tzung der Automorphismenanzahl von Funktionenk???rpern bei Primzahlcharakteristik, Mathematische Zeitschrift, vol.10, issue.1-4, pp.157-163, 1970.
DOI : 10.1007/BF01109838

Y. Sakai and K. Sakurai, Design of hyperelliptic cryptosystems in small charatcteristic and a software implementation over F2n, Advances in Cryptology Proc. Asiacrypt '98, 1998.

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.

J. Sattler and C. P. Schnorr, Generating random walks in groups, Ann. Univ. Sci. Budapest. Sect. Comput, vol.6, pp.65-79, 1985.

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

D. Shanks, Class number, a theory of factorization, and genera, Proc. Symp. Pure Math, pp.415-440, 1971.
DOI : 10.1090/pspum/020/0316385

J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, volume 151 of Grad. Texts in Math, 1994.

J. H. Silverman, The XEDNI calculus and the elliptic curve discrete logarithm problem, 1998.

N. Smart, The Discrete Logarithm Problem on Elliptic Curves of Trace One, Journal of Cryptology, vol.12, issue.3, 1997.
DOI : 10.1007/s001459900052

N. P. Smart, Elliptic Curve Cryptosystems over Small Fields of Odd Characteristic, Journal of Cryptology, vol.12, issue.2, pp.141-151, 1999.
DOI : 10.1007/PL00003820

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

A. Stein and E. Teske, Catching kangaroos in function elds, 1999.

H. Stichtenoth, ???ber die Automorphismengruppe eines algebraischen Funktionenk???rpers von Primzahlcharakteristik, Archiv der Mathematik, vol.179, issue.1, pp.527-544, 1973.
DOI : 10.1007/BF01228251

E. Teske, Speeding up Pollard's rho method for computing discrete logarithms Algorithmic Number Theory, Third International Symposium , ANTS-III, 1998.

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

P. 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

M. J. Wiener and R. J. Zuccherato, Faster Attacks on Elliptic Curve Cryptosystems, Selected Areas in Cryptography '98 5th Annual International Workshop, SAC'98, 1998.
DOI : 10.1007/3-540-48892-8_15