L. M. Adleman, A Subexponential Algorithm for the Discrete Logarithm Problem with Applications to Cryptography, Proceedings of the 20th Annual Symposium on Foundations of Computer Science, SFCS 1979, pp.55-60, 1979.

L. M. Adleman, The Function Field Sieve, ANTS 1994, pp.108-121, 1994.

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 1994, pp.28-40, 1994.

L. M. Adleman and M. Huang, Function Field Sieve Method for Discrete Logarithms over Finite Fields, Inform. and Comput, vol.151, issue.12, pp.5-16, 1999.

M. Bardet, Étude des Systèmes Algébriques Surdéterminés. Applications aux codes Correcteurs et à la Cryptographie, 2004.

M. Bardet, J. Faugère, and B. Salvy, Complexity of Gröbner Basis Computation for Semi-Regular Overdetermined Sequences over F2 with Solutions in F2, Technical Report, vol.5049, 2003.

M. Bardet, J. Faugère, B. Salvy, and B. Yang, Asymptotic Expansion of the Degree of Regularity for Semi-Regular Systems of Equations, The Effective Methods in Algebraic Geometry Conference, pp.1-14, 2005.

L. Bettale, J. Faugère, and L. Perret, Hybrid Approach for Solving Multivariate Systems over Finite Fields, Journal of Math. Cryptology, vol.3, issue.3, pp.177-197, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01148127

L. Bettale, J. Faugère, and L. Perret, Cryptanalysis of HFE, multi-HFE and Variants for Odd and Even Characteristic, Des. Codes Cryptography, pp.1-46, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00776072

B. Buchberger, Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, 1965.

H. Cohen and G. Frey, Handbook of Elliptic and Hyperelliptic Curve Cryptography . Discrete Mathematics and its Applications, 2005.

D. Coppersmith, Fast Evaluation of Logarithms in Fields of Characteristic Two, IEEE Transactions on Information Theory, vol.30, issue.4, pp.587-593, 1984.

C. Diem, On the Discrete Logarithm Problem in Elliptic Curves, Compositio Mathematica, vol.147, pp.75-104, 2011.

C. Diem, On the Discrete Logarithm Problem in Elliptic Curves II, 2011.

A. Enge and P. Gaudry, A General Framework for Subexponential Discrete Logarithm Algorithms, Acta Arith, vol.102, issue.1, pp.83-103, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00512717

J. Faugère, A New Efficient Algorithm for Computing Gröbner Basis (F4), Journal of Pure and Applied Algebra, vol.139, issue.1-3, pp.61-88, 1999.

J. Faugère, A New Efficient Algorithm for Computing Gröbner Bases without Reduction to Zero (F5), Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, pp.75-83, 2002.

J. Faugère and A. Joux, Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases, CRYPTO 2003, pp.44-60, 2003.

J. Faugère, A. Otmani, L. Perret, and J. Tillich, Algebraic Cryptanalysis of McEliece Variants with Compact Keys, EUROCRYPT 2010, pp.279-298, 2010.

J. Faugère, K. Fukuda, J. Van-der-hoeven, M. Joswig, and N. Takayama, FGb: A Library for Computing Gröbner Bases, ICMS 2010, pp.84-87, 2010.

J. Faugère, F. Levy-dit-vehel, and L. Perret, Cryptanalysis of MinRank, CRYPTO 2008, pp.280-296, 2008.

J. Faugère, M. Safey-el-din, and P. Spaenlehauer, Computing Loci of Rank Defects of Linear Matrices using Gröbner Bases and Applications to Cryptology, ISSAC 2010: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, pp.257-264, 2010.

J. Faugère, M. Safey-el-din, and P. Spaenlehauer, Gröbner Bases of Bihomogeneous Ideals Generated by Polynomials of Bidegree (1,1): Algorithms and Complexity, Journal of Symbolic Computation, vol.46, issue.4, pp.406-437, 2011.

J. Faugère and S. Rahmany, Solving Systems of Polynomial Equations with Symmetries using SAGBI-Gröbner bases, ISSAC 2009: Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, pp.151-158, 2009.

P. Gaudry, E. Thomé, N. Thériault, and C. Diem, A Double Large Prime Variation for Small Genus Hyperelliptic Index Calculus, Math. Comp, vol.76, issue.257, pp.475-492, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00000897

P. Gaudry, An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves, EUROCRYPT 2000, pp.19-34, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00512401

P. Gaudry, Index Calculus for Abelian Varieties of Small Simension and the Elliptic Curve Discrete Logarithm Problem, J. Symb. Comput, vol.44, issue.12, pp.1690-1702, 2009.

L. Granboulan, A. Joux, and J. Stern, Inverting HFE Is Quasipolynomial, CRYPTO 2006, pp.345-356, 2006.

A. Joux and R. Lercier, The Function Field Sieve in the Medium Prime Case, EUROCRYPT 2006, pp.254-270, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00456191

A. Kipnis and A. Shamir, Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization, CRYPTO 1999, pp.19-30, 1999.

N. Koblitz, Elliptic Curve Cryptosystems, Mathematics of Computation, vol.48, pp.203-209, 1987.

D. Lazard, Gröbner-Bases, Gaussian Elimination and Resolution of Systems of Algebraic Equations, EUROCAL 1983, pp.146-156, 1983.

F. S. Macaulay, The Algebraic Theory of Modular Systems, Cambridge Mathematical Library, vol.xxxi, 1916.

F. S. Macaulay, Some Properties of Enumeration in the Theory of Modular Systems, Proc. London Math. Soc. 26, pp.531-555, 1927.

V. S. Miller, Use of Elliptic Curves in Cryptography, CRYPTO 1985, pp.417-426, 1986.

J. Patarin, Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms, EUROCRYPT 1996, pp.33-48, 1996.

J. M. Rojas, Solving Degenerate Sparse Polynomial Systems Faster, J. Symbolic Computation, vol.28, pp.155-186, 1999.

I. Semaev, Summation Polynomials and the Discrete Logarithm Problem on Elliptic Curves, 2004.