A. Akavia, S. Goldwasser, and V. Vaikuntanathan, Simultaneous Hardcore Bits and Cryptography against Memory Attacks, Lecture Notes in Computer Science, vol.5444, pp.474-495, 2009.
DOI : 10.1007/978-3-642-00457-5_28

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.169.4112

M. R. Albrecht, P. Farshim, J. Faugère, and L. Perret, Polly Cracker, revisited, Advances in Cryptology ? ASIACRYPT 2011. full version available as Cryptology ePrint Archive, pp.179-196, 2011.
DOI : 10.1007/978-3-642-25385-0_10

URL : https://hal.archives-ouvertes.fr/hal-01112976

S. Arora and R. Ge, New Algorithms for Learning in Presence of Errors, Lecture Notes in Computer Science, vol.6755, pp.403-415, 2011.
DOI : 10.1007/978-3-540-85174-5_31

M. Bardet, ´ Etude des systèmes algébriques surdéterminés Applications aux codes correcteurs etàet`età la cryptographie, 2004.

M. Bardet, J. Faugère, and B. Salvy, Complexity study of Gröbner basis computation, 2002.

M. Bardet, J. Faugère, and B. Salvy, On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations, Proc. International Conference on Polynomial System Solving (ICPSS), pp.71-75, 2004.

M. Bardet, J. Faugère, and B. Salvy, On the Complexity of the F5 Gröbner basis Algorithm, Journal of Symbolic Computation, pp.1-24, 2014.

M. Bardet, J. Faugère, B. Salvy, and B. Yang, Asymptotic behaviour of the degree of regularity of semi-regular polynomial systems, Proc. of MEGA 2005, Eighth International Symposium on Effective Methods in Algebraic Geometry, 2005.

A. Becker, N. Gama, and A. Joux, Solving shortest and closest vector problems: The decomposition approach, IACR Cryptology ePrint Archive, p.685, 2013.

E. R. Berlekamp, R. J. Mceliece, C. A. Henk, and . Van-tilborg, On the inherent intractability of certain coding problems (Corresp.), IEEE Transactions on Information Theory, vol.24, issue.3, pp.384-386, 1978.
DOI : 10.1109/TIT.1978.1055873

L. Bettale, J. Faugère, and L. Perret, Hybrid approach for solving multivariate systems over finite fields, Journal of Mathematical Cryptology, vol.3, issue.3, pp.177-197, 2010.
DOI : 10.1515/JMC.2009.009

URL : https://hal.archives-ouvertes.fr/hal-01148127

W. Bosma, J. J. Cannon, and C. Playoust, The Magma Algebra System I: The User Language, Journal of Symbolic Computation, vol.24, issue.3-4, pp.3-4235, 1997.
DOI : 10.1006/jsco.1996.0125

Z. Brakerski, A. Langlois, C. Peikert, O. Regev, and D. Stehlé, Classical hardness of learning with errors, Proceedings of the 45th annual ACM symposium on Symposium on theory of computing, STOC '13, pp.575-584, 2013.
DOI : 10.1145/2488608.2488680

URL : https://hal.archives-ouvertes.fr/hal-00922194

Z. Brakerski and V. Vaikuntanathan, Efficient Fully Homomorphic Encryption from (Standard) LWE, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, pp.97-106, 2011.
DOI : 10.1109/FOCS.2011.12

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

B. Buchberger, G. E. Collins, R. G. Loos, and R. Albrecht, Computer algebra symbolic and algebraic computation, ACM SIGSAM Bulletin, vol.16, issue.4, pp.5-5, 1982.
DOI : 10.1145/1089310.1089312

C. Cid, S. Murphy, and M. J. Robshaw, Some Algebraic Aspects of the Advanced Encryption Standard, 2006.
DOI : 10.1007/11506447_6

D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, Proceedings of the nineteenth annual ACM conference on Theory of computing , STOC '87, pp.251-280, 1990.
DOI : 10.1145/28395.28396

URL : http://doi.org/10.1016/s0747-7171(08)80013-2

D. A. Cox, J. B. Little, and D. O. Shea, Ideals, Varieties and Algorithms, 2005.

D. J. Anick, Thin algebras of embedding dimension three, Journal of Algebra, vol.100, issue.1, pp.235-259, 1986.
DOI : 10.1016/0021-8693(86)90076-1

R. Demillo and R. Lipton, A probabilistic remark on algebraic program testing, Information Processing Letters, vol.7, issue.4, pp.192-194, 1978.
DOI : 10.1016/0020-0190(78)90067-4

N. Döttling and J. Müller-quade, Lossy Codes and a New Variant of the Learning-With-Errors Problem, Lecture Notes in Computer Science, vol.7881, pp.18-34, 2013.
DOI : 10.1007/978-3-642-38348-9_2

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), Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation ISSAC, pp.75-83, 2002.

J. Faugère, Françoise Levy dit Vehel, and Ludovic Perret. Cryptanalysis of minrank, Wagner [42], pp.280-296

J. Faugère, P. M. Gianni, D. Lazard, and T. Mora, Efficient Computation of Zero-dimensional Gr??bner Bases by Change of Ordering, Journal of Symbolic Computation, vol.16, issue.4, pp.329-344, 1993.
DOI : 10.1006/jsco.1993.1051

J. Faugère and A. Joux, Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gr??bner Bases, Lecture Notes in Computer Science, vol.2729, pp.44-60, 2003.
DOI : 10.1007/978-3-540-45146-4_3

R. Fröberg, An inequality for Hilbert series of graded algebras., MATHEMATICA SCANDINAVICA, vol.56, pp.117-144, 1985.
DOI : 10.7146/math.scand.a-12092

R. Fröberg and J. Hollman, Hilbert Series for Ideals Generated by Generic Forms, Journal of Symbolic Computation, vol.17, issue.2, pp.149-157, 1994.
DOI : 10.1006/jsco.1994.1008

L. François and . Gall, Powers of tensors and fast matrix multiplication, International Symposium on Symbolic and Algebraic Computation, pp.296-303, 2014.

C. Gentry, A fully homomorphic encryption scheme, 2009.

C. Jeannerod, C. Pernet, and A. Storjohann, Rank-profile revealing Gaussian elimination and the CUP matrix decomposition, Journal of Symbolic Computation, vol.56, pp.46-68, 2013.
DOI : 10.1016/j.jsc.2013.04.004

URL : https://hal.archives-ouvertes.fr/hal-00655543

D. Lazard, Gröbner-bases, Gaussian elimination and resolution of systems of algebraic equations, Proceedings of the European Computer Algebra Conference on Computer Algebra, 1983.

R. J. Mceliece, A Public-Key System Based on Algebraic Coding Theory, pp.114-116, 1978.

D. Micciancio and C. Peikert, Hardness of SIS and LWE with Small Parameters, Lecture Notes in Computer Science, vol.8042, issue.1, pp.21-39, 2013.
DOI : 10.1007/978-3-642-40041-4_2

C. Peikert, Public-key cryptosystems from the worst-case shortest vector problem, Proceedings of the 41st annual ACM symposium on Symposium on theory of computing, STOC '09, pp.333-342, 2009.
DOI : 10.1145/1536414.1536461

C. Peikert, V. Vaikuntanathan, and B. Waters, A Framework for Efficient and Composable Oblivious Transfer, Wagner [42], pp.554-571
DOI : 10.1007/978-3-540-85174-5_31

O. Regev, On lattices, learning with errors, random linear codes, and cryptography, STOC, pp.84-93, 2005.

O. Regev, On lattices, learning with errors, random linear codes, and cryptography, J. ACM, vol.56, issue.6, 2009.

J. T. Schwartz, Fast Probabilistic Algorithms for Verification of Polynomial Identities, Journal of the ACM, vol.27, issue.4, pp.701-717, 1980.
DOI : 10.1145/322217.322225

W. Stein, Sage Mathematics Software Version 6.2. The Sage Development Team, 2013.