R. Avanzi, S. Hoerder, D. Page, and M. Tunstall, Side-channel attacks on the McEliece and Niederreiter public-key cryptosystems, Etude des systèmes algébriques surdéterminés. Applications aux codes correcteurs etàetà la cryptographie, pp.271-281, 2004.
DOI : 10.1007/s13389-011-0024-9

M. Barbier and P. S. Barreto, Key reduction of McEliece's cryptosystem using list decoding, 2011 IEEE International Symposium on Information Theory Proceedings, pp.2681-2685, 2011.
DOI : 10.1109/ISIT.2011.6034058

M. Baldi, M. Bianchi, F. Chiaraluce, J. Rosenthal, and D. Schipani, Enhanced Public Key Security for the McEliece Cryptosystem, Journal of Cryptology, vol.29, issue.1, pp.1-27, 2014.
DOI : 10.1007/s00145-014-9187-8

T. P. Berger, P. L. Cayrel, P. Gaborit, and A. Otmani, Reducing Key Length of the McEliece Cryptosystem, Progress in Cryptology -Second International Conference on Cryptology in Africa, pp.77-97, 2009.
DOI : 10.1007/BFb0019850

URL : https://hal.archives-ouvertes.fr/hal-01081727

S. L. Paulo, P. Barreto, R. Cayrel, R. Misoczki, ]. W. Niebuhrbcp97a et al., Quasi-Dyadic CFS Signatures The Magma Algebra System I: The User Language The Magma algebra system I: The user language, Lecture Notes in Computer Science J. Symb. Comput. Journal of Symbolic Computation, vol.6584, issue.113, pp.336-349, 1997.

D. J. Bernstein, T. Chou, and P. Schwabe, McBits: Fast Constant-Time Code-Based Cryptography, Cryptographic Hardware and Embedded Systems -CHES 2013 -15th International Workshop Proceedings, pp.250-272, 2013.
DOI : 10.1007/978-3-642-40349-1_15

R. Elwyn, . P. Berlekampber99-]-t, and . Berger, Algebraic coding theory Failure of the McEliece Public-Key Cryptosystem Under Message-Resend and Related-Message Attack Cyclic alternant codes induced by an automorphism of a GRS code, Advances in Cryptology -CRYPTO '97, 17th Annual International Cryptology Conference Proceedings Finite fields: Theory, Applications and Algorithms, pp.39-213, 1968.

P. Thierry and . Berger, Goppa and related codes invariant under a prescribed permutation, IEEE Transactions on Information Theory, vol.46, issue.84, pp.2628-2633, 2000.

J. Daniel, . Bernstein, . Grover, . Mceliece, J. Luk-bettale et al., Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants, Proceedings of the Third International Conference on Post-Quantum Cryptography, PQCrypto'10 Public Key Cryptography, pp.73-80, 2010.

M. Bardet, J. Faugère, and B. Salvy, On the complexity of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:math> Gr??bner basis algorithm, Journal of Symbolic Computation, vol.70, issue.0, pp.49-70, 2015.
DOI : 10.1016/j.jsc.2014.09.025

B. Biswas, Aspects de mise en oeuvre de la cryptographie basée sur les codes, Thèse, ´ Ecole Polytechnique X, p.137, 2010.

A. Becker, A. Joux, A. May, and A. Meurer, Decoding Random Binary Linear Codes in 2 n/20: How 1???+???1???=???0 Improves Information Set Decoding, How to Mask the Structure of Codes for a Cryptographic Use. Designs Codes and Cryptography, pp.520-536, 1920.
DOI : 10.1007/978-3-642-29011-4_31

A. Bogdanov and C. Lee, Homomorphic encryption from codes. CoRR, abs/1111, pp.55-66, 2011.

S. L. Paulo, R. Barreto, R. Lindner, and . Misoczki, Monoidic Codes in Cryptography, Yang [Yan11], pp.179-199, 1920.

D. J. Bernstein, T. Lange, and C. Peters, Attacking and Defending the McEliece Cryptosystem, Post-Quantum Cryptography, Second International Workshop Proceedings, pp.31-46, 2008.
DOI : 10.1007/0-387-34799-2_10

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.3548

D. J. Bernstein, T. Lange, and C. Peters, Smaller Decoding Exponents: Ball-Collision Decoding, Lecture Notes in Computer Science, vol.6841, pp.743-760, 2011.
DOI : 10.1007/978-3-642-22792-9_42

URL : http://repository.tue.nl/714848

D. J. Bernstein, T. Lange, C. Peters, ]. E. Wild-mceliece-incognitobmvt78, R. Berlekamp et al., On the inherent intractability of certain coding problems Information Theory A New Algorithm for Finding Minimum-Weight Words in a Linear Code: Application to McEliece's Cryptosystem and to Narrow-Sense BCH Codes of Length 511, Proceedings of the 4th International Conference on Post-Quantum Cryptography Reed- Solomon codes and their applicationsCFS01] N. T. Courtois, M. Finiasz, and N. Sendrier. How to Achieve a McEliece-Based Digital Signature Scheme. Lecture Notes in Computer Science, pp.244-254, 1965.

A. Couvreur, P. Gaborit, V. Gauthier-umaña, A. Otmani, and J. Tillich, Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes. Designs, Codes and Cryptography, pp.641-666, 2014.
DOI : 10.1007/s10623-014-9967-z

URL : https://hal.archives-ouvertes.fr/hal-00830594

P. Cayrel, P. Gaborit, E. Prouff, ]. D. Cox, J. B. Little et al., Secure Implementation of the Stern Authentication and Signature Schemes for Low-Resource Devices Ideals, Varieties, and algorithms: an Introduction to Computational Algebraic Geometry and Commutative Algebra Algebraic Attacks on Stream Ciphers with Linear Feedback, CARDIS, volume 5189 of Lecture Notes in Computer Science EUROCRYPT, volume 2656 of Lecture Notes in Computer Science, pp.191-205, 2003.

A. Couvreur, I. Marquez-corbella, and R. Pellikaan, A polynomial time attack against algebraic geometry code based public key cryptosystems, 2014 IEEE International Symposium on Information Theory, pp.1446-1450, 2014.
DOI : 10.1109/ISIT.2014.6875072

URL : https://hal.archives-ouvertes.fr/hal-00937476

A. Couvreur, A. Otmani, and J. Tillich, Polynomial Time Attack on Wild McEliece over Quadratic Extensions, EUROCRYPT, page to appear, pp.30-134, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00931774

A. Couvreur, A. Otmani, J. Tillich, and V. Gauthier-umaña, A Polynomial-Time Attack on the BBCRS Cryptosystem, Public- Key Cryptography -PKC, page to appear, p.55, 2015.

L. Dallot, Towards a Concrete Security Proof of Courtois, Finiasz and Sendrier Signature Scheme, DBL14] 2014 IEEE International Symposium on Information Theory, pp.65-77, 2007.
DOI : 10.1007/978-3-540-88353-1_6

N. Döttling, R. Dowsley, J. Müller-quade, A. C. Nascimentodel75-]-p, and . Delsarte, A CCA2 Secure Variant of the McEliece Cryptosystem On subfield subcodes of modified Reed-Solomon codes McEliece and Niederreiter Cryptosystems That Resist Quantum Fourier Sampling Attacks, Advances in Cryptology ? CRYPTO 2011 [DMS03] I. Dumer, D. Micciancio, and M. Sudan. Hardness of approximating the minimum distance of a linear code. Information Theory, pp.6672-6680, 1975.

A. Dür, The automorphism groups of Reed-Solomon codes, Journal of Combinatorial Theory, Series A, vol.44, issue.1, pp.69-82, 1987.
DOI : 10.1016/0097-3165(87)90060-4

J. Faugère, A new efficient algorithm for computing Gröbner bases (F4), Journal of Pure and Applied Algebra, vol.139, issue.110, pp.1-361, 1999.

J. Charles and F. , 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 '02, pp.75-83, 2002.

J. Faugère, FGb: A Library for Computing Gr??bner Bases, Mathematical Software -ICMS 2010, pp.84-87, 2010.
DOI : 10.1007/978-3-642-15582-6_17

J. Faugère, P. Gaudry, and L. Huot, Sub-cubic change of ordering for Gröbner basis: a probabilistic approach, International Symposium on Symbolic and Algebraic Computation, IS- SAC '14, pp.170-177, 2014.

J. Faugère, P. M. Gianni, D. Lazard, and T. Mora, Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering

J. Faugère, V. Gauthier-umaña, A. Otmani, L. Perret, and J. Tillich, A distinguisher for high rate mceliece cryptosystems, pp.282-286, 2011.

J. Faugère, V. Gauthier-umaña, A. Otmani, L. Perret, and J. Tillich, A Distinguisher for High-Rate McEliece Cryptosystems, IEEE Transactions on Information Theory, vol.59, issue.10, pp.6830-6844, 2013.
DOI : 10.1109/TIT.2013.2272036

J. Faugère and A. Joux, Algebraic cryptanalysis of Hidden Field Equation (HFE) cryptosystems using Gröbner bases, Advances in Cryptology -CRYPTO 2003, pp.44-60, 2003.

J. Faugère, F. Levy-dit, L. Vehel, and . Perret, Cryptanalysis of MinRank, Advances in Cryptology -CRYPTO'08, pp.280-296, 2008.
DOI : 10.1007/978-3-540-85174-5_16

A. Jean-charles-faugère, L. Otmani, and . Perret, Frédéric de Portzamparc , and Jean-Pierre Tillich. Folding Alternant and Goppa Codes with Non- Trivial Automorphism Groups, IACR Cryptology ePrint Archive, pp.353-81, 2014.

A. Jean-charles-faugère, L. Otmani, . Perret, J. Frédéric-de-portzamparc, and . Tillich, Structural weakness of compact variants of the mceliece cryptosystem, 2014 IEEE International Symposium on Information Theory, pp.1717-1721, 2014.

F. C. Faugère, A. Otmani, L. Perret, F. De-portzamparc, and J. P. Tillich, Structural Cryptanalysis of McEliece-Like Schemes with Symmetric Keys, p.105

J. Faugère, A. Otmani, L. Perret, and J. Tillich, Algebraic Cryptanalysis of McEliece Variants with Compact Keys, Lecture Notes in Computer Science, vol.6110, issue.120, pp.279-298, 2010.
DOI : 10.1007/978-3-642-13190-5_14

J. Faugère, A. Otmani, L. Perret, and J. Tillich, Algebraic Cryptanalysis of McEliece Variants with Compact Keys ? Toward a Complexity Analysis, SCC '10: Proceedings of the 2nd International Conference on Symbolic Computation and Cryptography, pp.45-55, 2010.

J. Faugère, L. Perret, F. De-portzamparc, and R. O. , Algebraic Attack against Variants of McEliece with Goppa Polynomial of a Special Form, Palash Sarkar and Tetsu Iwata Advances in Cryptology -ASI- ACRYPT 2014 -20th International Conference on the Theory and Application BIBLIOGRAPHY of Cryptology and Information Security Proceedings, Part I, pp.21-41, 2014.
DOI : 10.1007/978-3-662-45611-8_2

J. Faugère and P. Spaenlehauer, Algebraic Cryptanalysis of the PKC???2009 Algebraic Surface Cryptosystem, Public Key Cryptography -PKC 2010, 13th International Conference on Practice and Theory in Public Key Cryptography Proceedings Encyclopedia of Cryptography and Security, pp.35-52, 2010.
DOI : 10.1007/978-3-642-13013-7_3

J. Faugère, M. Safey-el-din, and P. Spaenlehauer, Gr??bner bases of bihomogeneous ideals generated by polynomials of bidegree <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>: Algorithms and complexity, Journal of Symbolic Computation, vol.46, issue.4, pp.406-437, 1985.
DOI : 10.1016/j.jsc.2010.10.014

]. P. Gab05 and . Gaborit, Shorter keys for code based cryptography Post-Quantum Cryptography -5th International Workshop Toward a Secure Implementation of McEliece Decryption, Proceedings of the 2005 International Workshop on Coding and Cryptography (WCC 2005) Proceedings, volume 7932 of Lecture Notes in Computer Science Constructive Side-Channel Analysis and Secure Design -6th International Workshop, pp.81-91, 2005.

R. Michael, D. S. Garey, and . Johnson, Computers and Intractability; A Guide to the Theory of NP-Completeness, 1990.

K. Gandolfi, C. Mourtel, F. O. , D. Genkin, A. Shamir et al., Electromagnetic Analysis: Concrete Results RSA Key Extraction via Low- Bandwidth Acoustic Cryptanalysis, Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems, CHES '01 Advances in Cryptology -CRYPTO 2014 -34th Annual Cryptology Conference Proceedings, Part I, pp.251-261, 2001.

S. Heyse, ]. H. Janwa, and O. Moreno, McEliece Public Key Cryptosystems Using Algebraic- Geometric Codes. Designs Codes and Cryptography Semantically Secure McEliece Public-Key Cryptosystems-Conversions for McEliece PKC, Implementation of McEliece Based on Quasi-dyadic Goppa Codes for Embedded Devices Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography, PKC '01, pp.143-162, 1996.

C. Paul, J. Kocher, B. Jaffe, and . Jun, Differential Power Analysis, Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology, CRYPTO '99, pp.388-397, 1999.

C. Paul and . Kocher, Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems, Advances in Cryptology ? CRYPTO '96, pp.104-113, 1996.

D. Lazard, ]. P. Gröbner-baseslb88, E. F. Lee, and . Brickell, Gaussian Elimination and Resolution of Systems of Algebraic Equations An Observation on the Security of McEliece's Public-Key Cryptosystem, Proceedings of the European Computer Algebra Conference on Computer Algebra, EUROCAL '83 Advances in Cryptology -EUROCRYPT'88, pp.146-156, 1983.

R. H. Yuan-xing-li, X. Deng, and . Wang, On the equivalence of McEliece's and Niederreiter's public-key cryptosystems. Information Theory Towards an approach using algebraic properties of the ?subcode, Proceedings of the Workshop on Coding and Cryptography, WCC 2011, pp.271-273, 1994.

]. J. Matthieu-legeayleo82 and . Leon, Utilisation du groupe de permutations d'un code correcteur pour améliorer l'efficacité du décodage Computing automorphism groups of error-correcting codes. Information Theory A probabilistic algorithm for computing minimum weights of large error-correcting codes, Univ. Rennes IEEE Transactions on IEEE Transactions on Information Theory, vol.1, issue.29, pp.92496-5111354, 1982.

R. Lidl and H. Niederreiter, Finite Fields, p.130, 1997.
DOI : 10.1017/CBO9780511525926

N. [. Loidreau and . Sendrier, Weak keys in the McEliece public-key cryptosystem, IEEE Transactions on Information Theory, vol.47, issue.3, pp.1207-1211, 1920.
DOI : 10.1109/18.915687

G. Landais and N. Sendrier, Implementing CFS, Progress in Cryptology -INDOCRYPT 2012, 13th International Conference on Cryptology in India, pp.474-488, 2012.
DOI : 10.1007/978-3-642-34931-7_27

URL : https://hal.archives-ouvertes.fr/hal-00880644

S. Francis, S. L. Macaulay-paulo, and . Barreto, The Algebraic Theory of Modular Systems Compact McEliece Keys from Goppa Codes Revised Selected Papers, Selected Areas in Cryptography, 16th Annual International WorkshopMcE78] R. J. McEliece. A Public-Key System Based on Algebraic Coding Theory, pp.65-376, 1916.

A. Meurer, A. Coding-theoretic-alexander-may, E. Meurer, C. Thomae, J. Monico et al., Alexander May and Ilya Ozerov On Computing Nearest Neighbors with Applications to Decoding of Binary Linear Codes Using low density parity check codes in the McEliece cryptosystem The Theory of Error-Correcting Codes. North?Holland Cryptanalysis of the Sidelnikov cryptosystem MDPC-McEliece: New McEliece variants from Moderate Density Parity- Check codes Broadcast Attacks against Code- Based Schemes, Decoding Random Linear Codes iñ O(2 0.054n Eurocrypt 2015 Information Theory Proceedings. IEEE International Symposium on Eurocrypt Proceedings of the 2013 IEEE International Symposium on Information TheoryNIKM08] Ryo Nojima, Hideki Imai, Kazukuni Kobara, and Kirill Morozov. Semantic security for the McEliece cryptosystem without random oracles. Des. Codes Cryptography, pp.49-107, 1986.

R. Niebuhr, M. Meziani, S. Bulygin, J. Buchmann, ¨. Ors et al., Selecting parameters for secure McEliece-based cryptosystems, Cryptographic Hardware and Embedded Systems - CHES 2003, 5th International Workshop ProceedingsOS09] Raphael Overbeck and Nicolas Sendrier Post-Quantum Cryptography, pp.137-147, 2003.
DOI : 10.1007/s10207-011-0153-2

R. Overbeck, V. Attack, and . Overbeck, Structural Attacks for Public Key Cryptosystems based??on Gabidulin Codes, Proceedings of the 1st International Conference on Progress in Cryptology in Malaysia, Mycrypt'05, pp.50-63280, 1975.
DOI : 10.1007/s00145-007-9003-9

[. Pless, R. A. Brualdi, and W. C. Huffman, Handbook of Coding Theory Compact McEliece keys based on quasi-dyadic Srivastava codes, Per12b] Edoardo Persichetti. On a CCA2-secure variant of McEliece in the standard model. IACR Cryptology ePrint Archive, pp.49149-169, 1998.

C. Peters, Information-set decoding for linear codes over Fq URL: http://eprint.iacr.org Polynomial Codes Over Certain Finite Fields, Sen97] Nicolas Sendrier, pp.81-94, 1953.

]. N. Sen00 and . Sendrier, Finding the permutation between equivalent linear codes: The support splitting algorithm, IEEE Transactions on Information Theory, vol.46, issue.53, pp.1193-1203, 2000.

[. Sendrier, CryptosystèmesCryptosystèmesà clé publique basés sur les codes correcteurs d'erreurs, Sha94] I. Shafarevich. Basic Algebraic Geometry, Varieties in Projective Space, pp.54-167, 1994.

W. Peter and . Shor, Algorithms for Quantum Computation: Discrete Logarithms and Factoring, 35th Annual Symposium on Foundations of Computer Science, pp.20-22, 1994.

W. Peter, . Shor-i, . Ithaca, and U. Ny, ANTS, Algorithmic Number Theory, First International Symposium Proceedings Sidelnikov. A public-key cryptosystem based on binary Reed-Muller codes. Discrete Mathematics and ApplicationsSKHN75] Yasuo Sugiyama, Masao Kasahara, Shigeichi Hirasawa, and Toshihiko Namekawa. A method for solving key equation for decoding goppa codes. Information and Control, pp.289-5087, 1975.

[. Sugiyama, M. Kasahara, S. Hirasawa, and T. Namekawa, Further results on Goppa codes and their applications to constructing efficient binary codes. Information Theory, IEEE Transactions on, vol.22, issue.5, pp.518-526, 1976.

S. [. Sidelnikov, . V. Shestakovss01a-]-d, N. R. Sarwate, and . Shanbhag, On the insecurity of cryptosystems based on generalized Reed-Solomon codes Sendrier and G. Skersys. Permutation groups of error-correcting codes, WCC '99, Book of abstracts High-speed architectures for Reed-Solomon decoders. Very Large Scale Integration (VLSI) Systems, pp.439-444, 1992.

]. N. Ss01b, G. Sendrier, and . Skersys, On the Computation of the Automorphism Group of a Linear Code, IEEE ConferenceSS13a] Nicolas Sendrier and Dimitrios E. Simos. How easy is code equivalence over Fq? In WCC 2013 -International Workshop on Coding and Cryptography, p.54, 2001.

N. Sendrier and D. E. Simos, The Hardness of Code Equivalence over $\mathbb{F}_q$ and Its Application to Code-Based Cryptography, Gaborit [Gab13], pp.203-216
DOI : 10.1007/978-3-642-38616-9_14

A. Shoufan, F. Strenzke, H. G. Molter, M. Stöttingerste88, and ]. J. Stern, A Timing Attack against Patterson Algorithm in the McEliece PKC, Coding Theory and Applications, pp.161-175, 1988.
DOI : 10.1007/978-3-642-14423-3_12

E. Stinson, Advances in Cryptology -CRYPTO'93, Lecture Notes in Computer Science, vol.773, issue.5, pp.13-21, 1993.
DOI : 10.1007/3-540-48329-2

E. Stm-+-08-]-falko-strenzke, H. G. Tews, R. Molter, A. Overbeck, and . Shoufan, Side Channels in the McEliece PKC, Proceedings of the 2Nd International Workshop on Post-Quantum Cryptography, PQCrypto '08, pp.216-229, 2008.

F. Strenzke, Timing Attacks against the Syndrome Inversion in Code-Based Cryptosystems, Gaborit [Gab13], pp.217-230
DOI : 10.1007/978-3-642-38616-9_15

]. A. Swm-+-10, T. Shoufan, H. G. Wink, S. A. Molter, E. Huss et al., A Novel Cryptoprocessor Architecture for the McEliece Public-Key Cryptosystem. Computers Modified Euclidean algorithms for decoding Reed-Solomon codes, Information Theory ISIT 2009. IEEE International Symposium on, pp.1533-1546, 2009.

]. A. Var97a and . Vardy, The intractability of computing the minimum distance of a code Information Theory, IEEE Transactions on, vol.43, issue.6, pp.1757-1766, 1997.

A. Vardy, Algorithmic complexity in coding theory and the minimum distance problem, Proceedings of the twenty-ninth annual ACM symposium on Theory of computing , STOC '97, pp.92-109, 1997.
DOI : 10.1145/258533.258559

]. C. Wie06a and . Wieschebrink, Two np-complete problems in coding theory with an application in code based cryptography, Information Theory IEEE International Symposium on, pp.1733-1737, 2006.