C. Aguilar-melchor, N. Aragon, M. Bardet, S. Bettaieb, L. Bidoux et al.,

P. Deneuville, A. Gaborit, A. Hauteville, O. Otmani, J. Ruatta et al., ROLLO: Rank-Ouroboros, LAKE and LOCKER. Submission to the NIST Post-Quantum Standardization project, 2017.

C. Aguilar-melchor, N. Aragon, S. Bettaieb, L. Bidoux, O. Blazy et al., RQC: Rank Quasi-Cyclic. Submission to the NIST Post-Quantum Standardization project, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01946894

C. Aguilar-melchor, O. Blazy, J. Deneuville, P. Gaborit, and G. Zémor, Efficient encryption from random quasi-cyclic codes, IEEE Trans. Information Theory, vol.64, issue.5, pp.3927-3943, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01951335

D. Augot and M. Finiasz, A public key encryption scheme based on the polynomial reconstruction problem, Advanceds in Cryptology -EUROCRYPT 2003, vol.2656, pp.229-240, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00509191

R. Azarderakhsh, M. Campagna, C. Costello, L. De-feo, B. Hess et al., Supersingular Isogeny Key Encapsulation, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02171951

M. Bardet, P. Briaud, M. Bros, P. Gaborit, V. Neiger et al., An Algebraic Attack on Rank Metric Code-Based Cryptosystems, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02303015

M. Bardet, J. Faugère, B. Salvy, and P. Spaenlehauer, On the complexity of solving quadratic Boolean systems, J. Complexity, vol.29, issue.1, pp.53-75, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00655745

F. Chabaud and J. Stern, The cryptographic security of the syndrome decoding problem for rank distance codes, Advances in Cryptology ASIACRYPT'96, number 1163 in LNCS, pp.368-381, 1996.

N. Courtois, Efficient Zero-Knowledge Authentication Based on a Linear Algebra Problem MinRank, Advances in Cryptology -ASIACRYPT 2001, 7th International Conference on the Theory and Application of Cryptology and Information Security, vol.2248, pp.402-421, 2001.

P. Delsarte, Bilinear Forms over a Finite Field, with Applications to Coding Theory, J. Comb. Theory, Ser. A, vol.25, issue.3, pp.226-241, 1978.

J. Faugère, F. Levy-dit-vehel, and L. Perret, Cryptanalysis of MinRank, Advances in Cryptology -CRYPTO 2008, 28th Annual International Cryptology Conference, vol.5157, pp.280-296, 2008.

C. Faure and P. Loidreau, A New Public-Key Cryptosystem Based on the Problem of Reconstructing p-Polynomials, Coding and Cryptography International Workshop, pp.304-315, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00459607

E. Gabidulin, Theory of codes with maximum rank distance. Problems of Information Transmission, vol.21, pp.1-12, 1985.

E. M. Gabidulin, A Fast Matrix Decoding Algorithm for Rank-Error-Correcting Codes, Algebraic Coding, First French-Soviet Workshop, vol.573, pp.126-133, 1991.

P. Gaborit, A. Otmani, and H. Talé-kalachi, Polynomial-time key recovery attack on the Faure-Loidreau scheme based on Gabidulin codes, Des. Codes Cryptogr, vol.86, issue.7, pp.1391-1403, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02088213

L. Goubin and N. Courtois, Cryptanalysis of the TTM Cryptosystem, Advances in Cryptology -ASIACRYPT 2000, 6th International Conference on the Theory and Application of Cryptology and Information Security, vol.1976, pp.44-57, 2000.

A. Kipnis and A. Shamir, Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization, Advances in Cryptology -CRYPTO '99, 19th Annual International Cryptology Conference, vol.1666, pp.19-30, 1999.

D. Lazard, Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations, Computer Algebra, EUROCAL '83, European Computer Algebra Conference, vol.162, pp.146-156, 1983.

. Springer, , 1983.

P. Loidreau, A Welch-Berlekamp Like Algorithm for Decoding Gabidulin Codes, Coding and Cryptography, International Workshop, WCC 2005, vol.3969, pp.36-45, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00459611

P. Loidreau, On cellular codes and their cryptographic applications, Proceedings of ACCT 2014, Fourteenth International Workshop on Algebraic and Combinatorial Coding Theory, 2014.

Y. Medvedeva, Fast enumeration for Grassmannian space, 2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems, pp.48-52, 2012.

Ø. Ore, On a special class of polynomials, Transactions of the American Mathematical Society, vol.35, issue.3, pp.559-584, 1933.

Ø. Ore, Theory of non-commutative polynomials, Annals of mathematics, pp.480-508, 1933.

A. Paramonov and O. Tretjakov, An analogue of Berlekamp-Massey algorithm for decoding codes in rank metric, Proceedings of Moscow Inst. Physics and Technology (MIPT), 1991.

G. Richter and S. Plass, Fast decoding of rank-codes with rank errors and column erasures, Proceedings of the 2004 IEEE International Symposium on Information Theory, p.398, 2004.

R. M. Roth, Maximum-rank array codes and their application to crisscross error correction, IEEE Trans. Information Theory, vol.37, issue.2, pp.328-336, 1991.

N. Silberstein and T. Etzion, Enumerative Coding for Grassmannian Space, IEEE Trans. Information Theory, vol.57, issue.1, pp.365-374, 2011.

J. A. Verbel, J. Baena, D. Cabarcas, R. A. Perlner, and D. Smith-tone, On the Complexity of "Superdetermined" Minrank Instances, Post-Quantum Cryptography -10th International Conference, pp.167-186, 2019.

A. Wachter-zeh, V. B. Afanassiev, and V. Sidorenko, Fast decoding of Gabidulin codes, Des. Codes Cryptogr, vol.66, issue.1-3, pp.57-73, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00785122

A. Wachter-zeh, S. Puchinger, and J. Renner, Repairing the Faure-Loidreau Public-Key Cryptosystem, IEEE Int. Symp. Inf. Theory (ISIT), 2018.