C. Aguilar-melchor, N. Aragon, S. Bettaieb, L. Bidoux, O. Blazy et al., Rank quasi cyclic (RQC). first round submission to the NIST post-quantum cryptography call, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01946894

M. Alekhnovich, More on average case vs approximation complexity, Computational Complexity, vol.20, issue.4, pp.755-786, 2011.

N. Aragon, O. Blazy, J. Deneuville, P. Gaborit, A. Hauteville et al., LAKELow rAnk parity check codes Key Exchange-. first round submission to the NIST post-quantum cryptography call, 2017.

N. Aragon, O. Blazy, J. Deneuville, P. Gaborit, A. Hauteville et al., LOCKER-LOw rank parity ChecK codes EncRyption-. first round submission to the NIST post-quantum cryptography call, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01946962

N. Aragon, P. Gaborit, A. Hauteville, O. Ruatta, and G. Zémor, Ranksign-a signature proposal for the NIST's call-. first round submission to the NIST post-quantum cryptography call, 2017.

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, Advances in Cryptology-EUROCRYPT 2012, 2012.

E. Berlekamp, R. Mceliece, and H. Van-tilborg, On the inherent intractability of certain coding problems, IEEE Trans. Inform. Theory, vol.24, issue.3, pp.384-386, 1978.

J. Daniel, T. Bernstein, C. Lange, and . Peters, Smaller decoding exponents: ball-collision decoding, Advances in Cryptology-CRYPTO 2011, vol.6841, pp.743-760, 2011.

D. Boneh and M. K. Franklin, Identity-based encryption from the Weil pairing, Advances in Cryptology-CRYPTO, vol.2139, pp.213-229, 2001.

L. Both and A. May, Optimizing BJMM with Nearest Neighbors: Full Decoding in 2 2/21n and McEliece Security, WCC Workshop on Coding and Cryptography, 2017.

J. F. Buss, G. S. Frandsen, and J. O. Shallit, The computational complexity of some problems of linear algebra, J. Comput. System Sci, vol.58, issue.3, pp.572-596, 1999.

N. Courtois, Efficient zero-knowledge authentication based on a linear algebra problem MinRank, Advances in Cryptology-ASIACRYPT, vol.2248, pp.402-421, 2001.

N. Courtois, M. Finiasz, and N. Sendrier, How to achieve a McEliece-based digital signature scheme, Advances in Cryptology-ASIACRYPT, vol.2248, pp.157-174, 2001.
DOI : 10.1007/3-540-45682-1_10
URL : https://hal.archives-ouvertes.fr/inria-00072511

T. Debris, -. , and J. Tillich, , 2017.

N. Döttling and S. Garg, From selective IBE to full IBE and selective HIBE, Theory of Cryptography-15th International Conference, pp.372-408, 2017.

N. Döttling and S. Garg, Identity-based encryption from the Diffie-Hellman assumption, Advances in Cryptology-CRYPTO 2017, vol.10401, pp.537-569, 2017.

N. Döttling, S. Garg, M. Hajiabadi, and D. Masny, New constructions of identity-based and key-dependent message secure encryption schemes, Public-Key Cryptography-PKC 2018, vol.10769, pp.3-31, 2018.

I. Dumer, On minimum distance decoding of linear codes, Proc. 5th Joint Soviet-Swedish Int. Workshop Inform. Theory, pp.50-52, 1991.

J. Faugère, M. Safey-el-din, and P. Spaenlehauer, Computing loci of rank defects of linear matrices using gröbner bases and applications to cryptology, Symbolic and Algebraic Computation, International Symposium, ISSAC 2010, pp.257-264, 2010.

J. Faugère, F. Levy-dit-vehel, and L. Perret, Cryptanalysis of Minrank, Advances in Cryptology-CRYPTO 2008, vol.5157, pp.280-296, 2008.

M. Finiasz and N. Sendrier, Security bounds for the design of codebased cryptosystems, Advances in Cryptology-ASIACRYPT 2009, vol.5912, pp.88-105, 2009.

. M. Ernst and . Gabidulin, Attacks and counter-attacks on the GPT public key cryptosystem, Des. Codes Cryptogr, vol.48, issue.2, pp.171-177, 2008.

M. Ernst, A. V. Gabidulin, and . Ourivski, Modified GPT PKC with right scrambler, Electron. Notes Discrete Math, vol.6, pp.168-177, 2001.

E. M. Gabidulin, A. V. Paramonov, and O. V. Tretjakov, Ideals over a noncommutative ring and their applications to cryptography, Advances in Cryptology-EUROCRYPT'91, number 547 in LNCS, pp.482-489, 1991.

P. Gaborit, A. Hauteville, J. Duong-hieu-phan, and . Tillich, Identity-based encryption from rank metric, Advances in CryptologyCRYPTO2017, volume 10403 of LNCS, pp.194-226, 2017.
DOI : 10.1007/978-3-319-63697-9_7
URL : https://hal.archives-ouvertes.fr/hal-01589463

P. Gaborit, G. Murat, O. Ruatta, and G. Zémor, Low rank parity check codes and their application to cryptography, Proceedings of the Workshop on Coding and Cryptography WCC'2013, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00913719

P. Gaborit, O. Ruatta, and J. Schrek, On the complexity of the rank syndrome decoding problem. CoRR, abs/1301.1026, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01280904

P. Gaborit, O. Ruatta, and J. Schrek, On the complexity of the rank syndrome decoding problem, IEEE Trans. Information Theory, vol.62, issue.2, pp.1006-1019, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01280904

P. Gaborit, O. Ruatta, J. Schrek, and G. Zémor, New results for rank-based cryptography, Progress in Cryptology-AFRICACRYPT 2014, vol.8469, pp.1-12, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01261421

P. Gaborit, O. Ruatta, J. Schrek, and G. Zémor, Ranksign: An efficient signature algorithm based on the rank metric (extended version on arxiv), Post-Quantum Cryptography, vol.8772, pp.88-107, 2014.

P. Gaborit and G. Zémor, On the hardness of the decoding and the minimum distance problems for rank codes, IEEE Trans. Information Theory, vol.62, issue.12, pp.7245-7252, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01443111

C. Gentry, C. Peikert, and V. Vaikuntanathan, Trapdoors for hard lattices and new cryptographic constructions, Proceedings of the fortieth annual ACM symposium on Theory of computing, pp.197-206, 2008.
DOI : 10.1145/1374376.1374407

A. Kipnis and A. Shamir, Cryptanalysis of the HFE public key cryptosystem by relinearization, Advances in Cryptology-CRYPTO'99, vol.1666, pp.19-30, 1999.

J. Pil, E. F. Lee, and . Brickell, An observation on the security of McEliece's public-key cryptosystem, Advances in Cryptology-EUROCRYPT'88, vol.330, pp.275-280, 1988.

P. Loidreau, Asymptotic behaviour of codes in rank metric over finite fields, Des. Codes Cryptogr, vol.71, issue.1, pp.105-118, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00745087

A. May, A. Meurer, and E. Thomae, Decoding random linear codes in O(2 0.054n ), Advances in Cryptology-ASIACRYPT 2011, vol.7073, pp.107-124, 2011.
DOI : 10.1007/978-3-642-25385-0_6
URL : https://link.springer.com/content/pdf/10.1007%2F978-3-642-25385-0_6.pdf

A. May and I. Ozerov, On computing nearest neighbors with applications to decoding of binary linear codes, Advances in Cryptology-EUROCRYPT 2015, vol.9056, pp.203-228, 2015.

H. Niederreiter, Knapsack-type cryptosystems and algebraic coding theory. Problems of Control and Information Theory, vol.15, pp.159-166, 1986.

E. Prange, The use of information sets in decoding cyclic codes, IRE Transactions on Information Theory, vol.8, issue.5, pp.5-9, 1962.

R. Sakai, K. Ohgishi, and M. Kasahara, Cryptosystems based on pairing, SCIS 2000, 2000.

A. Shamir, Identity-based cryptosystems and signature schemes, Advances in Cryptology-CRYPTO, vol.84, pp.47-53, 1984.
DOI : 10.1007/3-540-39568-7_5

P. Spaenlenhauer, Résolution de systèmes multi-homogènes et determinantiels, 2012.

J. Stern, A method for finding codewords of small weight, Coding Theory and Applications, vol.388, pp.106-113, 1988.