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

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

V. D. Belousov, Osnovi teorii kvazigrup i lup, 1967.

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, 2009.
DOI : 10.1515/JMC.2009.009
URL : https://hal.archives-ouvertes.fr/hal-01148127

L. Bettale, J. Faugère, and L. Perret, Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants, PKC 2011, pp.441-458, 2011.
DOI : 10.1007/978-3-642-19379-8_27
URL : https://hal.archives-ouvertes.fr/hal-01287981

C. Bouillaguet, J. Faugère, P. Fouque, and L. Perret, Practical Cryptanalysis of the Identification Scheme Based on the Isomorphism of Polynomial with One Secret Problem, PKC 2011, pp.473-493, 2011.
DOI : 10.1007/978-3-642-19379-8_29
URL : https://hal.archives-ouvertes.fr/inria-00556671

Y. Chen, S. J. Knapskog, and D. Gligoroski, Multivariate quadratic quasigroups (MQQs): Construction, bounds and complexity, Inscrypt, 6th International Conference on Information Security and Cryptology, 2010.

J. Denes and A. D. Keedwell, Latin squares and their applications, 1974.

J. Ding, C. Wolf, and B. Yang, Invertible Cycles for Ultivariate Uadratic (q) Public Key Cryptography, PKC 2007, pp.266-281, 2007.

J. Ding, B. Yang, C. O. Chen, M. Chen, and C. Cheng, New Differential-Algebraic Attacks and Reparametrization of Rainbow, ACNS 2008, pp.242-257, 2008.
DOI : 10.1007/978-3-540-68914-0_15

J. C. Faugère, P. 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. Faugere, A new efficient algorithm for computing Gröbner basis, p.4, 2000.

J. Faugère, R. S. Ødegård, L. Perret, and D. Gligoroski, Analysis of the MQQ Public Key Cryptosystem, CANS 2010, pp.169-183, 2010.
DOI : 10.1007/978-3-642-17619-7_13

J. Faugère and L. Perret, Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects, EUROCRYPT 2006, pp.30-47, 2006.
DOI : 10.1007/11761679_3

P. Fouque, L. Granboulan, and J. Stern, Differential Cryptanalysis for Multivariate Schemes, EUROCRYPT 2005, pp.341-353, 2005.
DOI : 10.1007/11426639_20
URL : https://hal.archives-ouvertes.fr/inria-00563961

M. R. Garey and D. S. Johnson, Computers and Intractability. A guide to the theory of NP-Completeness, 1979.

D. Gligoroski, S. Markovski, and S. J. Knapskog, Public key block cipher based on multivariate quadratic quasigroups, Cryptology ePrint Archive Report, p.320, 2008.

D. Gligoroski, S. Markovski, and S. J. Knapskog, Multivariate quadratic trapdoor functions based on multivariate quadratic quasigroups, MATH 2008: Proceedings of the American Conference on Applied Mathematics, pp.44-49, 2008.

L. Goubin and N. T. Courtois, Cryptanalysis of the TTM Cryptosystem, ASIACRYPT 2000, pp.44-57, 2000.
DOI : 10.1007/3-540-44448-3_4

L. Goubin, N. T. Courtois, and C. Schlumbergersema, Cryptanalysis of the TTM Cryptosystem, ASIACRYPT 2000, pp.44-57, 2000.
DOI : 10.1007/3-540-44448-3_4

H. Imai and T. Matsumoto, Algebraic methods for constructing asymmetric cryptosystems, AAECC-3, pp.108-119, 1986.
DOI : 10.1007/3-540-16776-5_713

M. Kasahara and R. Sakai, A construction of public key cryptosystem for realizing ciphertext of size 100 bit and digital signature scheme, IEICE Transactions, vol.871, pp.102-109, 2004.

J. Katz, Digital Signatures, 2010.
DOI : 10.1007/978-0-387-27712-7

A. Kipnis and A. Shamir, Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization, CRYPTO 1999, pp.19-30, 1999.
DOI : 10.1007/3-540-48405-1_2

N. Koblitz, Elliptic curve cryptosystems, Mathematics of Computation, vol.48, issue.177, pp.203-209, 1987.
DOI : 10.1090/S0025-5718-1987-0866109-5

T. Matsumoto and H. Imai, Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption, CRYPT 1988, pp.419-453, 1988.
DOI : 10.1007/3-540-45961-8_39

V. S. Miller, Use of Elliptic Curves in Cryptography, CRYPTO 1985, pp.417-426, 1986.
DOI : 10.1007/3-540-39799-X_31

T. Moh, A public key system with signature and master key functions, Communications in Algebra, vol.168, issue.4, 1999.
DOI : 10.1145/359340.359342

M. S. Mohamed, J. Ding, J. Buchmann, and F. Werner, Algebraic Attack on the MQQ Public Key Cryptosystem, CANS 2009, pp.392-401, 2009.
DOI : 10.1007/978-3-642-10433-6_26

J. Patarin, Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms, ROCRYPT 1996, pp.33-48, 1996.
DOI : 10.1007/3-540-68339-9_4

J. Patarin, Cryptanalysis of the Matsumoto and Imai public key scheme of Eurocrypt 98, Designs, Codes and Cryptography, vol.20, issue.2, pp.175-209, 2000.
DOI : 10.1023/A:1008341625464

L. Perret, A Fast Cryptanalysis of the Isomorphism of Polynomials with One Secret Problem, EUROCRYPT 2005, pp.354-370, 2005.
DOI : 10.1007/11426639_21

L. Perret, Personal e-mail communication with Danilo Gligoroski, 2008.

A. Petzoldt, S. Bulygin, and J. Buchmann, Cyclicrainbow -a multivariate signature scheme with a partially cyclic public key based on rainbow, Cryptology ePrint Archive Report, vol.424, 2010.

R. L. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, vol.21, issue.2, pp.120-126, 1978.
DOI : 10.1145/359340.359342

S. Samardjiska, S. Markovski, and D. Gligoroski, Multivariate quasigroups defined by t-functions, Proceedings of SCC 2010 -The 2nd International Conference on Symbolic Computation and Cryptography, 2010.

S. Samardjiska, Y. Chen, and D. Gligoroski, Construction of Multivariate Quadratic Quasigroups (MQQs) in arbitrary Galois fields, 2011 7th International Conference on Information Assurance and Security (IAS), 2011.
DOI : 10.1109/ISIAS.2011.6122839

A. Shamir, Efficient Signature Schemes Based on Birational Permutations, CRYPTO 1993, pp.1-12, 1994.
DOI : 10.1007/3-540-48329-2_1

R. P. Singh, B. K. Sarma, and A. Saikia, Public key cryptography using permutation ppolynomials over finite fields, Cryptology ePrint Archive Report, vol.208, 2009.

J. D. Smith, An introduction to quasigroups and their representations, CRC, vol.48, 2007.
DOI : 10.1201/9781420010633

C. Wolf, A. Braeken, and B. Preneel, On the security of stepwise triangular systems, Designs, Codes and Cryptography, vol.27, issue.5, pp.285-302, 2006.
DOI : 10.1007/s10623-006-0015-5

C. Wolf and B. Preneel, Taxonomy of public key schemes based on the problem of multivariate quadratic equations, Cryptology ePrint Archive Report, p.77, 2005.

B. Yang and J. Chen, Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS, ACISP 2005, pp.518-531, 2005.
DOI : 10.1007/11506157_43

B. Yang, C. Cheng, B. Chen, and J. Chen, Implementing Minimized Multivariate PKC on Low-Resource Embedded Systems, SPC 2006, pp.73-88, 2006.
DOI : 10.1007/11734666_7