J. Baena, C. Clough, and J. Ding, Square-Vinegar Signature Scheme, PQCrypto '08: Proceedings of the 2nd International Workshop on Post-Quantum Cryptography, pp.17-30, 2008.
DOI : 10.1007/3-540-49649-1_4

M. Bardet, J. C. Faugère, B. Salvy, and B. Y. Yang, Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems, MEGA'05. (2005) Eighth International Symposium on Effective Methods in Algebraic Geometry

M. Bardet, Étude des systèmes algébriques surdéterminés. Applications aux codes correcteurs et à la cryptographie, 2004.

M. Bardet, J. C. 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. C. Faugère, B. Salvy, and B. Y. 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. A. Bennett, Products of skew-symmetric matrices, Bulletin of the American Mathematical Society, vol.25, issue.10, pp.455-458, 1919.
DOI : 10.1090/S0002-9904-1919-03224-8

D. S. Bernstein, Matrix mathematics. Theory, facts, and formulas, p.1139, 2009.

O. Billet and H. Gilbert, A Traceable Block Cipher, Lecture Notes in Computer Science, vol.2894, pp.331-346, 2003.
DOI : 10.1007/978-3-540-40061-5_21

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.235-265, 1997.
DOI : 10.1006/jsco.1996.0125

C. Chevalley, D??monstration d???une hypoth??se de M. Artin, Abhandlungen aus dem Mathematischen Seminar der Universit??t Hamburg, vol.11, issue.1, pp.73-75, 1935.
DOI : 10.1007/BF02940714

C. Clough, J. Baena, J. Ding, B. Y. Yang, and M. S. Chen, Square, a New Multivariate Encryption Scheme, Lecture Notes in Computer Science, vol.139, issue.1-3, pp.252-264, 2009.
DOI : 10.1007/BFb0028491

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.4468

J. Ding, C. Wolf, and B. Y. Yang, ???-Invertible Cycles for $\mathcal{M}$ ultivariate $\mathcal{Q}$ uadratic ( ${\mathcal{MQ}}$ ) Public Key Cryptography, Lecture Notes in Computer Science, vol.4450, pp.266-281, 2007.
DOI : 10.1007/978-3-540-71677-8_18

F. L. Dit-vehel and L. Perret, Polynomial Equivalence Problems and Applications to Multivariate Cryptosystems, Lecture Notes in Computer Science, vol.2904, pp.235-251, 2003.
DOI : 10.1007/978-3-540-24582-7_18

URL : https://hal.archives-ouvertes.fr/inria-00071464

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. C. 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. C. Faugère, A New Efficient Algorithm for Computing Gröbner Bases Without Reduction to Zero (F5), ISSAC '02: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, pp.75-83, 2002.

J. C. Faugère and L. Perret, Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects, Lecture Notes in Computer Science, vol.4004, pp.30-47, 2006.
DOI : 10.1007/11761679_3

A. Fiat and A. Shamir, How To Prove Yourself: Practical Solutions to Identification and Signature Problems, Lecture Notes in Computer Science, vol.263, pp.186-194, 1986.
DOI : 10.1007/3-540-47721-7_12

S. Fortin, The graph isomorphism problem, 1996.

P. A. Fuhrmann, A polynomial approach to linear algebra, 1996.

J. Fulman, Random matrix theory over finite fields, Bulletin of the American Mathematical Society, vol.39, issue.01, pp.51-85
DOI : 10.1090/S0273-0979-01-00920-X

URL : http://arxiv.org/pdf/math/0003195v2.pdf

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

W. Geiselmann, W. Meier, and R. Steinwandt, An attack on the isomorphisms of polynomials problem with one secret, International Journal of Information Security, vol.26, issue.1, pp.59-64, 2003.
DOI : 10.1007/s10207-003-0025-5

W. Geiselmann, R. Steinwandt, and T. Beth, Attacking the Affine Parts of SFLASH, Lecture Notes in Computer Science, vol.2260, pp.355-359, 2001.
DOI : 10.1007/3-540-45325-3_31

O. Goldreich, S. Micali, and A. Wigderson, Proofs that yield nothing but their validity and a methodology of cryptographic protocol design (extended abstract), pp.174-187, 1986.

S. Goldwasser, S. Micali, and C. Rackoff, The knowledge complexity of interactive proof-systems (extended abstract), pp.291-304, 1985.

N. Koblitz, Algebraic Aspects of Cryptography, Algorithms and Computation in Mathematics, vol.3, 1998.
DOI : 10.1007/978-3-662-03642-6

D. Lazard, Gr??bner bases, Gaussian elimination and resolution of systems of algebraic equations, Lecture Notes in Computer Science, vol.162, pp.146-156, 1983.
DOI : 10.1007/3-540-12868-9_99

R. Lidl and H. Niederreiter, Finite fields, 1997.
DOI : 10.1017/CBO9780511525926

V. Lyubashevsky, Lattice-Based Identification Schemes Secure Under Active Attacks, Lecture Notes in Computer Science, vol.4939, pp.162-179, 2008.
DOI : 10.1007/978-3-540-78440-1_10

J. Macwilliams, Orthogonal Matrices Over Finite Fields, The American Mathematical Monthly, vol.76, issue.2, pp.152-164, 1969.
DOI : 10.2307/2317262

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

D. Naccache, Topics in Cryptology -CT-RSA The Cryptographer's Track at RSA Conference, Proceedings, 2001.

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

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

J. Patarin, The Oil and Vinegar signature scheme, 1997.

J. Patarin, N. Courtois, and L. Goubin, FLASH, a Fast Multivariate Signature Algorithm, pp.298-307
DOI : 10.1007/3-540-45353-9_22

J. Patarin, N. Courtois, and L. Goubin, QUARTZ, 128-Bit Long Digital Signatures, pp.282-297
DOI : 10.1007/3-540-45353-9_21

J. Patarin, L. Goubin, and N. Courtois, Improved algorithms for isomorphisms of polynomials, In: EUROCRYPT, pp.184-200, 1998.
DOI : 10.1007/BFb0054126

L. Perret, A Fast Cryptanalysis of the Isomorphism of Polynomials with One Secret Problem, Lecture Notes in Computer Science, vol.3494, pp.354-370, 2005.
DOI : 10.1007/11426639_21

D. Pointcheval, A New Identification Scheme Based on the Perceptrons Problem, In: EUROCRYPT, pp.319-328, 1995.
DOI : 10.1007/3-540-49264-X_26

A. Shamir, An Efficient Identification Scheme Based on Permuted Kernels (extended abstract), Lecture Notes in Computer Science, vol.435, pp.606-609, 1989.
DOI : 10.1007/0-387-34805-0_54

J. Stern, A new identification scheme based on syndrome decoding, Lecture Notes in Computer Science, vol.773, pp.13-21, 1993.
DOI : 10.1007/3-540-48329-2_2

J. Stern, Designing Identification Schemes with Keys of Short Size, Lecture Notes in Computer Science, vol.839, pp.164-173, 1994.
DOI : 10.1007/3-540-48658-5_18

E. Warning, Bemerkung zur vorstehenden Arbeit von Herrn Chevalley, Abh. Math. Semin. Hamb. Univ, vol.11, pp.76-83, 1935.

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.