Solving underdefined systems of multivariate quadratic equations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2274, Issue , 2002, Pages 211-227

  Courtois, Nicolas ^a   Goubin, Louis ^a   Meier, Willi ^b   Tacier, Jean Daniel ^b  

^a SchlumbergerSema   (France)

^b FH Aargau   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOGRAPHY; ELECTRONIC DOCUMENT IDENTIFICATION SYSTEMS; POLYNOMIALS; PUBLIC KEY CRYPTOGRAPHY;

CHARACTERISTIC 2; DIGITAL SIGNATURE SCHEMES; MULTIVARIATE POLYNOMIAL; MULTIVARIATE QUADRATIC EQUATIONS; MULTIVARIATE SYSTEMS; OIL AND VINEGAR; QUADRATIC EQUATIONS; SIGNATURE SCHEME;

AUTHENTICATION;

EID: 84958969583     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45664-3_15     Document Type: Conference Paper

References (10)

1. N. Courtois, A. Klimov, J. Patarin, A. Shamir, Efficient Algorithms for Solving Overdeßned Systems of Multivariate Polynomial Equations, Advances in Cryptol-ogy - EUROCRYPT'2000, Proceedings, B. Preneel (Ed.), Lecture Notes in Computer Science, Springer Verlag, vol. 1807, pp. 392-407.
2. J.-Ch. Faugere, A new efficient algorithm for computing Gröbner bases (FA),Journal of Pure and Applied Algebra 139 (1999), pp. 61-88. See www.elsevier.com/locate/jpaa.
3. M. R. Garey, D. S. Johnson, Computers and Intractability, A Guide to the Theory of NP-completeness, W. H. Freeman and Company, New York, 1979.
4. A. Kipnis, J. Patarin, L. Goubin, Unbalanced Oil and Vinegar Signature Schemes, Advances in Cryptology - EUROCRYPT'99, Proceedings, J. Stern (Ed.), Lecture Notes in Computer Science, Springer Verlag, vol. 1592, pp. 206-222.
5. A. Kipnis, A. Shamir, Cryptanalysis of the Oil and Vinegar Signature Scheme, Advances in Cryptology - CRYPTO'98, Proceedings, H. Krawczyk (Ed.), Lecture Notes in Computer Science, Springer Verlag, vol. 1462, pp. 257-266.
6. A. Kipnis, A. Shamir, Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization, Advances in Cryptology - CRYPTO'99, Proceedings, M. Wiener (Ed.), Lecture Notes in Computer Science, Springer Verlag, vol. 1666, pp. 19-30.
7. R. Lidl, R. Niederreiter, Finite fields, Encyclopedia of mathematics and its applications, vol. 20, 1997.
8. A.J. Menezes, P.C. van Oorschot, S.A. Vanstone, Handbook of applied cryptography, CRC Press, 1996.
9. J. Patarin, N. Courtois, L. Goubin, FLASH, a Fast Multivariate Signature Algorithm, in Progress in Cryptology-CT-RSA 2001, D. Nacchache, ed., vol 2020, Springer Lecture Notes in Computer Science, pp. 298-307.
10. J. Patarin, L. Goubin, N. Courtois, Quartz, 128-bit long digital signatures, Cryptographers' Track RSA Conference 2001, San Francisco 8-12 Avril 2001, LNCS2020, Springer-Verlag. Also published in Proceedings of the First Open NESSIE Workshop, 13-14 November 2000, Leuven, Belgium.