On building hash functions from multivariate quadratic equations

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

Volumn 4586 LNCS, Issue , 2007, Pages 82-95

  Billet, Olivier ^a   Robshaw, Matt J B ^a   Peyrin, Thomas ^a  

^a ORANGE LABS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOGRAPHY; POLYNOMIALS;

HASH FUNCTIONS; IMAGE RESISTANCE; RANDOMLY DRAWN SYSTEMS;

MULTIVARIABLE CONTROL SYSTEMS;

EID: 38149109062     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-73458-1_7     Document Type: Conference Paper

References (34)

1. Aiello, W., Haber, S., Venkatesan, R.: New Constructions for Secure Hash Functions. In: Vaudenay, S. (ed.) FSE 1998. LNCS, vol. 1372, pp. 150-167. Springer, Heidelberg (1998)
2. Augot, D., Finiasz, M., Sendrier, N.: A Family of Fast Syndrome Based Cryptographic Hash Functions. In: Dawson, E., Vaudenay, S. (eds.) Mycrypt 2005. LNCS, vol. 3715, pp. 64-83. Springer, Heidelberg (2005)
3. Bardet, M., Faugère, J.-C., Salvy, B.: On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations. In: ICPSS, pp. 71-74 (2004)
4. Ber bain, C., Gilbert, H., Patarin, J.: QUAD: A Practical Stream Cipher with Provable Security. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 109-128. Springer, Heidelberg (2006)
5. Berbain, C.: Personal communication (November 21, 2006)
6. Bentahar, K., Page, D., Silverman, J.H., Saarinen, M.-J.O., Smart, N., LASH (2006) Available from: http://csrc.nist.gov/pki/HashWorkshop/2006/
7. Black, J., Rogaway, P., Shrimpton, T.: Black-Box Analysis of the Block-Cipher-Based Hash-Function Constructions from PGV. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 320-335. Springer, Heidelberg (2002)
8. Contini, S., Lenstra, A.K., Steinfeld, R.: VSH, an Efficient and Provable Collision-Resistant Hash Function. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 165-182. Springer, Heidelberg (2006)
9. Damgård, I.: A Design Principle for Hash Functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416-427. Springer, Heidelberg (1990)
10. Ding, J., Schmidt, D.: Rainbow, a New Multivariable Polynomial Signature Scheme. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164-175. Springer, Heidelberg (2005)
11. Fouque, P.-A., Granboulan, L., Stern, J.: Differential cryptanalysis for multivariate schemes. In: Cramer, R.J.F. (ed.) EUROCKYPT 2005. LNCS, vol. 3494, pp. 341-353. Springer, Heidelberg (2005)
12. Fraenkel, A.S., Yesha, Y.: Complexity of Problems in Games, Graphs, and Algebraic Equations. Discr. Appl. Math. 1, 15-30 (1979)
13. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman & Co. New York (1979)
14. Joux, A.: Multicollisions in Iterated Hash Functions. Application to Cascaded Constructions. In: Franklin, M.k. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 306-316. Springer, Heidelberg (2004)
15. n Work. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 474-490. Springer, Heidelberg (2005)
16. Kipnis, A., Patarin, J., Goubin, L.: Unbalanced Oil and Vinegar Signature Schemes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 206-222. Springer, Heidelberg (1999)
17. Lenstra, A.K., Page, D., Stam, M.: Discrete logarithm variants of VSH. In: Nguyen, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol. 4341, pp. 229-242. Springer, Heidelberg (2006)
18. Lidl, R., Niederreiter, H.: Finite Fields. Cambridge University Press, Cambridge (1997)
19. Menezes, A.J., Vanstone, S.A., Van Oorschot, P.C.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
20. Merkle, R.C.: One Way Hash Functions and DES. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 428-446. Springer, Heidelberg (1989)
21. National Institute of Standards and Technology. FIPS 197: Advanced Encryption Standard (November 2001) Available from: http://csrc.nist.gov
22. National Institute of Standards and Technology. FIPS 180-2: Secure Hash Standard (August 2002) http://csrc.nist.gov
23. Patarin, J.: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms. In: Maurer, U.M. (ed.) EU-ROCRYPT 1996. LNCS, vol. 1070, pp. 33-48. Springer, Heidelberg (1996)
24. Patarin, J., Courtois, N.T., Goubin, L.: QUARTZ, 128-Bit Long Digital Signatures. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 282-297. Springer, Heidelberg (2001)
25. Patarin, J., Courtois, N.T., Goubin, L.: FLASH, a Fast Multivariate Signature Algorithm. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 298-307. Springer, Heidelberg (2001)
26. Peyrin, T., Gilbert, H., Muller, F., Robshaw, M.J.B.: Combining Compression Functions and Block Cipher-based Hash Functions. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 315-331. Springer, Heidelberg (2006)
27. Preneel, B.: Analysis and design of cryptographic hash functions. Ph.D. thesis. Katholieke Universiteit Leuven (1993)
28. Ronald, L.: Rivest. RFC 1320: The MD4 Message-Digest Algorithm (April 1992)http://www.ietf.org/rfc/rfc1320.txt
29. Rivest, R.L.: RFC 1321: The MD5 Message-Digest Algorithm (April 1992) http://www.ietf.org/rfc/rfc1321.txt
30. Smid, M.E., Branstad, D.K.: Response to Comments of the NIST Proposed Digital Signature Standard. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 76-88. Springer, Heidelberg (1993)
31. Courtois, N., Goubin, L., Meier, W., Tacier, J.-D.: Solving Underdefined Systems of Multivariate Quadratic Equations. Public Key Cryptography, 211-227 (2002)
32. Wang, X., Yin, Y.L., Yu, H.: Finding Collisions in the Full SHA-1. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 17-36. Springer, Heidelberg (2001)
33. Wang, X., Yu, H.: How to Break MD5 and Other Hash Functions. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19-35. Springer, Heidelberg (2005)
34. Wolf, C., Preneel, B.: Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations, http://eprint.iacr.org/