Analysis of multivariate hash functions

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

Volumn 4817 LNCS, Issue , 2007, Pages 309-323

  Aumasson, Jean Philippe ^a   Meier, Willi ^a  

^a UNIVERSITY OF APPLIED SCIENCES AND ARTS NORTHWESTERN SWITZERLAND   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

AUTHENTICATION; MULTIVARIABLE CONTROL SYSTEMS; PROBABILITY;

CODING THEORY; HASH FUNCTIONS; MONOMIALS;

FUNCTIONS;

EID: 38149004458     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-76788-6_25     Document Type: Conference Paper

References (40)

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. Bard, G.V., Courtois, N.T., Jefferson, C.: Efficient methods for conversion and solution of sparse systems of low-degree multivariate polynomials over GF (2) via SAT-solvers. Cryptology ePrint Archive, Report 2007/024 (2007)
4. Bellare, M.: New proofs for NMAC and HMAC: Security without collision-resistance. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 602-619. Springer, Heidelberg (2006)
5. Bellare, M., Canetti, R., Krawczyk, H.: Keying hash functions for message authentication. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 1-15. Springer, Heidelberg (1996)
6. Bentahar, K., Page, D., Saarinen, M.-J.O., Silverman, J.H., Smart, N.: LASH. In: Second NIST Cryptographic Hash Function Workshop (2006)
7. Berbain, 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)
8. Billet, O., Robshaw, M.J.B., Peyrin, T.: On building hash functions from multivariate quadratic equations. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) ACISP. LNCS, vol. 4586, pp. 82-95. Springer, Heidelberg (2007)
9. Canetti, R., Micciancio, D., Reingold, O.: Perfectly one-way probabilistic hash functions (preliminary version). In: STOC, pp. 131-140 (1998)
10. Canteaut, A., Chabaud, F.: A new algorithm for finding minimum-weight words in a linear code: application to McEliece's cryptosystem and to narrow-sense BCH codes of length 511. IEEE Transactions on Information Theory 1(44), 367-378 (1998)
11. Contini, S., Lenstra, A.K., Steinfield, R.: VSH, an efficient and provable collisionresistant hash function. In Vaudenay [39] pp. 165-182
12. Contini, S., Lenstra, A.K., Steinfield, R.: VSH, an efficient and provable collision-resistant hash function. Cryptology ePrint Archive, Report, 2006/193. Extended version of [11]
13. Courtois, N.: Higher order correlation attacks, XL algorithm and cryptanalysis of Toyocrypt. In: Lee, P.J, Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 182-199. Springer, Heidelberg (2003)
14. k), application to HFE challenge 2 and Sflash-v2. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 201-217. Springer, Heidelberg (2004)
15. Courtois, N., Goubin, L., Meier, W., Tacier, J.-D.: Solving underdefined systems of multivariate quadratic equations. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 211-227. Springer, Heidelberg (2002)
16. Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392-407. Springer, Heidelberg (2000)
17. Courtois, N., Patarin, J.: About the XL algorithm over GF(2). In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 141-157. Springer, Heidelberg (2003)
18. Courtois, N., Pieprzyk, J.: Cryptanalysis of block ciphers with overdefined systems of equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267-287. Springer, Heidelberg (2002)
19. Diem, C.: The XL-algorithm and a conjecture from commutative algebra. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 323-337. Springer, Heidelberg (2004)
20. Ding, J., Yang, B.-Y.: Multivariates polynomials for hashing. Cryptology ePrint Archive, Report 2007/137 (2007)
21. Eén, N., Sörensson, N.: MINISAT. http://www.cs.chalmers.se/ Cs/Research/FormalMethods/MiniSat/
22. 4). Journal of Pure and Applied Algebra 139(61), 88 (1999)
23. 5). In: ISSAC, pp. 75-83. ACM Press, New York (2002)
24. Faugère, J.-C., Joux, A.: Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gröbner bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44-60. Springer, Heidelberg (2003)
25. Finiasz, M., Gaborit, P., Sendrier, N.: Improved fast syndrome based cryptographic hash functions. In: ECRYPT Workshop on hash functions (2007)
26. Garey, M., Johnson, D.: Computers and Intractability, a guide to the theory of NP-completeness, p. 251. Freeman, San Francisco (1979)
27. Haitner, I., Reingold, O.: A new interactive hashing theorem. In: IEEE Conference on Computational Complexity (2007)
28. Imai, H., Matsumoto, T.: A class of asymmetric crypto-systems based on polynomials over finite rings. In: IEEE International Symposium on Information Theory, pp. 131-132 (1983)
29. Lyubashevsky, V., Micciancio, D., Peikert, C., Rosen, A.: Provably secure FFT hashing. In: 2nd NIST Cryptographic Hash Function Workshop (2006)
30. McDonald, C., Charnes, C., Pieprzyk, J.: Attacking Bivium with MiniSat. Cryptology ePrint Archive, Report 2007/129
31. Naor, M., Reingold, O.: From unpredictability to indistinguishability: A simple construction of pseudo-random functions from MACs (extended abstract). In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 267-282. Springer, Heidelberg (1998)
32. NIST. Plan for new cryptographic hash functions http://www.nist.gov/hash- function/
33. Ong, H., Schnorr, C.-P., Shamir, A.: Efficient signature schemes based on polynomial equations. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 37-46. Springer, Heidelberg (1985)
34. Patarin, J.: Hidden fields equations (HFE) and isomorphisms of polynomials (IP). In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33-48. Springer, Heidelberg (1996)
35. Shannon, C.E.: Communication theory of secrecy systems. Bell systems technical journal 28, 646-714 (1949)
36. Tamassia, R., Triandopoulos, N.: Computational bounds on hierarchical data processing with applications to information security. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 153-165. Springer, Heidelberg (2005)
37. Tang, X., Feng, Y.: A new efficient algorithm for solving systems of multivariate polynomials equations. Cryptology ePrint Archive, Report 2005/312 (2005)
38. Raddum, H.v., Semaev, I.: New technique for solving sparse equation systems. Cryptology ePrint Archive, Report 2006/475 (2006)
39. Vaudenay, S. (ed.): EUROCRYPT 2006. LNCS, vol. 4004. Springer, Heidelberg (2006)
40. Yang, B.-Y., Chen, O.C.-H., Bernstein, D.J., Chen, J.: Analysis of QUAD. In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, Springer, Heidelberg (2007)