Abstract
This paper proposes a novel hash algorithm whose security is based on the multivariate nonlinear polynomial equations of NP-hard problem over a finite field and combines with HAIFA iterative framework. Over the current widely used hash algorithms, the new algorithm has the following advantages: its security is based on a recognized difficult mathematical problem; the hash length can be changed freely; its design can be automated such that users may construct specific hash function meeting the actual needs. Furthermore, we discuss the security, efficiency and performance of the new algorithm. Under some related difficult mathematical assumptions and theoretical analysis, the new algorithm is proven practical by the experiment results, and capable of achieving security of an ideal hash function by choosing suitable parameters. In addition, it can also be used as a pseudo-random number generator for the good randomness of its output.
Similar content being viewed by others
References
Wang X Y, Yu H B. How to break MD5 and other hash functions. In: Proceedings of EUROCRYPT 2005, LNCS, vol. 3494. Berlin: Springer-Verlag, 2005. 19–35
Wang X Y, Yao A, Yao F. Cryptanalysis of SHA-1 Hash Function. Cryptographic Hash Workshop, Invited Report, 2005
Wang X Y, Yu H B, Wang W, et al. Cryptanalysis on HMAC/NMAC-MD5 and MD5-MAC. In: Proceedings of EUROCRYPT 2009. Berlin: Springer-Verlag, 2009. 121–133
Yu H B, Wang X Y. Distinguishing attack on the secret-prefix MAC based on the 39-step SHA-256. In: Proceedings of ACISP 2009. Berlin: Springer-Verlag, 2009. 185–201
Zhang H N, Li L, Wang X Y. Fast correlation attack on stream cipher ABC v3. Sci China Ser F-Inf Sci, 2008, 51: 936–947.
NIST. Plan for new cryptographic hash functions. http://www.nist.gov/hash-function/
Yuan Z, Wang W, Jia K T, et al. New birthday attacks on some MACs based on block ciphers. In: Proceedings of CRYPTO 2009. Berlin: Springer-Verlag, 2009. 209–230
Ding J T. Multivariate Public Key Cryptosystems. Berlin: Springer-Verlag, 2006. 11–190
Aumasson J, Meier W. Analysis of multivariate hash functions. In: Proceedings of ICISC 2007, LNCS, vol. 4817. Berlin: Springer-Verlag, 2007. 309–323
Bettale L, Faugère J C, Perret L. Security analysis of multivariate polynomial for hashing. In: Proceedings of Inscrypt 2008, LNCS 5487, Vol. 347. Berlin: Springer-Verlag, 2009. 115–124
Biham E, Dunkelman O. A framework for iterative hash functions-HAIFA, ePrint report 2007/278, 2007
Faugère J C. A new efficient algorithm for computing Grobner bases without reduction to zero (F5). In: Proceedings of ISSAC2002. New York: ACM Press, 2002. 75–83
Shamir A, Patarin J, Courtois N, et al. Efficient algorithms for solving overdefined systems of multivariate polynomial equation. In: Proceedings of Eurocrypt2000, LNCS, vol. 1807. Berlin: Springer-Verlag, 2000. 392–407
Courtois N, Pieprzyk J. Cryptanalysis of Block ciphers with overdefined systems of equations, In: Proceedings of Asiacrypt 2002, LNCS, vol. 2501. Berlin: Springer-Verlag, 2002. 267–287
Bardet M, Faugère J C, Salvy B. On the complexity of Grobner basis computation of semi-regular overdetermined algebraic equations. In: Proceedings of ICPSS 2004. Berlin: Springer-Verlag, 2004. 71–74
Raddum H V, Semaev I. New technique for solving sparse equation systems. Cryptology ePrint Archive, Report 2006/475
Tang X J, Feng Y. Applying dixon resultants in cryptography. J Software, 2007, 18: 1738–1745
Ding J, Yang B Y. Multivariates polynomials for hashing. Cryptology ePrint Archive, Report 2007/137, 2007
Lucks. A failure-friendly design principle for hash functions. In: Proceedings of ASIACRYPT2005, LNCS, vol. 3788. Berlin: Springer-Verlag, 2005. 474–494
Joux A. Multicollisions in iterated Hash functions. Application to cascaded constructions. In: Proceedings of Crypto 2004, LNCS, vol. 3152. Berlin: Springer-Verlag, 2004. 306–316
Kelsey J, Schneier B. Second preimages on n-bit hash functions for much less than 2n. In: Proceedings of Eurocrypt 2005, LNCS vol. 3494. Berlin: Springer-Verlag, 2005. 474–490
Kelsey J, Kohno T. Herding Hash functions and the nostradamus attack. In: Proceedings of Eurocrypt2006, LNCS, vol. 4004. Berlin: Springer-Verlag, 2006. 183–200
Rukbin A, Soto J, Nechvatal J, et al. A statistical test suit for random pseudorandom number generator for cryptographic applications. In: NIST Special Publication 800-22, 2001, http://csrc.nist.gov/rng/SP800-22b.pdf.
Wang H Z, Zhang H G, Guan H M, et al. A new perturbation algorithm and enhancing security of SFLASH signature scheme. Sci China Inf Sci, 2010, 53: 760–768
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, H., Zhang, H., Wu, Q. et al. Design theory and method of multivariate hash function. Sci. China Inf. Sci. 53, 1977–1987 (2010). https://doi.org/10.1007/s11432-010-4062-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-010-4062-1