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Quasigroup String Transformations and Hash Function Design

A Case Study: The NaSHA Hash Function
  • Aleksandra Mileva
  • Smile Markovski

Abstract

In this paper we propose two new types of compression functions, based on quasigroup string transformations. The first type uses known quasigroup string transformations, defined elsewhere, by changing alternately the transformation direction, going forward and backward through the string. Security of this design depends of the chosen quasigroup string transformation, the order of the quasigroup and the properties satisfied by the quasigroup operations. We illustrate how this type of compression function is applied in the design of the cryptographic hash function NaSHA. The second type of compression function uses new generic quasigroup string transformation, which combine two orthogonal quasigroup operations into a single one. This, in fact, is deployment of the concept of multipermutation for perfect generation of confusion and diffusion. One implementation of this transformation is by extended Feistel network FA,B,C which has at least two orthogonal mates as orthomorphisms: its inverse \(F^{-1}_{A,B,C}\) and its square \(F^{2}_{A,B,C}\).

Keywords

Compression Function Hash Function Design Quasigroup String Transformation Orthogonal Quasigroups NaSHA 

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References

  1. 1.
    Markovski, S., Gligoroski, D., Andova, S.: Using Quasigroups for one-one Secure Encoding. In: Proceedings of VIII Conference on Logic and Computer Science, LIRA 1997, Novi Sad, pp. 157–162 (1997)Google Scholar
  2. 2.
    Dvorský, J., Ochodková, E., Snášel, V.: Hash Function based on Large Quasigroups. In: Proceedings of Velikonocni kriptologie, Brno, pp. 1–9 (2002)Google Scholar
  3. 3.
    Snášel, V., Abraham, A., Dvorský, J., Krömer, P., Platoš, J.: Hash Function based on Large Quasigroups. In: Allen, G., Nabrzyski, J., Seidel, E., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2009. LNCS, vol. 5544, pp. 521–529. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Markovski, S., Gligoroski, D., Bakeva, V.: On Infinite Class of Strongly Collision Resistant Hash Functions “Edon-F” with Variable Length of Output. In: Proceedings of 1st Conference on Discrete Mathematics and Informatics for Industry, Thessaloniki, pp. 302–308 (2003)Google Scholar
  5. 5.
    Gligoroski, D., Markovski, S., Kocarev, L.: Edon-R, an Infinite Family of Cryptographic Hash Functions. In: The Second NIST Cryptographic Hash Workshop, UCSB, Santa Barbara, pp. 275–285 (2006)Google Scholar
  6. 6.
    Gligoroski, D., Knapskog, S.J.: Edon-R (256, 384, 512) - an Efficient Implementation of Edon-R Family of Cryptographic Hash Functions. Cryptology ePrint Archive, Report 2007/154 (2007)Google Scholar
  7. 7.
    Gligoroski, D., Ødegård, R.S., Mihova, M., Knapskog, S.J., Kocarev, L., Drápal, A., Klima, V.: Cryptographic Hash Function Edon-R. Submission to NIST SHA-3 competition (2008)Google Scholar
  8. 8.
    Gligoroski, D.: Candidate one-way Functions and one-way Permutations based on quasigroup String Transformations. Cryptology ePrint Archive, Report 2005, 352 (2005)Google Scholar
  9. 9.
    Markovski, S., Gligoroski, D., Bakeva, V.: Quasigroup String Processing – Part I. Contributions, Sec. Math. Tech. Sci., MANU, XX, 1-2, 13–28 (1999)Google Scholar
  10. 10.
    Markovski, S., Mileva, A.: Generating huge quasigroups from small non-linear bijections via extended Feistel network. Quasigroups and Related Systems 17, 91–106 (2009)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Markovski, S., Mileva, A.: NaSHA. Submission to NIST SHA-3 competition (2008)Google Scholar
  12. 12.
    National Institute of Standards and Technology: Announcing Request for Candidate Algorithm Nominations for a New Cryptographic Hash Algorithm (SHA-3) Family. Federal Register 72(212), 62212–62220 (November 2007)Google Scholar
  13. 13.
    Wang, X., Yu, H.: How to Break MD5 and Other Hash Functions. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Wang, X., Yu, H., Yin, L.: Efficient Collision Search Attacks on SHA-0. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 1–16. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Wang, X., Yin, L., Yu, H.: Finding Collisions in the Full SHA-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 17–36. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Schnorr, C.P., Vaudenay, S.: Black Box Cryptanalysis of Hash Networks Based on Multipermutations. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 47–57. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  17. 17.
    Lucks, S.: A Failure-Friendly Design Principle for Hash Functions. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 474–494. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Coron, J.-S., Dodis, Y., Malinaud, C., Puniya, P.: Merkle-damgård revisited: How to construct a hash function. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 430–448. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Ji, L., Liangyu, X., Xu, G.: Collision attacks on NaSHA-512. Cryptology ePrint Archive, Report 2008/519 (2008)Google Scholar
  20. 20.
    Markovski, S., Mileva, A.: NaSHA. In: First SHA-3 Candidate Conference (2008), http://csrc.nist.gov/groups/ST/hash/sha-3/Round1/Feb2009/documents/NaSHAforweb.pdf
  21. 21.
    Vaudenay, S.: On the Need for Multipermutations: Cryptanalysis of MD4 and SAFER. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 286–297. Springer, Heidelberg (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Aleksandra Mileva
    • 1
  • Smile Markovski
    • 2
  1. 1.Faculty of InformaticsUGDStipRepublic of Macedonia
  2. 2.Faculty of Natural ScienceUKIMSkopjeRepublic of Macedonia

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