Advertisement

On the Security of the Double-Block-Length Hash Function NCASH

  • Tapadyoti BanerjeeEmail author
  • Dipanwita Roy Chowdhury
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1116)

Abstract

In this work, we study the security analysis of a newly proposed Non-linear Cellular Automata-based Hash function, NCASH. The uncomplicated structure of this double-block-length hash function instigates us to scrutinize its construction by analyzing the security of the design. Here, we have performed a security analysis with respect to the standard model of concrete security. In addition, structural security has also been investigated by performing the correlation analysis. We have examined the security bound of this scheme by using the random oracle model. The Preimage or Second Preimage Resistance and Collision Resistance of NCASH-256 are 2\(^{256}\) and 2\(^{128}\) respectively. According to the best of our knowledge, these bounds provide better security comparing with most of the other acclaimed existing schemes.

Keywords

Cellular automata Double-block-length hash Correlation analysis Random oracle model 

References

  1. 1.
    Armknecht, F., Fleischmann, E., Krause, M., Lee, J., Stam, M., Steinberger, J.: The preimage security of double-block-length compression functions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 233–251. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-25385-0_13CrossRefGoogle Scholar
  2. 2.
    Banerjee, T., Roy Chowdhury, D.: NCASH: non-linear cellular automata based hash function. In: The 5th International Conference on Mathematics and Computing (ICMC 2019), (Presented) (2019)Google Scholar
  3. 3.
    Belfedhal, A.E., Faraoun, K.M.: Building secure and fast cryptographic hash functions using programmable cellular automata. J. Comput. Inf. Technol. 23(4), 317–328 (2015)CrossRefGoogle Scholar
  4. 4.
    Bellare, M.: A note on negligible functions. J. Cryptol. 15(4) (2002). https://link.springer.com/content/pdf/10.1007MathSciNetCrossRefGoogle Scholar
  5. 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).  https://doi.org/10.1007/3-540-68697-5_1CrossRefGoogle Scholar
  6. 6.
    Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Keccak sponge function family main document. Submission to NIST (Round 2), 3(30) (2009) Google Scholar
  7. 7.
    Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Duplexing the sponge: single-pass authenticated encryption and other applications. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 320–337. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-28496-0_19CrossRefGoogle Scholar
  8. 8.
    Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM (JACM) 51(4), 557–594 (2004)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Daemen, J., Govaerts, R., Vandewalle, J.: A framework for the design of one-way hash functions including cryptanalysis of Damgård’s one-way function based on a cellular automaton. In: Imai, H., Rivest, R.L., Matsumoto, T. (eds.) ASIACRYPT 1991. LNCS, vol. 739, pp. 82–96. Springer, Heidelberg (1993).  https://doi.org/10.1007/3-540-57332-1_7CrossRefGoogle Scholar
  10. 10.
    Damgård, I.B.: A design principle for hash functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416–427. Springer, New York (1990).  https://doi.org/10.1007/0-387-34805-0_39CrossRefGoogle Scholar
  11. 11.
    Dworkin, M.J.: SHA-3 standard: Permutation-based hash and extendable-output functions. Technical report (2015). https://ws680.nist.gov/publication/get_pdf.cfm?pub_id=919061
  12. 12.
    Eastlake, D., Jones, P.: Us Secure Hash Algorithm 1 (SHA1). Technical report (2001). https://tools.ietf.org/html/rfc3174?ref=driverlayer.com
  13. 13.
    Echandouri, B., Hanin, C., Omary, F., Elbernoussi, S.: Keyed-CAHASH: a new fast keyed hash function based on cellular automata for authentication. Int. J. Comput. Sci. Appl. 14(2), 64–180 (2017)Google Scholar
  14. 14.
    Fleischmann, E., Forler, C., Lucks, S., Wenzel, J.: Weimar-DM: a highly secure double-length compression function. In: Susilo, W., Mu, Y., Seberry, J. (eds.) ACISP 2012. LNCS, vol. 7372, pp. 152–165. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-31448-3_12CrossRefGoogle Scholar
  15. 15.
    Fleischmann, E., Gorski, M., Lucks, S.: Security of cyclic double block length hash functions. In: Parker, M.G. (ed.) IMACC 2009. LNCS, vol. 5921, pp. 153–175. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-10868-6_10CrossRefzbMATHGoogle Scholar
  16. 16.
    Ghosh, S., Sengupta, A., Saha, D., Chowdhury, D.R.: A scalable method for constructing non-linear cellular automata with period \(2^n\)-1. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds.) ACRI 2014. LNCS, vol. 8751, pp. 65–74. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-11520-7_8CrossRefGoogle Scholar
  17. 17.
    Hirose, S.: Provably secure double-block-length hash functions in a black-box model. In: Park, C., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 330–342. Springer, Heidelberg (2005).  https://doi.org/10.1007/11496618_24CrossRefGoogle Scholar
  18. 18.
    Hirose, S.: Some plausible constructions of double-block-length hash functions. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 210–225. Springer, Heidelberg (2006).  https://doi.org/10.1007/11799313_14CrossRefGoogle Scholar
  19. 19.
    Hortensius, P.D., McLeod, R.D., Pries, W., Miller, D.M., Card, H.C.: Cellular automata-based pseudorandom number generators for built-in self-test. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 8(8), 842–859 (1989)CrossRefGoogle Scholar
  20. 20.
    Koblitz, N., Menezes, A.J.: The random oracle model: a twenty-year retrospective. Des. Codes Cryptogr. 77(2), 587–610 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Kuila, S., Saha, D., Pal, M., Chowdhury, D.R.: CASH: cellular automata based parameterized hash. In: Chakraborty, R.S., Matyas, V., Schaumont, P. (eds.) SPACE 2014. LNCS, vol. 8804, pp. 59–75. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-12060-7_5CrossRefGoogle Scholar
  22. 22.
    Lai, X., Massey, J.L.: Hash functions based on block ciphers. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 55–70. Springer, Heidelberg (1993).  https://doi.org/10.1007/3-540-47555-9_5CrossRefGoogle Scholar
  23. 23.
    Lee, J., Kwon, D.: The security of abreast-DM in the ideal cipher model. IEICE Trans. Fund. Electron. Commun. Comput. Sci. 94(1), 104–109 (2011)CrossRefGoogle Scholar
  24. 24.
    Lee, J., Stam, M., Steinberger, J.: The collision security of tandem-DM in the ideal cipher model. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 561–577. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22792-9_32CrossRefzbMATHGoogle Scholar
  25. 25.
    Lucks, S.: Design principles for iterated hash functions. IACR Cryptol. ePrint Arch. 2004, 253 (2004)Google Scholar
  26. 26.
    Mihaljevic, M., Zheng, Y., Imai, H.: A fast cryptographic hash function basedon linear cellular automata over GF(q). (1998). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.112.8559&rep=rep1&type=pdf
  27. 27.
    Miyaji, A., Rashed, M.: A new (n, 2n) double block length hash function based on single key scheduling. In: 2015 IEEE 29th International Conference on Advanced Information Networking and Applications, pp. 564–570. IEEE (2015)Google Scholar
  28. 28.
    Pal Chaudhuri, P., Roy Chowdhury, D., Nandi, S., Chattopadhyay, S.: Additive Cellular Automata: Theory and Applications, vol. 1. John Wiley & Sons, Chichester (1997) zbMATHGoogle Scholar
  29. 29.
    Rivest, R.: The MD5 Message-Digest algorithm. Technical report (1992). https://tools.ietf.org/pdf/rfc1321.pdf
  30. 30.
    Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E.: A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, NIST Special Publication 800–22. Technical report, Booz-Allen and Hamilton Inc Mclean Va (2001)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Crypto Research Lab, Department of Computer Science and EngineeringIIT KharagpurKharagpurIndia

Personalised recommendations