Advertisement

Characterizing Collision and Second-Preimage Resistance in Linicrypt

  • Ian McQuoidEmail author
  • Trevor Swope
  • Mike Rosulek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11891)

Abstract

Linicrypt (Carmer & Rosulek, Crypto 2016) refers to the class of algorithms that make calls to a random oracle and otherwise manipulate values via fixed linear operations. We give a characterization of collision-resistance and second-preimage resistance for a significant class of Linicrypt programs (specifically, those that achieve domain separation on their random oracle queries via nonces). Our characterization implies that collision-resistance and second-preimage resistance are equivalent, in an asymptotic sense, for this class. Furthermore, there is a polynomial-time procedure for determining whether such a Linicrypt program is collision/second-preimage resistant.

References

  1. 1.
    Bellare, M., Micciancio, D.: A new paradigm for collision-free hashing: incrementality at reduced cost. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 163–192. Springer, Heidelberg (1997).  https://doi.org/10.1007/3-540-69053-0_13CrossRefGoogle Scholar
  2. 2.
    Bernstein, D.J., et al.: SPHINCS: practical stateless hash-based signatures. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 368–397. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46800-5_15CrossRefGoogle Scholar
  3. 3.
    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).  https://doi.org/10.1007/3-540-45708-9_21CrossRefGoogle Scholar
  4. 4.
    Bos, J.N.E., Chaum, D.: Provably unforgeable signatures. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 1–14. Springer, Heidelberg (1993).  https://doi.org/10.1007/3-540-48071-4_1CrossRefGoogle Scholar
  5. 5.
    Carmer, B., Rosulek, M.: Linicrypt: a model for practical cryptography. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 416–445. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53015-3_15CrossRefGoogle Scholar
  6. 6.
    Dahmen, E., Okeya, K., Takagi, T., Vuillaume, C.: Digital signatures out of second-preimage resistant hash functions. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 109–123. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-88403-3_8CrossRefGoogle Scholar
  7. 7.
    Even, S., Goldreich, O., Micali, S.: On-line/off-line digital schemes. In: Brassard, G. (ed.) CRYPTO’89. LNCS, vol. 435, pp. 263–275. Springer, Heidelberg (1990)Google Scholar
  8. 8.
    Hülsing, A.: W-OTS+ - shorter signatures for hash-based signature schemes. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds.) AFRICACRYPT 13. LNCS, vol. 7918, pp. 173–188. Springer, Heidelberg (2013)Google Scholar
  9. 9.
    Impagliazzo, R.: A personal view of average-case complexity. In: Proceedings of the Tenth Annual Structure in Complexity Theory Conference, Minneapolis, Minnesota, USA, 19–22 June, 1995, pp. 134–147. IEEE Computer Society (1995)Google Scholar
  10. 10.
    Lamport, L.: Constructing digital signatures from a one-way function. Technical report SRI-CSL-98, SRI International Computer Science Laboratory, October 1979Google Scholar
  11. 11.
    Merkle, R.C.: A digital signature based on a conventional encryption function. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 369–378. Springer, Heidelberg (1988).  https://doi.org/10.1007/3-540-48184-2_32CrossRefGoogle Scholar
  12. 12.
    Preneel, B., Govaerts, R., Vandewalle, J.: Hash functions based on block ciphers: a synthetic approach. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 368–378. Springer, Heidelberg (1994).  https://doi.org/10.1007/3-540-48329-2_31CrossRefGoogle Scholar
  13. 13.
    Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–304. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45708-9_19CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.Oregon State UniversityCorvallisUSA

Personalised recommendations