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Verifiable Pattern Matching on Outsourced Texts

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Security and Cryptography for Networks (SCN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9841))

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Abstract

In this paper we consider a scenario where a user wants to outsource her documents to the cloud, so that she can later reliably delegate (to the cloud) pattern matching operations on these documents. We propose an efficient solution to this problem that relies on the homomorphic MAC for polynomials proposed by Catalano and Fiore in [14]. Our main contribution are new methods to express pattern matching operations (both in their exact and approximate variants) as low degree polynomials, i.e. polynomials whose degree solely depends on the size of the pattern. To better assess the practicality of our schemes, we propose a concrete implementation that further optimizes the efficiency of the homomorphic MAC from [14]. Our implementation shows that the proposed protocols are extremely efficient for the client, while remaining feasible at server side.

A full version of this paper is available at http://www.dmi.unict.it/diraimondo/uploads/papers/vpm-full.pdf.

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Notes

  1. 1.

    In particular the degree of these polynomials solely depends on the size of pattern string and is independent of the size of the texts.

  2. 2.

    Notice that in [14] a solution where the size of \(\pi \) can be made independent of d is also proposed. This solution however is computationally much less efficient as it imposes larger parameters.

  3. 3.

    Indeed, our first implementations show that this cost can quickly become unbearable even for texts of few thousands characters.

  4. 4.

    Moreover this pre-processing has to be done by the text owner (the weak client in our scenario) and cannot be delegated to the untrusted cloud server.

  5. 5.

    Recall that in the homomorphic MAC scheme from [14] the size of the tags grows with the degree of the arithmetic circuit.

  6. 6.

    Notice that the fact that we consider low degree polynomials is crucial here. Our technique is efficient solely because \(\ell \) does not need to be too big to be able to interpolate correctly at the end.

  7. 7.

    These timings are not reported in this paper but are available upon request.

  8. 8.

    We stress that we focused on our optimized techniques, as they are better than the alternative solutions discussed before in essentially all settings considered here.

References

  1. Agrawal, S., Boneh, D.: Homomorphic MACs: MAC-based integrity for network coding. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 292–305. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  2. Applebaum, B., Ishai, Y., Kushilevitz, E.: Computationally private randomizing polynomials and their applications. Comput. Complex. 15(2), 115–162 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Applebaum, B., Ishai, Y., Kushilevitz, E.: From secrecy to soundness: efficient verification via secure computation. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 152–163. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Attrapadung, N., Libert, B.: Homomorphic network coding signatures in the standard model. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 17–34. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Attrapadung, N., Libert, B., Peters, T.: Computing on authenticated data: new privacy definitions and constructions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 367–385. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  6. Attrapadung, N., Libert, B., Peters, T.: Efficient completely context-hiding quotable and linearly homomorphic signatures. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 386–404. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Backes, M., Barbosa, M., Fiore, D., Reischuk, R.M.: ADSNARK: nearly practical and privacy-preserving proofs on authenticated data. In: 2015 IEEE Symposium on Security and Privacy, pp. 271–286. IEEE Computer Society Press (2015)

    Google Scholar 

  8. Backes, M., Fiore, D., Reischuk, R.M.: Verifiable delegation of computation on outsourced data. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) ACM CCS 13, pp. 863–874. ACM Press, November 2013

    Google Scholar 

  9. Baeza-Yates, R.A., Gonnet, G.H.: A new approach to text searching. Commun. ACM 35(10), 74–82 (1992)

    Article  Google Scholar 

  10. Boneh, D., Freeman, D., Katz, J., Waters, B.: Signing a linear subspace: signature schemes for network coding. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 68–87. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Boneh, D., Freeman, D.M.: Homomorphic signatures for polynomial functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 149–168. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Boneh, D., Freeman, D.M.: Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 1–16. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Catalano, D.: Homomorphic signatures and message authentication codes. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 514–519. Springer, Heidelberg (2014)

    Google Scholar 

  14. Catalano, D., Fiore, D.: Practical homomorphic MACs for arithmetic circuits. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 336–352. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Catalano, D., Fiore, D., Gennaro, R., Nizzardo, L.: Generalizing homomorphic MACs for arithmetic circuits. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 538–555. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  16. Catalano, D., Fiore, D., Gennaro, R., Vamvourellis, K.: Algebraic (trapdoor) one-way functions and their applications. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 680–699. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  17. Catalano, D., Fiore, D., Gennaro, R., Vamvourellis, K.: Algebraic (trapdoor) one-way functions: constructions and applications. Theoret. Comput. Sci. 592, 143–165 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Catalano, D., Fiore, D., Nizzardo, L.: Programmable hash functions go private: constructions and applications to (homomorphic) signatures with shorter public keys. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 254–274. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  19. Catalano, D., Fiore, D., Warinschi, B.: Adaptive pseudo-free groups and applications. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 207–223. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Catalano, D., Fiore, D., Warinschi, B.: Efficient network coding signatures in the standard model. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 680–696. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  21. Catalano, D., Fiore, D., Warinschi, B.: Homomorphic signatures with efficient verification for polynomial functions. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 371–389. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  22. Crochemore, M., Rytter, W.: Text Algorithms. Oxford University Press, Oxford (1994)

    MATH  Google Scholar 

  23. Desmedt, Y.: Computer security by redefining what a computer is. In: NSPW (1993)

    Google Scholar 

  24. Faro, S., Lecroq, T.: The exact online string matching problem: a review of the most recent results. ACM Comput. Surv. 45(2), 13 (2013)

    Article  MATH  Google Scholar 

  25. Freeman, D.M.: Improved security for linearly homomorphic signatures: a generic framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 697–714. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  26. Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  27. Gennaro, R., Katz, J., Krawczyk, H., Rabin, T.: Secure network coding over the integers. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 142–160. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  28. Gennaro, R., Wichs, D.: Fully homomorphic message authenticators. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 301–320. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  29. Gorbunov, S., Vaikuntanathan, V., Wichs, D.: Leveled fully homomorphic signatures from standard lattices. In: 47th ACM STOC, pp. 469–477. ACM Press (2015)

    Google Scholar 

  30. Granlund, T., GMP Development Team.: GNU MP: The GNU Multiple Precision Arithmetic Library, 6.1.0 edn (2016)

    Google Scholar 

  31. Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  32. Kärkkäinen, J., Chae Na, J.: Faster filters for approximate string matching. In: Proceedings of the Nine Workshop on Algorithm Engineering and Experiments, ALENEX 2007, New Orleans, Louisiana, USA, January 6, 2007. SIAM (2007)

    Google Scholar 

  33. Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  34. Koch, W., Libgcrypt Development Team.: Libgcrypt, 1.7.0 edn (2016)

    Google Scholar 

  35. Landau, G.M., Vishkin, U.: Efficient string matching with k mismatches. Theor. Comput. Sci. 43, 239–249 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  36. Micali, S., Rivest, R.L.: Transitive signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 236–243. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  37. Papadopoulos, D., Papamanthou, C., Tamassia, R., Triandopoulos, N.: Practical authenticated pattern matching with optimal proof size. Proc. VLDB Endowment 8(7), 750–761 (2015)

    Article  Google Scholar 

  38. Shoup, V.: NTL: A Library for doing Number Theory, 9.7.1 edn (2016)

    Google Scholar 

  39. Yi, X.: Directed transitive signature scheme. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 129–144. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Acknowledgements

This research was supported in part by a FIR 2014 grant by the University of Catania. Thanks to Nuno Tiago Ferreira de Carvalho for his Homomorphic MACs library (Available at https://bitbucket.org/ntfc/cf-homomorphic-mac/).

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy

    Dario Catalano, Mario Di Raimondo & Simone Faro

Authors
  1. Dario Catalano
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  2. Mario Di Raimondo
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  3. Simone Faro
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Correspondence to Mario Di Raimondo .

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Editors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, New York, USA

    Vassilis Zikas

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Catalano, D., Di Raimondo, M., Faro, S. (2016). Verifiable Pattern Matching on Outsourced Texts. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_18

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  • DOI: https://doi.org/10.1007/978-3-319-44618-9_18

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