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Optimal Authenticated Data Structures with Multilinear Forms

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Pairing-Based Cryptography - Pairing 2010 (Pairing 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6487))

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Abstract

Cloud computing and cloud storage are becoming increasingly prevalent. In this paradigm, clients outsource their data and computations to third-party service providers. Data integrity in the cloud therefore becomes an important factor for the functionality of these web services.Authenticated data structures, implemented with various cryptographic primitives, have been widely studied as a means of providing efficient solutions to data integrity problems (e.g., Merkle trees). In this paper, we introduce a new authenticated dictionary data structure that employs multilinear forms, a cryptographic primitive proposed by Silverberg and Boneh in 2003 [10], the construction of which, however, remains an open problem to date. Our authenticated dictionary is optimal, that is, it does not add any extra asymptotic cost to the plain dictionary data structure, yielding proofs of constant size, i.e., asymptotically equal to the size of the answer, while maintaining other relevant complexities logarithmic. Instead, solutions based on cryptographic hashing (e.g., Merkle trees) require proofs of logarithmic size [40]. Because multilinear forms are not known to exist yet, our result can be viewed from a different angle: if one could prove that optimal authenticated dictionaries cannot exist in the computational model, irrespectively of cryptographic primitives, then our solution would imply that cryptographically interesting multilinear form generators cannot exist as well (i.e., it can be viewed as a reduction). Thus, we provide an alternative avenue towards proving the nonexistence of multilinear form generators in the context of general lower bounds for authenticated data structures [40] and for memory checking [18], a model similar to the authenticated data structures model.

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References

  1. Applebaum, B., Ishai, Y., Kushilevitz, E.: From secrecy to soundness: Efficient verification via secure computation. In: Proc. Int. Colloquium on Automata, Languages and Programming (ICALP), pp. 152–163 (2010)

    Google Scholar 

  2. Atallah, M.J., Cho, Y., Kundu, A.: Efficient data authentication in an environment of untrusted third-party distributors. In: Proc. Int. Conference on Data Engineering (ICDE), pp. 696–704 (2008)

    Google Scholar 

  3. Au, M.H., Tsang, P.P., Susilo, W., Mu, Y.: Dynamic universal accumulators for DDH groups and their application to attribute-based anonymous credential systems. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 295–308. Springer, Heidelberg (2009)

    Google Scholar 

  4. Baric, N., Pfitzmann, B.: Collision-free accumulators and fail-stop signature schemes without trees. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 480–494. Springer, Heidelberg (1997)

    Google Scholar 

  5. Benaloh, J., de Mare, M.: One-way accumulators: A decentralized alternative to digital signatures. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 274–285. Springer, Heidelberg (1993)

    Google Scholar 

  6. Blum, M., Evans, W.S., Gemmell, P., Kannan, S., Naor, M.: Checking the correctness of memories. Algorithmica 12(2/3), 225–244 (1994)

    Article  MathSciNet  Google Scholar 

  7. Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. J. Cryptology 21(2), 149–177 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Boneh, D., Franklin, M.K.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Boneh, D., Mironov, I., Shoup, V.: A secure signature scheme from bilinear maps. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 98–110. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Boneh, D., Silverberg, A.: Applications of multilinear forms to cryptography. Contemporary Mathematics 324(1), 71–90 (2003)

    MathSciNet  Google Scholar 

  11. Camenisch, J., Kohlweiss, M., Soriente, C.: An accumulator based on bilinear maps and efficient revocation for anonymous credentials. In: Proc. Public Key Cryptography (PKC), pp. 481–500 (2009)

    Google Scholar 

  12. Camenisch, J., Lysyanskaya, A.: Dynamic accumulators and application to efficient revocation of anonymous credentials. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 61–76. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Cheon, J.H., Lee, D.H.: A note on self-bilinear maps. Korean Mathematical Society 46(2), 303–309 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Chung, K.-M., Kalai, Y., Vadhan, S.: Improved delegation of computation using fully homomorphic encryption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 483–501. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  16. Damgård, I., Triandopoulos, N.: Supporting non-membership proofs with bilinear-map accumulators. Cryptology ePrint Archive, Report 2008/538 (2008)

    Google Scholar 

  17. Devanbu, P., Gertz, M., Kwong, A., Martel, C., Nuckolls, G., Stubblebine, S.: Flexible authentication of XML documents. Journal of Computer Security 6, 841–864 (2004)

    Google Scholar 

  18. Dwork, C., Naor, M., Rothblum, G.N., Vaikuntanathan, V.: How efficient can memory checking be? In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 503–520. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. 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 

  20. Gennaro, R., Halevi, S., Rabin, T.: Secure hash-and-sign signatures without the random oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 123–139. Springer, Heidelberg (1999)

    Google Scholar 

  21. Goodrich, M.T., Tamassia, R., Hasic, J.: An efficient dynamic and distributed cryptographic accumulator. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, pp. 372–388. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  22. Goodrich, M.T., Tamassia, R., Triandopoulos, N.: Super-efficient verification of dynamic outsourced databases. In: Malkin, T.G. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 407–424. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Hohenberger, S., Lysyanskaya, A.: How to securely outsource cryptographic computations. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 264–282. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  24. Joux, A.: A one-round protocol for tripartite Diffie-Hellman. J. Cryptology 17(4), 263–276 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  25. Lee, H.-M., Ha, K.J., Ku, K.-M.: ID-based multi-party authenticated key agreement protocols from multilinear forms. In: Zhou, J., López, J., Deng, R.H., Bao, F. (eds.) ISC 2005. LNCS, vol. 3650, pp. 104–117. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Li, J., Li, N., Xue, R.: Universal accumulators with efficient nonmembership proofs. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 253–269. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  27. Martel, C., Nuckolls, G., Devanbu, P., Gertz, M., Kwong, A., Stubblebine, S.G.: A general model for authenticated data structures. Algorithmica 39(1), 21–41 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  28. Menezes, A., Vanstone, S., Okamoto, T.: Reducing elliptic curve logarithms to logarithms in a finite field. In: Proc. Symposium on Theory of Computing (STOC), pp. 80–89 (1991)

    Google Scholar 

  29. Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, Heidelberg (1989)

    Google Scholar 

  30. Naor, M., Nissim, K.: Certificate revocation and certificate update. In: Proc. USENIX Security Symposium (USENIX), pp. 217–228 (1998)

    Google Scholar 

  31. Naor, M., Rothblum, G.N.: The complexity of online memory checking. J. ACM 56(1) (2009)

    Google Scholar 

  32. Nguyen, L.: Accumulators from bilinear pairings and applications. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 275–292. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  33. Papamanthou, C., Tamassia, R.: Time and space efficient algorithms for two-party authenticated data structures. In: Qing, S., Imai, H., Wang, G. (eds.) ICICS 2007. LNCS, vol. 4861, pp. 1–15. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  34. Papamanthou, C., Tamassia, R.: Update-optimal authenticated structures based on lattices. Cryptology ePrint Archive, Report 2010/128 (2010)

    Google Scholar 

  35. Papamanthou, C., Tamassia, R., Triandopoulos, N.: Authenticated hash tables. In: Proc. ACM Conference on Computer and Communications Security (CCS), pp. 437–448 (2008)

    Google Scholar 

  36. Papamanthou, C., Tamassia, R., Triandopoulos, N.: Cryptographic accumulators for authenticated hash tables. Cryptology ePrint Archive, Report 2009/625 (2009)

    Google Scholar 

  37. Papamanthou, C., Tamassia, R., Triandopoulos, N.: Optimal authentication of set operations on dynamic sets. Cryptology ePrint Archive, Report 2010/455 (2010)

    Google Scholar 

  38. Sander, T., Ta-Shma, A., Yung, M.: Blind, auditable membership proofs. In: Proc. Financial Cryptography (FC), pp. 53–71 (2001)

    Google Scholar 

  39. Tamassia, R.: Authenticated data structures. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 2–5. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  40. Tamassia, R., Triandopoulos, N.: Computational bounds on hierarchical data processing with applications to information security. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 153–165. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  41. Tamassia, R., Triandopoulos, N.: Efficient content authentication in peer-to-peer networks. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 354–372. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  42. Wang, P., Wang, H., Pieprzyk, J.: A new dynamic accumulator for batch updates. In: Qing, S., Imai, H., Wang, G. (eds.) ICICS 2007. LNCS, vol. 4861, pp. 98–112. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  43. Yuan, H., Atallah, M.J.: Efficient distributed third-party data authentication for tree hierarchies. In: Proc. Int. Conference on Distributed Computing Systems (ICDCS), pp. 184–193 (2008)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Brown University, Providence, RI, USA

    Charalampos Papamanthou & Roberto Tamassia

  2. RSA Laboratories, Cambridge, MA, USA

    Nikos Triandopoulos

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  1. Charalampos Papamanthou
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  2. Roberto Tamassia
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  3. Nikos Triandopoulos
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Editors and Affiliations

  1. Technicolor, Security and Content Protection Labs, 1 avenue de Belle Fontaine, 35576, Cesson-Sévigné Cedex, France

    Marc Joye

  2. Japan Advanced Institute of Science and Technology (JAIST), 923-1292, Nomi, Ishikawa, Japan

    Atsuko Miyaji

  3. National Institute of Advanced Industrial Science and Technoloy (AIST), 101-0021, Tokyo, Japan

    Akira Otsuka

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Papamanthou, C., Tamassia, R., Triandopoulos, N. (2010). Optimal Authenticated Data Structures with Multilinear Forms. In: Joye, M., Miyaji, A., Otsuka, A. (eds) Pairing-Based Cryptography - Pairing 2010. Pairing 2010. Lecture Notes in Computer Science, vol 6487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17455-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-17455-1_16

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