Abstract
We study the design of protocols for set-operation verification, namely the problem of cryptographically checking the correctness of outsourced set operations performed by an untrusted server over a dynamic collection of sets that are owned (and updated) by a trusted source. We present new authenticated data structures that allow any entity to publicly verify a proof attesting the correctness of primitive set operations such as intersection, union, subset and set difference. Based on a novel extension of the security properties of bilinear-map accumulators as well as on a primitive called accumulation tree, our protocols achieve optimal verification and proof complexity (i.e., only proportional to the size of the query parameters and the answer), as well as optimal update complexity (i.e., constant), while incurring no extra asymptotic space overhead. The proof construction is also efficient, adding a logarithmic overhead to the computation of the answer of a set-operation query. In contrast, existing schemes entail high communication and verification costs or high storage costs. Applications of interest include efficient verification of keyword search and database queries. The security of our protocols is based on the bilinear q-strong Diffie-Hellman assumption.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
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)
Atallah, M.J., Cho, Y., Kundu, A.: Efficient data authentication in an environment of untrusted third-party distributors. In: Int. Conference on Data Engineering (ICDE), pp. 696–704 (2008)
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)
Baeza-Yates, R., Ribeiro-Neto, B.: Modern Information Retrieval. Addison-Wesley Publishing Company, Reading (1999)
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)
Benabbas, S., Gennaro, R., Vahlis, Y.: Verifiable delegation of computation over large datasets. In: Int. Cryptology Conference, CRYPTO (2011)
Blum, M., Evans, W.S., Gemmell, P., Kannan, S., Naor, M.: Checking the correctness of memories. Algorithmica 12(2/3), 225–244 (1994)
Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. J. Cryptology 21(2), 149–177 (2008)
Boneh, D., Waters, B.: Conjunctive, subset, and range queries on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 535–554. Springer, Heidelberg (2007)
Canard, S., Gouget, A.: Multiple denominations in E-cash with compact transaction data. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 82–97. Springer, Heidelberg (2010)
Chung, K.-M., Kalai, Y., Liu, F.-H., Raz, R.: Memory delegation. In: Int. Cryptology Conference, CRYPTO (2011)
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)
Damgård, I., Triandopoulos, N.: Supporting non-membership proofs with bilinear-map accumulators. Cryptology ePrint Archive, Report 2008/538 (2008), http://eprint.iacr.org/
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)
Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004)
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)
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)
Goodrich, M.T., Tamassia, R., Schwerin, A.: Implementation of an authenticated dictionary with skip lists and commutative hashing. In: DARPA Information Survivability Conference and Exposition II (DISCEX II), pp. 68–82 (2001)
Goodrich, M.T., Tamassia, R., Triandopoulos, N.: Super-efficient verification of dynamic outsourced databases. In: Malkin, T. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 407–424. Springer, Heidelberg (2008)
Goodrich, M.T., Tamassia, R., Triandopoulos, N.: Efficient authenticated data structures for graph connectivity and geometric search problems. Algorithmica 60(3), 505–552 (2011)
Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.P.: Certifying algorithms for recognizing interval graphs and permutation graphs. In: Symposium on Discrete Algorithms (SODA), pp. 158–167 (2003)
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)
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)
Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, Heidelberg (1990)
Minsky, Y., Trachtenberg, A., Zippel, R.: Set reconciliation with nearly optimal communication complexity. IEEE Transactions on Information Theory 49(9), 2213–2218 (2003)
Morselli, R., Bhattacharjee, S., Katz, J., Keleher, P.J.: Trust-preserving set operations. In: Int. Conference on Computer Communications, INFOCOM (2004)
Naor, M., Nissim, K.: Certificate revocation and certificate update. In: USENIX Security Symposium, pp. 217–228 (1998)
Nguyen, L.: Accumulators from bilinear pairings and applications. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 275–292. Springer, Heidelberg (2005)
Pang, H., Tan, K.-L.: Authenticating query results in edge computing. In: Int. Conference on Data Engineering (ICDE), pp. 560–571 (2004)
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)
Papamanthou, C., Tamassia, R.: Cryptography for efficiency: Authenticated data structures based on lattices and parallel online memory checking. In: Cryptology ePrint Archive, Report 2011/102 (2011), http://eprint.iacr.org/
Papamanthou, C., Tamassia, R., Triandopoulos, N.: Authenticated hash tables. In: Int. Conference on Computer and Communications Security (CCS), pp. 437–448 (2008)
Papamanthou, C., Tamassia, R., Triandopoulos, N.: Optimal authenticated data structures with multilinear forms. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 246–264. Springer, Heidelberg (2010)
Preparata, F.P., Sarwate, D.V.: Computational complexity of Fourier transforms over finite fields. Mathematics of Computation 31(139), 740–751 (1977)
Preparata, F.P., Shamos, M.I.: Computational Geometry: An Introduction. Springer, New York (1985)
Tamassia, R.: Authenticated data structures. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 2–5. Springer, Heidelberg (2003)
Tamassia, R., Triandopoulos, N.: Certification and authentication of data structures. In: Alberto Mendelzon Workshop on Foundations of Data Management (2010)
Yang, Y., Papadias, D., Papadopoulos, S., Kalnis, P.: Authenticated join processing in outsourced databases. In: Int. Conf. on Management of Data (SIGMOD), pp. 5–18 (2009)
Yiu, M.L., Lin, Y., Mouratidis, K.: Efficient verification of shortest path search via authenticated hints. In: Int. Conference on Data Engineering (ICDE), pp. 237–248 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 International Association for Cryptologic Research
About this paper
Cite this paper
Papamanthou, C., Tamassia, R., Triandopoulos, N. (2011). Optimal Verification of Operations on Dynamic Sets. In: Rogaway, P. (eds) Advances in Cryptology – CRYPTO 2011. CRYPTO 2011. Lecture Notes in Computer Science, vol 6841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22792-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-22792-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22791-2
Online ISBN: 978-3-642-22792-9
eBook Packages: Computer ScienceComputer Science (R0)