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2020 | OriginalPaper | Buchkapitel

Two-Sided Malicious Security for Private Intersection-Sum with Cardinality

verfasst von : Peihan Miao, Sarvar Patel, Mariana Raykova, Karn Seth, Moti Yung

Erschienen in: Advances in Cryptology – CRYPTO 2020

Verlag: Springer International Publishing

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Abstract

Private intersection-sum with cardinality allows two parties, where each party holds a private set and one of the parties additionally holds a private integer value associated with each element in her set, to jointly compute the cardinality of the intersection of the two sets as well as the sum of the associated integer values for all the elements in the intersection, and nothing beyond that.

We present a new construction for private intersection sum with cardinality that provides malicious security with abort and guarantees that both parties receive the output upon successful completion of the protocol. A central building block for our constructions is a primitive called shuffled distributed oblivious PRF (DOPRF), which is a PRF that offers oblivious evaluation using a secret key shared between two parties, and in addition to this allows obliviously permuting the PRF outputs of several parallel oblivious evaluations. We present the first construction for shuffled DOPRF with malicious security. We further present several new sigma proof protocols for relations across Pedersen commitments, ElGamal encryptions, and Camenisch-Shoup encryptions that we use in our main construction, for which we develop new batching techniques to reduce communication.

We implement and evaluate the efficiency of our protocol and show that we can achieve communication cost that is only \(4{-}5{\times }\) greater than the most efficient semi-honest protocol. When measuring monetary cost of executing the protocol in the cloud, our protocol is \(25{\times }\) more expensive than the semi-honest protocol. Our construction also allows for different parameter regimes that enable trade-offs between communication and computation.

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Nächstes Kapitel Private Set Intersection in the Internet Setting from Lightweight Oblivious PRF

See https://cloud.google.com/compute/network-pricing/ for the network cost and https://cloud.google.com/compute/vm-instance-pricing for the computation cost.

Concurrent to our work, Pinkas at el. [55] present a new one-sided malicious PSI that achieves better efficiency than [61], but we note that their protocol also does not easily support our two-sided functionality.

Agrawal, R., Evfimievski, A., Srikant, R.: Information sharing across private databases. In: Proceedings of the 2003 ACM SIGMOD International Conference on Management of Data (2003)

Applebaum, B., Ringberg, H., Freedman, M.J., Caesar, M., Rexford, J.: Collaborative, privacy-preserving data aggregation at scale. In: Atallah, M.J., Hopper, N.J. (eds.) PETS 2010. LNCS, vol. 6205, pp. 56–74. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14527-8_4CrossRef

Baldi, P., Baronio, R., De Cristofaro, E., Gasti, P., Tsudik, G.: Countering GATTACA: efficient and secure testing of fully-sequenced human genomes. In: ACM CCS (2011)

Barić, 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). https://doi.org/10.1007/3-540-69053-0_33CrossRef

Bayer, S., Groth, J.: Efficient zero-knowledge argument for correctness of a shuffle. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 263–280. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_17CrossRef

Belenkiy, M., Camenisch, J., Chase, M., Kohlweiss, M., Lysyanskaya, A., Shacham, H.: Randomizable proofs and delegatable anonymous credentials. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 108–125. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_7CrossRef

Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: ACM CCS (1993)

Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_4CrossRef

Boudot, F.: Efficient proofs that a committed number lies in an interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45539-6_31CrossRefMATH

10.

Bursztein, E., Hamburg, M., Lagarenne, J., Boneh, D.: OpenConflict: preventing real time map hacks in online games. In: IEEE Symposium on Security and Privacy (2011)

11.

Camenisch, J., Kohlweiss, M., Rial, A., Sheedy, C.: Blind and anonymous identity-based encryption and authorised private searches on public key encrypted data. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 196–214. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00468-1_12CrossRefMATH

12.

Camenisch, J., Michels, M.: Proving in zero-knowledge that a number is the product of two safe primes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 107–122. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_8CrossRefMATH

13.

Camenisch, J., Shoup, V.: Practical verifiable encryption and decryption of discrete logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_8CrossRef

14.

Camenisch, J., Stadler, M.: Efficient group signature schemes for large groups. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 410–424. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052252CrossRef

15.

Camenisch, J., Zaverucha, G.M.: Private intersection of certified sets. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 108–127. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03549-4_7CrossRef

16.

Ciampi, M., Orlandi, C.: Combining private set-intersection with secure two-party computation. In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 464–482. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98113-0_25CrossRef

17.

Dachman-Soled, D., Malkin, T., Raykova, M., Yung, M.: Efficient robust private set intersection. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 125–142. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01957-9_8CrossRef

18.

Damgard, I.: On \(\Sigma \)-protocols (2002). http://www.cs.au.dk/~ivan/Sigma.pdf

19.

Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44586-2_9CrossRefMATH

20.

De Cristofaro, E., Gasti, P., Tsudik, G.: Fast and private computation of cardinality of set intersection and union. In: Pieprzyk, J., Sadeghi, A.-R., Manulis, M. (eds.) CANS 2012. LNCS, vol. 7712, pp. 218–231. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35404-5_17CrossRef

21.

De Cristofaro, E., Kim, J., Tsudik, G.: Linear-complexity private set intersection protocols secure in malicious model. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 213–231. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_13CrossRefMATH

22.

Debnath, S.K., Dutta, R.: Secure and efficient private set intersection cardinality using bloom filter. In: Lopez, J., Mitchell, C.J. (eds.) ISC 2015. LNCS, vol. 9290, pp. 209–226. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23318-5_12CrossRef

23.

Dodis, Y., Yampolskiy, A.: A verifiable random function with short proofs and keys. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 416–431. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30580-4_28CrossRef

24.

Dong, C., Chen, L., Wen, Z.: When private set intersection meets big data: an efficient and scalable protocol. In: ACM CCS (2013)

25.

Egert, R., Fischlin, M., Gens, D., Jacob, S., Senker, M., Tillmanns, J.: Privately computing set-union and set-intersection cardinality via bloom filters. In: Foo, E., Stebila, D. (eds.) ACISP 2015. LNCS, vol. 9144, pp. 413–430. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19962-7_24CrossRefMATH

26.

ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31, 469–472 (1985)MathSciNetCrossRef

27.

Falk, B.H., Noble, D., Ostrovsky, R.: Private set intersection with linear communication from general assumptions (2018)

28.

Falk, B.H., Noble, D., Ostrovsky, R.: Private set intersection with linear communication from general assumptions. In: WPES@CCS (2019)

29.

Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12CrossRef

30.

Freedman, M.J., Hazay, C., Nissim, K., Pinkas, B.: Efficient set intersection with simulation-based security. J. Cryptol. 29, 115–155 (2016)MathSciNetCrossRef

31.

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). https://doi.org/10.1007/978-3-540-24676-3_1CrossRef

32.

Fujisaki, E., Okamoto, T.: Statistical zero knowledge protocols to prove modular polynomial relations. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16–30. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052225CrossRef

33.

Gennaro, R., Leigh, D., Sundaram, R., Yerazunis, W.: Batching schnorr identification scheme with applications to privacy-preserving authorization and low-bandwidth communication devices. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 276–292. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30539-2_20CrossRef

34.

Groth, J.: Linear algebra with sub-linear zero-knowledge arguments. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 192–208. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_12CrossRef

35.

Hazay, C., Lindell, Y.: Efficient protocols for set intersection and pattern matching with security against malicious and covert adversaries. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 155–175. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78524-8_10CrossRef

36.

Hazay, C., Nissim, K.: Efficient set operations in the presence of malicious adversaries. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 312–331. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_19CrossRef

37.

Huang, Y., Evans, D., Katz, J.: Private set intersection: are garbled circuits better than custom protocols? In: NDSS (2012)

38.

Huberman, B.A., Franklin, M., Hogg, T.: Enhancing privacy and trust in electronic communities. In: ACM Conference on Electronic Commerce (1999)

39.

Ion, M., et al.: Private intersection-sum protocol with applications to attributing aggregate ad conversions. Cryptology ePrint Archive, Report 2017/738 (2017). https://eprint.iacr.org/2017/738

40.

Jarecki, S., Liu, X.: Efficient oblivious pseudorandom function with applications to adaptive OT and secure computation of set intersection. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 577–594. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00457-5_34CrossRefMATH

41.

Kissner, L., Song, D.: Privacy-preserving set operations. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005). https://doi.org/10.1007/11535218_15CrossRef

42.

Kolesnikov, V., Kumaresan, R., Rosulek, M., Trieu, N.: Efficient batched oblivious PRF with applications to private set intersection. In: ACM CCS (2016)

43.

Kolesnikov, V., Matania, N., Pinkas, B., Rosulek, M., Trieu, N.: Practical multi-party private set intersection from symmetric-key techniques. In: ACM CCS (2017)

44.

Lambæk, M.: Breaking and fixing private set intersection protocols. Cryptology ePrint Archive, Report 2016/665 (2016). https://eprint.iacr.org/2016/665

45.

Li, M., Cao, N., Yu, S., Lou, W.: FindU: privacy-preserving personal profile matching in mobile social networks. In: IEEE INFOCOM (2011)

46.

Miao, P., Patel, S., Raykova, M., Seth, K., Yung, M.: Two-sided malicious security for private intersection-sum with cardinality. Cryptology ePrint Archive, Report 2020/385 (2020). https://eprint.iacr.org/2020/385

47.

Mitsunari, S., Sakai, R., Kasahara, M.: A new traitor tracing. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 85, 481–484 (2002)

48.

Nagaraja, S., Mittal, P., Hong, C.Y., Caesar, M., Borisov, N.: BotGrep: finding P2P bots with structured graph analysis. In: USENIX Security (2010)

49.

Nagy, M., De Cristofaro, E., Dmitrienko, A., Asokan, N., Sadeghi, A.R.: Do i know you?: efficient and privacy-preserving common friend-finder protocols and applications. In: ACSAC (2013)

50.

Narayanan, A., Thiagarajan, N., Lakhani, M., Hamburg, M., Boneh, D., et al.: Location privacy via private proximity testing. In: NDSS, vol. 11 (2011)

51.

Narayanan, G.S., Aishwarya, T., Agrawal, A., Patra, A., Choudhary, A., Rangan, C.P.: Multi party distributed private matching, set disjointness and cardinality of set intersection with information theoretic security. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds.) CANS 2009. LNCS, vol. 5888, pp. 21–40. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10433-6_2CrossRefMATH

52.

Pagh, R., Rodler, F.F.: Cuckoo hashing. J. Algorithms (2004)

53.

Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_9CrossRef

54.

Pinkas, B., Rosulek, M., Trieu, N., Yanai, A.: SpOT-light: lightweight private set intersection from sparse OT extension. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 401–431. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_13CrossRef

55.

Pinkas, B., Rosulek, M., Trieu, N., Yanai, A.: PSI from PaXoS: fast, malicious private set intersection. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 739–767. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_25CrossRef

56.

Pinkas, B., Schneider, T., Segev, G., Zohner, M.: Phasing: private set intersection using permutation-based hashing. In: USENIX Security (2015)

57.

Pinkas, B., Schneider, T., Tkachenko, O., Yanai, A.: Efficient circuit-based PSI with linear communication. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 122–153. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_5CrossRef

58.

Pinkas, B., Schneider, T., Weinert, C., Wieder, U.: Efficient circuit-based PSI via cuckoo hashing. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 125–157. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_5CrossRef

59.

Pinkas, B., Schneider, T., Zohner, M.: Faster private set intersection based on OT extension. In: USENIX Security (2014)

60.

Rindal, P., Rosulek, M.: Improved private set intersection against malicious adversaries. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 235–259. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56620-7_9CrossRef

61.

Rindal, P., Rosulek, M.: Malicious-secure private set intersection via dual execution. In: ACM CCS (2017)

62.

Segal, A., Ford, B., Feigenbaum, J.: Catching bandits and only bandits: privacy-preserving intersection warrants for lawful surveillance. In: FOCI (2014)

63.

Vaidya, J., Clifton, C.: Secure set intersection cardinality with application to association rule mining. J. Comput. Secur. 13, 593–622 (2005)CrossRef

Titel: Two-Sided Malicious Security for Private Intersection-Sum with Cardinality
verfasst von: Peihan Miao
Sarvar Patel
Mariana Raykova
Karn Seth
Moti Yung
Verlag: Springer International Publishing
Buch: Advances in Cryptology – CRYPTO 2020
Print ISBN: 978-3-030-56876-4

Electronic ISBN: 978-3-030-56877-1

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-56877-1_1

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