Abstract
We propose a 2-party UC-secure protocol that can compute any function securely. The protocol requires only two messages, communication that is poly-logarithmic in the size of the circuit description of the function, and the workload for one of the parties is also only poly-logarithmic in the size of the circuit. This implies, for instance, delegatable computation that requires no expensive off-line phase and remains secure even if the server learns whether the client accepts its results. To achieve this, we define two new notions of extractable hash functions, propose an instantiation based on the knowledge of exponent in an RSA group, and build succinct zero-knowledge arguments in the CRS model.
The authors acknowledge support from the Danish National Research Foundation and The National Science Foundation of China (under the grant 61061130540) for the Sino-Danish Center for the Theory of Interactive Computation, within part of this work was performed; and from the CFEM research center, supported by the Danish Strategic Research Council.
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References
Aiello, W., Bhatt, S., Ostrovsky, R., Rajagopalan, S.R.: Fast Verification of Any Remote Procedure Call: Short Witness-Indistinguishable One-Round Proofs for NP. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 463–474. Springer, Heidelberg (2000)
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, Part I. LNCS, vol. 6198, pp. 152–163. Springer, Heidelberg (2010)
Arora, S., Safra, S.: Probabilistic checking of proofs: A new characterization of np. J. ACM 45(1), 70–122 (1998)
Bitansky, N., Canetti, R., Chiesaz, A., Tromer, E.: From extractable collision resistance to succinct non- interactive arguments of knowledge, and back again. Cryptology ePrint Archive, Report 2011/443 (2011)
Babai, L., Fortnow, L., Levin, L.A., Szegedy, M.: Checking computations in polylogarithmic time. In: STOC, pp. 21–31 (1991)
Benabbas, S., Gennaro, R., Vahlis, Y.: Verifiable Delegation of Computation over Large Datasets. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 111–131. Springer, Heidelberg (2011)
Bellare, M., Palacio, A.: Towards Plaintext-Aware Public-Key Encryption Without Random Oracles. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 48–62. Springer, Heidelberg (2004)
Bellare, M., Ristenpart, T.: Multi-Property-Preserving Hash Domain Extension and the EMD Transform. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 299–314. Springer, Heidelberg (2006)
Ben-Sasson, E., Sudan, M.: Simple pcps with poly-log rate and query complexity. In: STOC, pp. 266–275 (2005)
Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) lwe. In: FOCS (2011)
Brakerski, Z., Vaikuntanathan, V.: Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505–524. Springer, Heidelberg (2011)
Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptology 13(1), 143–202 (2000)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS, pp. 136–145 (2001)
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)
Di Crescenzo, G., Lipmaa, H.: Succinct NP Proofs from an Extractability Assumption. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds.) CiE 2008. LNCS, vol. 5028, pp. 175–185. Springer, Heidelberg (2008)
Cleve, R.: Limits on the security of coin flips when half the processors are faulty (extended abstract). In: STOC, pp. 364–369 (1986)
Damgård, I.: Towards Practical Public Key Systems Secure against Chosen Ciphertext Attacks. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 445–456. Springer, Heidelberg (1992)
Dent, A.W.: The Cramer-Shoup Encryption Scheme Is Plaintext Aware in the Standard Model. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 289–307. Springer, Heidelberg (2006)
Damgård, I., Faust, S., Hazay, C.: Secure two-party computation with low communication. Cryptology ePrint Archive, Report 2011/508 (2011), http://eprint.iacr.org/
Dinur, I.: The pcp theorem by gap amplification. J. ACM 54(3), 12 (2007)
Dwork, C., Langberg, M., Naor, M., Nissim, K., Reingold, O.: Succinct np proofs and spooky interactions (2004), http://www.openu.ac.il/home/mikel/papers/spooky.ps
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178 (2009)
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)
Gordon, D., Katz, J., Kolesnikov, V., Malkin, T., Raykov, M., Vahlis, Y.: Secure computation with sublinear amortized work. Cryptology ePrint Archive, Report 2011/482 (2011)
Goldwasser, S., Levin, L.A.: Fair Computation of General Functions in Presence of Immoral Majority. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 77–93. Springer, Heidelberg (1991)
Goldwasser, S., Lin, H., Rubinstein, A.: Delegation of computation without rejection problem from designated verifier cs-proofs. Cryptology ePrint Archive, Report 2011/456 (2011)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229 (1987)
Goldreich, O.: Foundations of Cryptography: Basic Applications. Cambridge University Press (2004)
Groth, J.: Short Pairing-Based Non-interactive Zero-Knowledge Arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010)
Groth, J.: Minimizing non-interactive zero-knowledge proofs using fully homomorphic encryption. Cryptology ePrint Archive, Report 2011/012 (2011)
Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: STOC, pp. 99–108 (2011)
Hada, S., Tanaka, T.: On the Existence of 3-Round Zero-Knowledge Protocols. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 408–423. Springer, Heidelberg (1998)
Ishai, Y., Kushilevitz, E., Ostrovsky, R., Prabhakaran, M., Sahai, A.: Efficient Non-interactive Secure Computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 406–425. Springer, Heidelberg (2011)
Ishai, Y., Kushilevitz, E., Paskin, A.: Secure Multiparty Computation with Minimal Interaction. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 577–594. Springer, Heidelberg (2010)
Ishai, Y., Prabhakaran, M., Sahai, A.: Founding Cryptography on Oblivious Transfer – Efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008)
Ishai, Y., Prabhakaran, M., Sahai, A.: Secure Arithmetic Computation with No Honest Majority. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 294–314. Springer, Heidelberg (2009)
Kilian, J.: A note on efficient zero-knowledge proofs and arguments (extended abstract). In: STOC, pp. 723–732 (1992)
Katz, J., Koo, C.-Y.: Round-Efficient Secure Computation in Point-to-Point Networks. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 311–328. Springer, Heidelberg (2007)
Kushilevitz, E., Ostrovsky, R.: Replication is not needed: Single database, computationally-private information retrieval. In: FOCS, pp. 364–373 (1997)
Lindell, Y., Pinkas, B.: Secure Two-Party Computation via Cut-and-Choose Oblivious Transfer. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 329–346. Springer, Heidelberg (2011)
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)
Micali, S.: Computationally sound proofs. SIAM J. Comput. 30(4), 1253–1298 (2000)
Naor, M.: On Cryptographic Assumptions and Challenges. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 96–109. Springer, Heidelberg (2003)
Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: STOC, pp. 590–599 (2001)
Nielsen, J.B., Orlandi, C.: LEGO for Two-Party Secure Computation. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 368–386. Springer, Heidelberg (2009)
Polishchuk, A., Spielman, D.A.: Nearly-linear size holographic proofs. In: STOC, pp. 194–203 (1994)
Pinkas, B., Schneider, T., Smart, N.P., Williams, S.C.: Secure Two-Party Computation is Practical. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 250–267. Springer, Heidelberg (2009)
van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully Homomorphic Encryption over the Integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)
Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167 (1986)
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Damgård, I., Faust, S., Hazay, C. (2012). Secure Two-Party Computation with Low Communication. In: Cramer, R. (eds) Theory of Cryptography. TCC 2012. Lecture Notes in Computer Science, vol 7194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28914-9_4
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