Adaptively Secure Garbling with Near Optimal Online Complexity

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10821)

Abstract

We construct an adaptively secure garbling scheme with an online communication complexity of \(n+m+\mathsf {poly}(\log |C|, \lambda )\) where \(C: \{0,1\}^n \rightarrow \{0,1\}^{m}\) is the circuit being garbled, and \(\lambda \) is the security parameter. The security of our scheme can be based on (polynomial hardness of) the Computational Diffie-Hellman (CDH) assumption, or the Factoring assumption or the Learning with Errors assumption. This is nearly the best achievable in the standard model (i.e., without random oracles) as the online communication complexity must be larger than both n and m. The online computational complexity of our scheme is \(O(n+m)+\mathsf {poly}(\log |C|, \lambda )\). Previously known standard model adaptively secure garbling schemes had asymptotically worse online cost or relied on exponentially hard computational assumptions.

References

  1. [ABSV15]
    Ananth, P., Brakerski, Z., Segev, G., Vaikuntanathan, V.: From selective to adaptive security in functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 657–677. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_32CrossRefGoogle Scholar
  2. [AF90]
    Abadi, M., Feigenbaum, J.: Secure circuit evaluation. J. Cryptol. 2(1), 1–12 (1990)CrossRefMATHGoogle Scholar
  3. [AIK04]
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Cryptography in NC\(^0\). In: 45th Annual Symposium on Foundations of Computer Science, Rome, Italy, 17–19 October 2004, pp. 166–175. IEEE Computer Society Press (2004)Google Scholar
  4. [AIK05]
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Computationally private randomizing polynomials and their applications. In: Proceedings of the 20th Annual IEEE Conference on Computational Complexity, CCC 2005, Washington, DC, USA, pp. 260–274. IEEE Computer Society (2005)Google Scholar
  5. [AIK10]
    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).  https://doi.org/10.1007/978-3-642-14165-2_14CrossRefGoogle Scholar
  6. [AIKW13]
    Applebaum, B., Ishai, Y., Kushilevitz, E., Waters, B.: Encoding functions with constant online rate or how to compress garbled circuits keys. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 166–184. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40084-1_10CrossRefGoogle Scholar
  7. [App14]
    Applebaum, B.: Bootstrapping obfuscators via fast pseudorandom functions. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 162–172. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-45608-8_9Google Scholar
  8. [AS16]
    Ananth, P., Sahai, A.: Functional encryption for turing machines. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9562, pp. 125–153. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49096-9_6CrossRefGoogle Scholar
  9. [Ben89]
    Bennett, C.H.: Time/space trade-offs for reversible computation. SIAM J. Comput. 18(4), 766–776 (1989)MathSciNetCrossRefMATHGoogle Scholar
  10. [BGG+14]
    Boneh, D., Gentry, C., Gorbunov, S., Halevi, S., Nikolaenko, V., Segev, G., Vaikuntanathan, V., Vinayagamurthy, D.: Fully key-homomorphic encryption, arithmetic circuit abe and compact garbled circuits. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 533–556. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-55220-5_30CrossRefGoogle Scholar
  11. [BHR12a]
    Bellare, M., Hoang, V.T., Rogaway, P.: Adaptively secure garbling with applications to one-time programs and secure outsourcing. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 134–153. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-34961-4_10CrossRefGoogle Scholar
  12. [BHR12b]
    Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) 19th Conference on Computer and Communications Security, ACM CCS 12, Raleigh, NC, USA, 16–18 October 2012, pp. 784–796. ACM Press (2012)Google Scholar
  13. [BLSV18]
    Brakerski, Z., Lombardi, A., Segev, G., Vaikuntanathan, V.: Anonymous IBE, leakage resilience and circular security from new assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) Eurocrypt 2018. LNCS, vol. 10821, pp. 535–564. Springer, Cham (2018). https://eprint.iacr.org/2017/967Google Scholar
  14. [BMR90]
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: 22nd Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, 14–16 May 1990, pp. 503–513. ACM Press (1990)Google Scholar
  15. [CDG+17]
    Cho, C., Döttling, N., Garg, S., Gupta, D., Miao, P., Polychroniadou, A.: Laconic oblivious transfer and its applications. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 33–65. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63715-0_2CrossRefGoogle Scholar
  16. [DG17]
    Döttling, N., Garg, S.: Identity-based encryption from the diffie-hellman assumption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 537–569. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_18CrossRefGoogle Scholar
  17. [DGHM18]
    Döttling, N., Garg, S., Hajiabadi, M., Masny, D.: New constructions of identity-based and key-dependent message secure encryption schemes. In: PKC (2018, to appear). https://eprint.iacr.org/2017/978
  18. [FNO15]
    Frederiksen, T.K., Nielsen, J.B., Orlandi, C.: Privacy-free garbled circuits with applications to efficient zero-knowledge. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 191–219. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46803-6_7Google Scholar
  19. [GGP10]
    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).  https://doi.org/10.1007/978-3-642-14623-7_25CrossRefGoogle Scholar
  20. [GHL+14]
    Gentry, C., Halevi, S., Lu, S., Ostrovsky, R., Raykova, M., Wichs, D.: Garbled RAM revisited. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 405–422. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-55220-5_23CrossRefGoogle Scholar
  21. [GKP+13]
    Goldwasser, S., Kalai, Y.T., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: Reusable garbled circuits and succinct functional encryption. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th Annual ACM Symposium on Theory of Computing, Palo Alto, CA, USA, 1–4 June 2013, pp. 555–564. ACM Press (2013)Google Scholar
  22. [GKR08]
    Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: One-time programs. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 39–56. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-85174-5_3CrossRefGoogle Scholar
  23. [GLO15]
    Garg, S., Lu, S., Ostrovsky, R.: Black-box garbled RAM. In: Guruswami, V. (ed.) 56th Annual Symposium on Foundations of Computer Science, Berkeley, CA, USA, 17–20 October 2015, pp. 210–229. IEEE Computer Society Press (2015)Google Scholar
  24. [GLOS15]
    Garg, S., Lu, S., Ostrovsky, R., Scafuro, A.: Garbled RAM from one-way functions. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th Annual ACM Symposium on Theory of Computing, Portland, OR, USA, 14–17 June 2015, pp. 449–458. ACM Press (2015)Google Scholar
  25. [GPSZ17]
    Garg, S., Pandey, O., Srinivasan, A., Zhandry, M.: Breaking the sub-exponential barrier in obfustopia. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10212, pp. 156–181. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-56617-7_6CrossRefGoogle Scholar
  26. [GS16]
    Garg, S., Srinivasan, A.: Single-key to multi-key functional encryption with polynomial loss. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 419–442. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53644-5_16CrossRefGoogle Scholar
  27. [GVW12]
    Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption with bounded collusions via multi-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 162–179. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_11CrossRefGoogle Scholar
  28. [HJO+16]
    Hemenway, B., Jafargholi, Z., Ostrovsky, R., Scafuro, A., Wichs, D.: Adaptively secure garbled circuits from one-way functions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 149–178. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53015-3_6CrossRefGoogle Scholar
  29. [JKK+17]
    Jafargholi, Z., Kamath, C., Klein, K., Komargodski, I., Pietrzak, K., Wichs, D.: Be adaptive, avoid overcommitting. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 133–163. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_5CrossRefGoogle Scholar
  30. [JKO13]
    Jawurek, M., Kerschbaum, F., Orlandi, C.: Zero-knowledge using garbled circuits: how to prove non-algebraic statements efficiently. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) 20th Conference on Computer and Communications Security, ACM CCS 13, Berlin, Germany, 4–8 November 2013, pp. 955–966. ACM Press (2013)Google Scholar
  31. [JSW17]
    Jafargholi, Z., Scafuro, A., Wichs, D.: Adaptively indistinguishable garbled circuits. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 40–71. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70503-3_2CrossRefGoogle Scholar
  32. [JW16]
    Jafargholi, Z., Wichs, D.: Adaptive security of Yao’s garbled circuits. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9985, pp. 433–458. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_17CrossRefGoogle Scholar
  33. [LM16]
    Li, B., Micciancio, D.: Compactness vs collusion resistance in functional encryption. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 443–468. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53644-5_17CrossRefGoogle Scholar
  34. [LO13]
    Lu, S., Ostrovsky, R.: How to garble RAM programs? In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 719–734. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38348-9_42CrossRefGoogle Scholar
  35. [LP09]
    Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. J. Cryptol. 22(2), 161–188 (2009)MathSciNetCrossRefMATHGoogle Scholar
  36. [LV16]
    Lin, H., Vaikuntanathan, V.: Indistinguishability obfuscation from DDH-like assumptions on constant-degree graded encodings. In: Dinur, I. (ed.) 57th Annual Symposium on Foundations of Computer Science, New Brunswick, NJ, USA, 9–11 October 2016, pp. 11–20. IEEE Computer Society Press (2016)Google Scholar
  37. [MNPS04]
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay - secure two-party computation system. In: Proceedings of the 13th USENIX Security Symposium, San Diego, CA, USA, 9–13 August 2004, pp. 287–302 (2004)Google Scholar
  38. [Nie02]
    Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: the non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45708-9_8CrossRefGoogle Scholar
  39. [PTC76]
    Paul, W.J., Tarjan, R.E., Celoni, J.R.: Space bounds for a game on graphs. Mathe. Syst. Theor. 10(1), 239–251 (1976)MathSciNetCrossRefMATHGoogle Scholar
  40. [SS10]
    Sahai, A., Seyalioglu, H.: Worry-free encryption: functional encryption with public keys. In: Al-Shaer, E., Keromytis, A.D., Shmatikov, V. (eds.) 17th Conference on Computer and Communications Security, ACM CCS 10, Chicago, Illinois, USA, 4–8 October 2010, pp. 463–472. ACM Press (2010)Google Scholar
  41. [Yao82]
    Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: 23rd Annual Symposium on Foundations of Computer Science, Chicago, Illinois, 3–5 November 1982, pp. 160–164. IEEE Computer Society Press (1982)Google Scholar
  42. [Yao86]
    Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: 27th Annual Symposium on Foundations of Computer Science, Toronto, Ontario, Canada, 27–29 October 1986, pp. 162–167. IEEE Computer Society Press (1986)Google Scholar

Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA

Personalised recommendations