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Simpler Constructions of Asymmetric Primitives from Obfuscation

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Progress in Cryptology – INDOCRYPT 2020 (INDOCRYPT 2020)

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Abstract

We revisit constructions of asymmetric primitives from obfuscation and give simpler alternatives. We consider public-key encryption, (hierarchical) identity-based encryption ((H)IBE), and predicate encryption. Obfuscation has already been shown to imply PKE by Sahai and Waters (STOC’14) and full-fledged functional encryption by Garg et al. (FOCS’13). We simplify all these constructions and reduce the necessary assumptions on the class of circuits that the obfuscator needs to support. Our PKE scheme relies on just a PRG and does not need any puncturing.

Our IBE and bounded HIBE schemes convert natural key-delegation mechanisms from (recursive) applications of puncturable PRFs to IBE and HIBE schemes. Our most technical contribution is an unbounded HIBE, which uses (public-coin) differing-inputs obfuscation for circuits and whose proof relies on a pebbling-based hybrid argument by Fuchsbauer et al. (ASIACRYPT’14). All our constructions are anonymous, support arbitrary inputs, and have compact keys and ciphertexts.

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Notes

  1. 1.

    Although the proof of this construction is somewhat complex, the construction itself is relatively simple given that it achieves an unbounded number of levels.

  2. 2.

    We note that public-coin diO is not known to suffer from impossibility results that apply to its private-coin counterpart [GGHW14, BSW16].

  3. 3.

    Since our construction relies on public-coin diO, it must be hard to find a differing input even when given the coins used to sample the circuits (whose obfuscations should be indistinguishable). As a hash collision results in a differing input, it must be hard to find one even given the coins used to sample the hash function.

  4. 4.

    Note that this is not the case if we only use one encryption of 1 (i.e. if we remove \(h_{21}\) and \(h_{22}\)).

References

  1. Abdalla, M., et al.: Searchable encryption revisited: consistency properties, relation to anonymous IBE, and extensions. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 205–222. Springer, Heidelberg (2005). https://doi.org/10.1007/11535218_13

    Chapter  Google Scholar 

  2. Abusalah, H., Fuchsbauer, G., Pietrzak, K.: Constrained PRFs for unbounded inputs. Cryptology ePrint Archive, report 2014/840 (2014)

    Google Scholar 

  3. Ananth, P., Jain, A., Lin, H., Matt, C., Sahai, A.: Indistinguishability obfuscation without multilinear maps: new paradigms via low degree weak pseudorandomness and security amplification. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 284–332. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_10

    Chapter  Google Scholar 

  4. 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_6

    Chapter  Google Scholar 

  5. Ananth, P., Sahai, A.: Projective arithmetic functional encryption and indistinguishability obfuscation from degree-5 multilinear maps. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 152–181. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56620-7_6

    Chapter  Google Scholar 

  6. Brakerski, Z., Chandran, N., Goyal, V., Jain, A., Sahai, A., Segev, G.: Hierarchical functional encryption. In: Papadimitriou, C.H. (ed.) ITCS 2017, vol. 4266, pp. 8:1–8:27, 67. LIPIcs, January 2017

    Google Scholar 

  7. Brakerski, Z., Döttling, N., Garg, S., Malavolta, G.: Candidate iO from homomorphic encryption schemes. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 79–109. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_4

    Chapter  Google Scholar 

  8. Brakerski, Z., Döttling, N., Garg, S., Malavolta, G.: Factoring and pairings are not necessary for iO: circular-secure LWE suffices. IACR Cryptology ePrint Archive 2020/1024 (2020)

    Google Scholar 

  9. Bennett, C.H.: Time/space trade-offs for reversible computation. SIAM J. Comput. 18(4), 766–776 (1989)

    Article  MathSciNet  Google Scholar 

  10. Barak, B., et al.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6:1–6:48 (2012)

    Article  MathSciNet  Google Scholar 

  11. Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 501–519. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_29

    Chapter  Google Scholar 

  12. Bartusek, J., Lepoint, T., Ma, F., Zhandry, M.: New techniques for obfuscating conjunctions. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 636–666. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_22

    Chapter  Google Scholar 

  13. Boneh, D., Lewi, K., Raykova, M., Sahai, A., Zhandry, M., Zimmerman, J.: Semantically secure order-revealing encryption: multi-input functional encryption without obfuscation. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 563–594. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_19

    Chapter  Google Scholar 

  14. Bitansky, N., Nishimaki, R., Passelègue, A., Wichs, D.: From cryptomania to obfustopia through secret-key functional encryption. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 391–418. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53644-5_15

    Chapter  Google Scholar 

  15. Bitansky, N., Paneth, O.: ZAPs and non-interactive witness indistinguishability from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 401–427. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_16

    Chapter  MATH  Google Scholar 

  16. Bellare, M., Stepanovs, I., Waters, B.: New negative results on differing-inputs obfuscation. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 792–821. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_28

    Chapter  Google Scholar 

  17. Bitansky, N., Vaikuntanathan, V.: Indistinguishability obfuscation from functional encryption. In: Guruswami, V. (ed.) 56th FOCS, pp. 171–190. IEEE Computer Society Press, October 2015

    Google Scholar 

  18. 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). https://doi.org/10.1007/978-3-540-70936-7_29

    Chapter  Google Scholar 

  19. Boneh, D., Waters, B.: Constrained pseudorandom functions and their applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8270, pp. 280–300. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42045-0_15

    Chapter  Google Scholar 

  20. Boneh, D., Zhandry, M.: Multiparty key exchange, efficient traitor tracing, and more from indistinguishability obfuscation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 480–499. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_27

    Chapter  Google Scholar 

  21. Chung, K.-M., Lin, H., Pass, R.: Constant-round concurrent zero-knowledge from indistinguishability obfuscation. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 287–307. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_14

    Chapter  Google Scholar 

  22. Canetti, R., Rothblum, G.N., Varia, M.: Obfuscation of hyperplane membership. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 72–89. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_5

    Chapter  MATH  Google Scholar 

  23. Chen, Y., Vaikuntanathan, V., Wee, H.: GGH15 beyond permutation branching programs: proofs, attacks, and candidates. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 577–607. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_20

    Chapter  Google Scholar 

  24. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_2

    Chapter  Google Scholar 

  25. Fuchsbauer, G., Konstantinov, M., Pietrzak, K., Rao, V.: Adaptive security of constrained PRFs. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 82–101. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8_5

    Chapter  Google Scholar 

  26. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th FOCS, pp. 40–49. IEEE Computer Society Press, October 2013

    Google Scholar 

  27. Garg, S., Gentry, C., Halevi, S., Wichs, D.: On the implausibility of differing-inputs obfuscation and extractable witness encryption with auxiliary input. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 518–535. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_29

    Chapter  Google Scholar 

  28. Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792–807 (1986)

    Article  MathSciNet  Google Scholar 

  29. Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 467–476. ACM Press, June 2013

    Google Scholar 

  30. Gay, R., Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from simple-to-state hard problems: new assumptions, new techniques, and simplification. IACR Cryptology ePrint Archive 2020/764 (2020)

    Google Scholar 

  31. Goyal, R., Koppula, V., Waters, B.: Lockable obfuscation. In: Umans, C. (ed.) 58th FOCS, pp. 612–621. IEEE Computer Society Press, October 2017

    Google Scholar 

  32. Goldreich, O.: Foundations of Cryptography: Basic Tools, vol. 1. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  33. Gay, R., Pass, R.: Indistinguishability obfuscation from circular security. IACR Cryptology ePrint Archive 2020/1010 (2020)

    Google Scholar 

  34. Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Juels, A., Wright, R.N., De Capitani di Vimercati, S. (eds.) ACM CCS 2006, pp. 89–98. ACM Press, October/November 2006. Available as Cryptology ePrint Archive Report 2006/309

    Google Scholar 

  35. Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36178-2_34

    Chapter  Google Scholar 

  36. Galbraith, S.D., Zobernig, L.: Obfuscating finite automata. IACR Cryptology ePrint Archive 2020/1009 (2020)

    Google Scholar 

  37. Hsiao, C.-Y., Reyzin, L.: Finding collisions on a public road, or do secure hash functions need secret coins? In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 92–105. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_6

    Chapter  Google Scholar 

  38. Hohenberger, S., Sahai, A., Waters, B.: Replacing a random oracle: full domain hash from indistinguishability obfuscation. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 201–220. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_12

    Chapter  Google Scholar 

  39. Hubacek, P., Wichs, D.: On the communication complexity of secure function evaluation with long output. In: Roughgarden, T. (ed.) ITCS 2015, pp. 163–172. ACM, January 2015

    Google Scholar 

  40. Ishai, Y., Pandey, O., Sahai, A.: Public-coin differing-inputs obfuscation and its applications. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 668–697. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_26

    Chapter  Google Scholar 

  41. Jain, A., Lin, H., Matt, C., Sahai, A.: How to leverage hardness of constant-degree expanding polynomials over \(\mathbb{R}\) to build \(i\cal{O}\). In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11476, pp. 251–281. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_9

    Chapter  Google Scholar 

  42. Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from well-founded assumptions. CoRR, abs/2008.09317 (2020)

    Google Scholar 

  43. Kiayias, A., Papadopoulos, S., Triandopoulos, N., Zacharias, T.: Delegatable pseudorandom functions and applications. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) ACM CCS 2013, pp. 669–684. ACM Press, November 2013

    Google Scholar 

  44. Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_9

    Chapter  Google Scholar 

  45. Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_4

    Chapter  Google Scholar 

  46. Lin, H., Pass, R., Seth, K., Telang, S.: Indistinguishability obfuscation with non-trivial efficiency. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9615, pp. 447–462. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49387-8_17

    Chapter  Google Scholar 

  47. Lin, H., Tessaro, S.: Indistinguishability obfuscation from trilinear maps and block-wise local PRGs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 630–660. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_21

    Chapter  Google Scholar 

  48. Lewko, A., Waters, B.: Unbounded HIBE and attribute-based encryption. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 547–567. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_30

    Chapter  Google Scholar 

  49. Matsuda, T., Hanaoka, G.: Chosen ciphertext security via point obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 95–120. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_5

    Chapter  Google Scholar 

  50. Pandey, O., Prabhakaran, M., Sahai, A.: Obfuscation-based non-black-box simulation and four message concurrent zero knowledge for NP. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 638–667. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_25

    Chapter  Google Scholar 

  51. Sahai, A., Waters, B.: How to use indistinguishability obfuscation: deniable encryption, and more. In: Shmoys, D.B. (ed.) 46th ACM STOC, pp. 475–484. ACM Press, May/June 2014

    Google Scholar 

  52. Waters, B.: A punctured programming approach to adaptively secure functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 678–697. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_33

    Chapter  Google Scholar 

  53. Wichs, D., Zirdelis, G.: Obfuscating compute-and-compare programs under LWE. In: Umans, C. (ed.) 58th FOCS, pp. 600–611. IEEE Computer Society Press, October 2017

    Google Scholar 

  54. Zhandry, M.: The magic of ELFs. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 479–508. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_18

    Chapter  Google Scholar 

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Acknowledgments

Farshim was supported by the European Research Council under the European Community’s Seventh Framework Programme (FP7/ 2007–2013 Grant Agreement no. 339563 - CryptoCloud). Fuchsbauer is supported by the Vienna Science and Technology Fund (WWTF) through project VRG18-002; work done while at Inria and supported by the French ANR Project ANR-16-CE39-0002 EfTrEC. Passelègue was supported in part from a DARPA/ARL SAFEWARE award, NSF Frontier Award 1413955, NSF grants 1619348, 1228984, 1136174, and 1065276, BSF grant 2012378, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant.

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Authors and Affiliations

  1. University of York, York, UK

    Pooya Farshim

  2. TU Wien, Vienna, Austria

    Georg Fuchsbauer

  3. Inria and ENS Lyon, Lyon, France

    Alain Passelègue

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  1. Pooya Farshim
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  2. Georg Fuchsbauer
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  1. Inria Paris, Paris, France

    Karthikeyan Bhargavan

  2. University of Klagenfurt, Klagenfurt, Austria

    Elisabeth Oswald

  3. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Manoj Prabhakaran

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Farshim, P., Fuchsbauer, G., Passelègue, A. (2020). Simpler Constructions of Asymmetric Primitives from Obfuscation. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds) Progress in Cryptology – INDOCRYPT 2020. INDOCRYPT 2020. Lecture Notes in Computer Science(), vol 12578. Springer, Cham. https://doi.org/10.1007/978-3-030-65277-7_32

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