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Constrained PRFs for Unbounded Inputs

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Topics in Cryptology - CT-RSA 2016 (CT-RSA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9610))

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Abstract

A constrained pseudorandom function \(F:\mathcal{K} \times \mathcal{X} \rightarrow \mathcal{Y}\) for a family \(\mathcal{T}\subseteq 2^\mathcal{X}\) of subsets of \(\mathcal X\) is a function where for any key \(k \in \mathcal{K}\) and set \(S\in \mathcal{T}\) one can efficiently compute a constrained key \(k_S\) which allows to evaluate \(F(k,\cdot )\) on all inputs \(x\in S\), while even given this key, the outputs on all inputs \(x \notin S\) look random. At Asiacrypt’13 Boneh and Waters gave a construction which supports the most general set family so far. Its keys \(k_C\) are defined for sets decided by boolean circuits C and enable evaluation of the PRF on any \(x \in \mathcal{X}\) where \(C(x)=1\). In their construction the PRF input length and the size of the circuits C for which constrained keys can be computed must be fixed beforehand during key generation.

We construct a constrained PRF that has an unbounded input length and whose constrained keys can be defined for any set recognized by a Turing machine. The only a priori bound we make is on the description size of the machines. We prove our construction secure assuming public-coin differing-input obfuscation.

As applications of our constrained PRF we build a broadcast encryption scheme where the number of potential receivers need not be fixed at setup (in particular, the length of the keys is independent of the number of parties) and the first identity-based non-interactive key exchange protocol with no bound on the number of parties that can agree on a shared key.

Supported by the European Research Council, ERC Starting Grant (259668-PSPC).

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Notes

  1. 1.

    As outlined in the introduction, we assume that every set in \(\mathcal{S}\) can be specified by a short and efficiently computable predicate.

  2. 2.

    W.l.o.g. we assume from now on that \(\mathcal{K}\cap \mathcal{K}_{\mathcal{C}}=\emptyset \), as this can always be achieved by simply prepending a ‘0’ to elements from \(\mathcal{K}\) and a ‘1’ to elements from \(\mathcal{K}_{\mathcal{C}}\).

References

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

    Google Scholar 

  2. Ananth, P., Boneh, D., Garg, S., Sahai, A., Zhandry, M.: Differing-inputs obfuscation and applications. In: Cryptology ePrint Archive, Report 2013/689 (2013). http://eprint.iacr.org/2013/689

  3. Barak, B., Goldreich, O.: Universal arguments and their applications. SIAM J. Comput. 38(5), 1661–1694 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6:1–6:48 (2012)

    Article  MathSciNet  Google Scholar 

  5. Bellare, M., Stepanovs, I., Tessaro, S.: Poly-many hardcore bits for any one-way function and a framework for differing-inputs obfuscation. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 102–121. Springer, Heidelberg (2014)

    Google Scholar 

  6. Bitansky, N., Canetti, R., Chiesa, A., Goldwasser, S., Lin, H., Rubinstein, A., Tromer, E.: The hunting of the SNARK. IACR Cryptology ePrint Archive, 2014:580 (2014)

    Google Scholar 

  7. Bitansky, N., Canetti, R., Chiesa, A., Tromer, E.: Recursive composition and bootstrapping for SNARKS and proof-carrying data. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 111–120. ACM Press, June 2013

    Google Scholar 

  8. Boneh, D., Gentry, C., Waters, B.: Collusion resistant broadcast encryption with short ciphertexts and private keys. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 258–275. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Boneh, D., Hamburg, M.: Generalized identity based and broadcast encryption schemes. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 455–470. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Boneh, D., Waters, B.: Constrained pseudorandom functions and their applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 280–300. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Boneh, D., Waters, B., Zhandry, M.: Low overhead broadcast encryption from multilinear maps. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 206–223. Springer, Heidelberg (2014)

    Google Scholar 

  12. Boneh, D., Zhandry, M.: Multiparty key exchange, efficient traitor tracing, and more from indistinguishability obfuscation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 480–499. Springer, Heidelberg (2014)

    Google Scholar 

  13. Boyle, E., Chung, K.-M., Pass, R.: On extractability obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 52–73. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476–493. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  16. Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  17. Freire, E.S.V., Hofheinz, D., Paterson, K.G., Striecks, C.: Programmable hash functions in the multilinear setting. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 513–530. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  18. Fuchsbauer, G., Konstantinov, M., Pietrzak, K., Rao, V.: Adaptive security of constrained PRFs. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 82–101. Springer, Heidelberg (2014)

    Google Scholar 

  19. Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  20. 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 

  21. 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, Part I. LNCS, vol. 8616, pp. 518–535. Springer, Heidelberg (2014)

    Google Scholar 

  22. Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd ACM STOC, pp. 99–108. ACM Press, June 2011

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. Hofheinz, D., Kamath, A., Koppula, V., Waters, B.: Adaptively secure constrained pseudorandom functions. In: Cryptology ePrint Archive, Report 2014/720 (2014). http://eprint.iacr.org/

  25. Hohenberger, S., Koppula, V., Waters, B.: Adaptively secure puncturable pseudorandom functions in the standard model. In: Cryptology ePrint Archive, Report 2014/521 (2014). http://eprint.iacr.org/2014/521

  26. 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)

    Chapter  Google Scholar 

  27. Ishai, Y., Pandey, O., Sahai, A.: Public-coin differing-inputs obfuscation and its applications. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 668–697. Springer, Heidelberg (2015)

    Google Scholar 

  28. 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 

  29. Koppula, V., Lewko, A.B., Waters, B.: Indistinguishability obfuscation for turing machines with unbounded memory. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, pp. 419–428. ACM Press, June 2015

    Google Scholar 

  30. Langlois, A., Stehlé, D., Steinfeld, R.: GGHLite: more efficient multilinear maps from ideal lattices. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 239–256. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  31. Pass, R., Seth, K., Telang, S.: Indistinguishability obfuscation from semantically-secure multilinear encodings. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 500–517. Springer, Heidelberg (2014)

    Google Scholar 

  32. Phan, D.H., Pointcheval, D., Strefler, M.: Security notions for broadcast encryption. In: Lopez, J., Tsudik, G. (eds.) ACNS 2011. LNCS, vol. 6715, pp. 377–394. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  33. 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 

  34. Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: SCIS 2000, Okinawa, Japan, January 2000

    Google Scholar 

  35. Yao, D., Fazio, N., Dodis, Y., Lysyanskaya, A.: ID-based encryption for complex hierarchies with applications to forward security and broadcast encryption. In: Atluri, V., Pfitzmann, B., McDaniel, P. (eds.) ACM CCS 2004, pp. 354–363. ACM Press, October 2004

    Google Scholar 

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Authors and Affiliations

  1. Institute of Science and Technology Austria, Klosterneuburg, Austria

    Hamza Abusalah, Georg Fuchsbauer & Krzysztof Pietrzak

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  1. Hamza Abusalah
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  2. Georg Fuchsbauer
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  3. Krzysztof Pietrzak
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Correspondence to Hamza Abusalah .

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  1. NEC Cloud Systems Research Laboratories, Kawasaki, Japan

    Kazue Sako

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Abusalah, H., Fuchsbauer, G., Pietrzak, K. (2016). Constrained PRFs for Unbounded Inputs. In: Sako, K. (eds) Topics in Cryptology - CT-RSA 2016. CT-RSA 2016. Lecture Notes in Computer Science(), vol 9610. Springer, Cham. https://doi.org/10.1007/978-3-319-29485-8_24

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  • DOI: https://doi.org/10.1007/978-3-319-29485-8_24

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