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Replacing a Random Oracle: Full Domain Hash from Indistinguishability Obfuscation

  • Susan Hohenberger
  • Amit Sahai
  • Brent Waters
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8441)

Abstract

Our main result gives a way to instantiate the random oracle with a concrete hash function in “full domain hash” applications. The term full domain hash was first proposed by Bellare and Rogaway [BR93, BR96] and referred to a signature scheme from any trapdoor permutation that was part of their seminal work introducing the random oracle heuristic. Over time the term full domain hash has (informally) encompassed a broader range of notable cryptographic schemes including the Boneh-Franklin [BF01] IBE scheme and Boneh-Lynn-Shacham (BLS) [BLS01] signatures. All of the above described schemes required a hash function that had to be modeled as a random oracle to prove security. Our work utilizes recent advances in indistinguishability obfuscation to construct specific hash functions for use in these schemes. We then prove security of the original cryptosystems when instantiated with our specific hash function.

Of particular interest, our work evades the impossibility results of Dodis, Oliveira, and Pietrzak [DOP05], who showed that there can be no black-box construction of hash functions that allow Full-Domain Hash Signatures to be based on trapdoor permutations, and its extension by Dodis, Haitner, and Tentes [DHT12] to the RSA Full-Domain Hash Signatures. This indicates our techniques applying indistinguishability obfuscation may be useful for circumventing other black-box impossibility proofs.

Keywords

Hash Function Signature Scheme Random Oracle Random Oracle Model Message Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [BB04a]
    Boneh, D., Boyen, X.: Secure identity based encryption without random oracles. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443–459. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. [BB04b]
    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)CrossRefGoogle Scholar
  3. [BBP04]
    Bellare, M., Boldyreva, A., Palacio, A.: An uninstantiable random-oracle-model scheme for a hybrid-encryption problem. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 171–188. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. [BF01]
    Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. [BGI+01]
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. [BGI+12]
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6 (2012)CrossRefMathSciNetGoogle Scholar
  7. [BGI14]
    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)CrossRefGoogle Scholar
  8. [BGLS03]
    Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. [BGW05]
    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)CrossRefGoogle Scholar
  10. [BHK13]
    Bellare, M., Hoang, V.T., Keelveedhi, S.: Instantiating Random Oracles via UCEs. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 398–415. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. [BLS01]
    Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. [BNN07]
    Bellare, M., Namprempre, C., Neven, G.: Unrestricted aggregate signatures. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 411–422. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. [Boy08]
    Boyen, X.: A tapestry of identity-based encryption: practical frameworks compared. IJACT 1(1), 3–21 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  14. [BR93]
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security, pp. 62–73 (1993)Google Scholar
  15. [BR96]
    Bellare, M., Rogaway, P.: The exact security of digital signatures - how to sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  16. [BW13]
    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)CrossRefGoogle Scholar
  17. [Can97]
    Canetti, R.: Towards realizing random oracles: Hash functions that hide all partial information. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 455–469. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  18. [CGH98]
    Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited (preliminary version). In: STOC, pp. 209–218 (1998)Google Scholar
  19. [CHK07]
    Canetti, R., Halevi, S., Katz, J.: A forward-secure public-key encryption scheme. J. Cryptology 20(3), 265–294 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  20. [Coc01]
    Cocks, C.: An identity based encryption scheme based on quadratic residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 360–363. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  21. [CS98]
    Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  22. [DHT12]
    Dodis, Y., Haitner, I., Tentes, A.: On the instantiability of hash-and-sign RSA signatures. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 112–132. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. [DOP05]
    Dodis, Y., Oliveira, R., Pietrzak, K.: On the generic insecurity of the full domain hash. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 449–466. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  24. [FHPS13]
    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)CrossRefGoogle Scholar
  25. [GGH+13]
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS (2013)Google Scholar
  26. [GGM84]
    Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions (extended abstract). In: FOCS, pp. 464–479 (1984)Google Scholar
  27. [GK03]
    Goldwasser, S., Kalai, Y.T.: On the (in)security of the Fiat-Shamir paradigm. In: FOCS, pp. 102–113 (2003)Google Scholar
  28. [HSW13]
    Hohenberger, S., Sahai, A., Waters, B.: Full domain hash from (leveled) multilinear maps and identity-based aggregate signatures. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 494–512. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  29. [HSW14]
    Hohenberger, S., Sahai, A., Waters, B.: Replacing a random oracle: Full domain hash from indistinguishability obfuscation. In: Eurocrypt (2014), Full version available at http://eprint.iacr.org/2013/509
  30. [KPTZ13]
    Kiayias, A., Papadopoulos, S., Triandopoulos, N., Zacharias, T.: Delegatable pseudorandom functions and applications. In: ACM Conference on Computer and Communications Security, pp. 669–684 (2013)Google Scholar
  31. [KS98]
    Kaliski, B., Staddon, J.: PKCS #1: RSA Cryptography Specifications Version 2.0 (1998)Google Scholar
  32. [RSA78]
    Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  33. [Sha83]
    Shamir, A.: On the generation of cryptographically strong pseudorandom sequences. ACM Trans. Comput. Syst. 1(1), 38–44 (1983)CrossRefMathSciNetGoogle Scholar
  34. [SW13]
    Sahai, A., Waters, B.: How to use indistinguishability obfuscation: Deniable encryption, and more. Cryptology ePrint Archive, Report 2013/454 (2013) (to appear in STOC, 2014), http://eprint.iacr.org/

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Susan Hohenberger
    • 1
  • Amit Sahai
    • 2
  • Brent Waters
    • 3
  1. 1.Johns Hopkins UniversityUSA
  2. 2.UCLAUSA
  3. 3.University of Texas at AustinUSA

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