Advertisement

Verifiable Random Functions from Identity-Based Key Encapsulation

  • Michel Abdalla
  • Dario Catalano
  • Dario Fiore
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5479)

Abstract

We propose a methodology to construct verifiable random functions from a class of identity based key encapsulation mechanisms (IB-KEM) that we call VRF suitable. Informally, an IB-KEM is VRF suitable if it provides what we call unique decryption (i.e. given a ciphertext C produced with respect to an identity \({\it{ID}}\), all the secret keys corresponding to identity \({\it{ID}}'\), decrypt to the same value, even if \({\it{ID}}\neq {\it{ID}}'\)) and it satisfies an additional property that we call pseudorandom decapsulation. In a nutshell, pseudorandom decapsulation means that if one decrypts a ciphertext C, produced with respect to an identity \({\it{ID}}\), using the decryption key corresponding to any other identity \({\it{ID}}'\) the resulting value looks random to a polynomially bounded observer. Interestingly, we show that most known IB-KEMs already achieve pseudorandom decapsulation. Our construction is of interest both from a theoretical and a practical perspective. Indeed, apart from establishing a connection between two seemingly unrelated primitives, our methodology is direct in the sense that, in contrast to most previous constructions, it avoids the inefficient Goldreich-Levin hardcore bit transformation.

Keywords

Random Function Random Oracle Security Parameter Identity Space Identity Base Encryption 
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. 1.
    Bentahar, K., Farshim, P., Malone-Lee, J., Smart, N.P.: Generic constructions of identity-based and certificateless KEMs. Journal of Cryptology 21(2), 178–199 (2008)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Boneh, D., Boyen, X.: Efficient selective-ID secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    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
  4. 4.
    Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Boneh, D., Gentry, C., Hamburg, M.: Space-efficient identity based encryptionwithout pairings. In: 48th FOCS, Providence, USA, pp. 647–657. IEEE Computer Society Press, Los Alamitos (2007)Google Scholar
  7. 7.
    Canetti, R., Halevi, S., Katz, J.: A forward-secure public-key encryption scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Chase, M., Lysyanskaya, A.: Simulatable vRFs with applications to multi-theorem NIZK. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 303–322. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Cheon, J.H.: Security analysis of the strong diffie-hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1–11. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Dodis, Y.: Efficient construction of (Distributed) verifiable random functions. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 1–17. Springer, Heidelberg (2002)Google Scholar
  12. 12.
    Dodis, Y., Puniya, P.: Verifiable random permutations. Cryptology ePrint Archive, Report 2006/078 (2006), http://eprint.iacr.org/
  13. 13.
    Dodis, Y., Yampolskiy, A.: A verifiable random function with short proofs and keys. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 416–431. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Gentry, C.: Practical identity-based encryption without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: 21st ACM STOC, Seattle, Washington, USA, May 15–17, pp. 25–32. ACM Press, New York (1989)Google Scholar
  16. 16.
    Goldwasser, S., Ostrovsky, R.: Invariant signatures and non-interactive zero-knowledge proofs are equivalent. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 228–245. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  17. 17.
    Jarecki, S., Shmatikov, V.: Handcuffing big brother: an abuse-resilient transaction escrow scheme. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 590–608. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Liskov, M.: Updatable zero-knowledge databases. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 174–198. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Luby, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM Journal on Computing 17(2) (1988)Google Scholar
  20. 20.
    Lysyanskaya, A.: Unique signatures and verifiable random functions from the DH-DDH separation. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 597–612. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  21. 21.
    Micali, S., Rabin, M.O., Vadhan, S.P.: Verifiable random functions. In: 40th FOCS, October 17–19, pp. 120–130. IEEE Computer Society Press, New York (1999)Google Scholar
  22. 22.
    Micali, S., Reyzin, L.: Soundness in the public-key model. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 542–565. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  23. 23.
    Micali, S., Rivest, R.L.: Micropayments revisited. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 149–163. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  24. 24.
    Naor, M., Reingold, O.: Number-theoretic constructions of efficient pseudo-random functions. In: 38th FOCS, Miami Beach, Florida, October 19–22, pp. 458–467. IEEE Computer Society Press, Los Alamitos (1997)Google Scholar
  25. 25.
    Sakai, R., Kasahara, M.: Id based cryptosystems with pairing on elliptic curve. In: 2003 Symposium on Cryptography and Information Security – SCIS 2003, Hamamatsu, Japan (2003), http://eprint.iacr.org/2003/054
  26. 26.
    Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  27. 27.
    Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michel Abdalla
    • 1
  • Dario Catalano
    • 2
  • Dario Fiore
    • 2
  1. 1.CNRS–LIENS, Ecole Normale SupérieureParisFrance
  2. 2.Dipartimento di Matematica e InformaticaUniversità di CataniaItaly

Personalised recommendations