Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles

  • Mihir Bellare
  • Marc Fischlin
  • Adam O’Neill
  • Thomas Ristenpart
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5157)


We strengthen the foundations of deterministic public-key encryption via definitional equivalences and standard-model constructs based on general assumptions. Specifically we consider seven notions of privacy for deterministic encryption, including six forms of semantic security and an indistinguishability notion, and show them all equivalent. We then present a deterministic scheme for the secure encryption of uniformly and independently distributed messages based solely on the existence of trapdoor one-way permutations. We show a generalization of the construction that allows secure deterministic encryption of independent high-entropy messages. Finally we show relations between deterministic and standard (randomized) encryption.


Encryption Scheme Random Oracle Message Space Deterministic Scheme Semantic Security 
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.


  1. 1.
    Bellare, M.: The Goldreich-Levin Theorem (manuscript),
  2. 2.
    Bellare, M., Boldyreva, A., Micali, S.: Public-key encryption in a multi-user setting: Security proofs and improvements. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 259–274. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Bellare, M., Boldyreva, A., O’Neill, A.: Deterministic and efficiently searchable encryption. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 535–552. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Bellare, M., Fischlin, M., O’Neill, A., Ristenpart, T.: Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles. Full version of this paper. IACR ePrint archive (2008)
  5. 5.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Conference on Computer and Communications Security – CCS 1993, pp. 62–73. ACM, New York (1993)CrossRefGoogle Scholar
  6. 6.
    Bellare, M., Rogaway, P.: Robust computational secret sharing and a unified account of classical secret-sharing goals. In: Conference on Computer and Communications Security – CCS 2007, pp. 172–184. ACM, New York (2007)Google Scholar
  7. 7.
    Bellare, M., Rogaway, P.: The security of triple encryption and a framework for code-based game-playing proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Bellare, M., Sahai, A.: Non-malleable encryption: Equivalence between two notions, and an indistinguishability-based characterization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 519–536. Springer, Heidelberg (1999)Google Scholar
  9. 9.
    Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudo-random number generator. SIAM Journal on Computing 15, 364–383 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Blum, M., Goldwasser, S.: An efficient probabilistic public-key encryption scheme which hides all partial information. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 289–302. Springer, Heidelberg (1984)CrossRefGoogle Scholar
  11. 11.
    Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudorandom bits. SIAM Journal on Computing 13, 850–864 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Boldyreva, A., Fehr, S., O’Neill, A.: On notions of security for deterministic encryption, and efficient constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 335–359. Springer, Heidelberg (2008)Google Scholar
  13. 13.
    Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public key encryption with keyword search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 506–522. Springer, Heidelberg (2004)Google Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    Canetti, R., Micciancio, D., Reingold, O.: Perfectly one-way probabilistic hash functions (Preliminary version). In: Symposium on the Theory of Computation – STOC 1998, pp. 131–141 (1998)Google Scholar
  16. 16.
    Damgaard, I., Hofheinz, D., Kiltz, E., Thorbek, R.: Public-key encryption with non-interactive opening. In: Malkin, T. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 239–255. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Desrosiers, S.: Entropic security in quantum cryptography. arXiv e-Print quant-ph/0703046 (2007),
  18. 18.
    Desrosiers, S., Dupuis, F.: Quantum entropic security and approximate quantum encryption. arXiv e-Print quant-ph/0707.0691 (2007),
  19. 19.
    Dodis, Y., Smith, A.: Entropic security and the encryption of high entropy messages. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 556–577. Springer, Heidelberg (2005)Google Scholar
  20. 20.
    El Gamal, T.: A public-key cryptosystem and a signature scheme based on discrete logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  21. 21.
    Goldreich, O.: A uniform complexity treatment of encryption and zero-knowledge. Journal of Cryptology 6, 21–53 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Goldreich, O., Levin, L.: A hard-core predicate for all one-way functions. In: Symposium on the Theory of Computation – STOC 1989, pp. 25–32. ACM, New York (1989)Google Scholar
  23. 23.
    Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and Systems Sciences 28(2), 412–426 (1984)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Micali, S., Rackoff, C., Sloan, R.: The notion of security for probabilistic cryptosystems. SIAM Journal on Computing 17(2), 412–426 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Symposium on the Theory of Computing – STOC 2008, pp. 187–196. ACM, New York (2008)Google Scholar
  26. 26.
    Russell, A., Wang, H.: How to fool an unbounded adversary with a short key. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 133–148. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  27. 27.
    Song, D., Wagner, D., Perrig, A.: Practical techniques for searches on encrypted data. In: Symposium on Security and Privacy, pp. 44–55. IEEE, Los Alamitos (2000)Google Scholar
  28. 28.
    Yao, A.: Theory and applications of trapdoor functions. In: Symposium on Foundations of Computer Science – FOCS 1982, pp. 80–91. IEEE, Los Alamitos (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mihir Bellare
    • 1
  • Marc Fischlin
    • 2
  • Adam O’Neill
    • 3
  • Thomas Ristenpart
    • 1
  1. 1.Dept. of Computer Science & EngineeringUniversity of California at San DiegoLa JollaUSA
  2. 2.Dept. of Computer ScienceDarmstadt University of TechnologyDarmstadtGermany
  3. 3.College of ComputingGeorgia Institute of TechnologyAtlantaUSA

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