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A Note on the (Im)possibility of Using Obfuscators to Transform Private-Key Encryption into Public-Key Encryption

  • Satoshi Hada
  • Kouichi Sakurai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4752)

Abstract

Transforming private-key encryption schemes into public-key encryption schemes is an interesting application of program obfuscation. The idea is that, given a private-key encryption scheme, an obfuscation of an encryption program with a private key embedded is used as a public key and the private key is used for decryption as it is. The security of the resulting public-key encryption scheme would be ensured because obfuscation is unintelligible and the public key is expected to leak no information on the private key. This paper investigates the possibility of general-purpose obfuscators for such a transformation, i.e., obfuscators that can transform an arbitrary private-key encryption scheme into a secure public-key encryption scheme. Barak et al. have shown a negative result, which says that there is a deterministic private-key encryption scheme that is unobfuscatable in the sense that, given any encryption program with a private key embedded, one can efficiently compute the private key. However, it is an open problem whether their result extends to probabilistic encryption schemes, where we should consider a relaxed notion of obfuscators, i.e., sampling obfuscators. Programs obfuscated by sampling obfuscators do not necessarily compute the same function as the original program, but produce the same distribution as the original program. In this paper, we show that there is a probabilistic private-key encryption scheme that can not be transformed into a secure public-key encryption scheme by sampling obfuscators which have a special property regarding input-output dependency of encryption programs. Our intention is not to claim that the required special property is reasonable. Rather, we claim that general-purpose obfuscators for the transformation, if they exist, must be a sampling obfuscator which does NOT have the special property.

Keywords

Encryption Scheme Random Input Pseudorandom Function Oracle Access Random Coin 
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.

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References

  1. 1.
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (Im)possibility of Obfuscating Programs ECCC, Report No. 57, 2001. (In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001))Google Scholar
  2. 2.
    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
  3. 3.
    Canetti, R., Micciancio, D., Reingold, O.: Perfectly One-way Probabilistic Hash Functions. In: Proceedings of 30st STOC (1998)Google Scholar
  4. 4.
    Davies, D.W.: Some Regular Properties of the DES. In: McCurley, K.S., Ziegler, C.D. (eds.) CRYPTO 1982. LNCS, vol. 1440, Springer, Heidelberg (1982)Google Scholar
  5. 5.
    Diffie, W., Hellman, M.: New Directions in Cryptography. IEEE Trans. Inform. Theory 22(6), 644–654 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Dodis, Y., Smith, A.: Correcting Errors without Leaking Partial Information. In: Proceedings of 37th STOC (2005)Google Scholar
  7. 7.
    Goldreich, O.: Foundations of Cryptography: Volume II Basic Applications. Cambridge University Press, Cambridge (2004)Google Scholar
  8. 8.
    Goldreich, O., Goldwasser, S., Micali, S.: How to Construct Random Functions. Journal of the ACM 33(4), 792–807 (1986)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Goldreich, O., Oren, Y.: Definitions and Properties of Zero-Knowledge Proof Systems. Journal of Cryptology 7(1), 1–32 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Goldwasser, S., Kalai, Y.T.: On the Impossibility of Obfuscation with Auxiliary Input. In: Proceedings of FOCS 2005, pp. 553–562 (2005)Google Scholar
  11. 11.
    Goldwasser, S., Micali, S.: Probabilistic Encryption. J. Comput. System Sci. 28, 270–299 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Goldwasser, S., Rothblum, G.N.: On Best-Possible Obfuscation. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, Springer, Heidelberg (2007)Google Scholar
  13. 13.
    Hada, S.: Zero-Knowledge and Code Obfusacation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 443–457. Springer, Heidelberg (2000), http://www.springer.com/east/home/generic/search/results?SGWID=5-40109-22-2128743-0 CrossRefGoogle Scholar
  14. 14.
    Hofheinz, D., Malone-Lee, J., Stam, M.: Obfuscation for Cryptographic Purposes. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, Springer, Heidelberg (2007)Google Scholar
  15. 15.
    Hohenberger, S., Rothblum, G.N., Shelat, A., Vaikuntanathan, V.: Securely Obfuscating Re-Encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, Springer, Heidelberg (2007)Google Scholar
  16. 16.
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proceedings of 21st STOC (1989)Google Scholar
  17. 17.
    Lynn, B., Prabhakaran, M., Sahai, A.: Positive Results and Techniques for Obfuscation. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, Springer, Heidelberg (2004)Google Scholar
  18. 18.
    Wee, H.: On Obfuscating Point Functions. In: Proceedings of STOC 2005, pp. 523–532 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Satoshi Hada
    • 1
  • Kouichi Sakurai
    • 2
  1. 1.Tokyo Research Laboratory, IBM Research, 1623-14, Shimotsuruma, Yamato, Kanagawa 242-8502Japan
  2. 2.Dept. of Computer Science and Communication Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, Fukuoka 819-0395Japan

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