A Coin-Free Oracle-Based Augmented Black Box Framework

  • Kyosuke YamashitaEmail author
  • Mehdi Tibouchi
  • Masayuki Abe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11821)


After the work of Impagliazzo and Rudich (STOC, 1989), the black box framework has become one of the main research domain of cryptography. However black box techniques say nothing about non-black box techniques such as making use of zero-knowledge proofs. Brakerski et al. introduced a new black box framework named augmented black box framework, in which they gave a zero-knowledge proof oracle in addition to a base primitive oracle (TCC, 2011). They showed a construction of a non-interactive zero knowledge proof system based on a witness indistinguishable proof system oracle. They presented augmented black box construction of chosen ciphertext secure public key encryption scheme based on chosen plaintext secure public key encryption scheme and augmented black box separation between one-way function and key agreement.

In this paper we simplify the work of Brakerski et al. by introducing a proof system oracle without witness indistinguishability, named coin-free proof system oracle, that aims to give the same construction and separation results of previous work. As a result, the augmented black box framework becomes easier to handle. Since our oracle is not witness indistinguishable, our result encompasses the result of previous work.


Black box construction Zero-knowledge proof NIZK Witness indistinguishability 


  1. 1.
    Boneh, D., Papakonstantinou, P., Rackoff, C., Vahlis, Y., Waters, B.: On the impossibility of basing identity based encryption on trapdoor permutations. In: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, pp. 283–292. IEEE Computer Society, Washington, DC, USA (2008).
  2. 2.
    Brakerski, Z., Katz, J., Segev, G., Yerukhimovich, A.: Limits on the power of zero-knowledge proofs in cryptographic constructions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 559–578. Springer, Heidelberg (2011). Scholar
  3. 3.
    Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22, 644–654 (1976). Scholar
  4. 4.
    Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: Proceedings of the Twenty-second Annual ACM Symposium on Theory of Computing, STOC 1990. pp. 416–426. ACM, New York (1990).
  5. 5.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems. In: Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing, STOC 1985, pp. 291–304. ACM, New York (1985).
  6. 6.
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proceedings of the Twenty-first Annual ACM Symposium on Theory of Computing, STOC 1989, pp. 44–61. ACM, New York (1989).
  7. 7.
    Karp, R.M.: Reducibility among Combinatorial Problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. The IBM Research Symposia Series, pp. 85–103. Springer, Boston (1972). Scholar
  8. 8.
    Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing, STOC 1990. pp. 427–437. ACM, New York (1990).
  9. 9.
    Reingold, O., Trevisan, L., Vadhan, S.: Notions of reducibility between cryptographic primitives. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 1–20. Springer, Heidelberg (2004). Scholar
  10. 10.
    Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: Proceedings of the 40th Annual Symposium on Foundations of Computer Science. FOCS 1999, p. 543. IEEE Computer Society, Washington, DC (1999)Google Scholar
  11. 11.
    Yamashita, K., Tibouchi, M., Abe, M.: A coin-free oracle-based augmented black box framework. Cryptology ePrint Archive, Report 2019/859 (2019).
  12. 12.
    Yao, A.C.: Theory and application of trapdoor functions. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, SFCS 1982, pp. 80–91. IEEE Computer Society, Washington, DC (1982).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kyosuke Yamashita
    • 1
    Email author
  • Mehdi Tibouchi
    • 1
    • 2
  • Masayuki Abe
    • 1
    • 2
  1. 1.Graduate School of InformaticsKyoto UniversityKyotoJapan
  2. 2.Secure Platform Laboratories, NTT CorporationTokyoJapan

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