4-Round Resettably-Sound Zero Knowledge

  • Kai-Min Chung
  • Rafail Ostrovsky
  • Rafael Pass
  • Muthuramakrishnan Venkitasubramaniam
  • Ivan Visconti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8349)


While 4-round constructions of zero-knowledge arguments are known based on the existence of one-way functions, constuctions of resettably-sound zero-knowledge arguments require either stronger assumptions (the existence of a fully-homomorphic encryption scheme), or more communication rounds. We close this gap by demonstrating a 4- round resettably-sound zero-knowledge argument for NP based on the existence of one-way functions.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barak, B., Goldreich, O.: Universal arguments and their applications. In: Computational Complexity, pp. 162–171 (2002)Google Scholar
  2. 2.
    Barak, B., Goldreich, O., Goldwasser, S., Lindell, Y.: Resettably-sound zero-knowledge and its applications. In: FOCS 2002, pp. 116–125 (2001)Google Scholar
  3. 3.
    Bellare, M., Goldreich, O.: On defining proofs of knowledge. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 390–420. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  4. 4.
    Bellare, M., Jakobsson, M., Yung, M.: Round-optimal zero-knowledge arguments based on any one-way function. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 280–305. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Bitansky, N., Paneth, O.: From the impossibility of obfuscation to a new non-black-box simulation technique. In: FOCS (2012)Google Scholar
  6. 6.
    Bitansky, N., Paneth, O.: On the impossibility of approximate obfuscation and applications to resettable cryptography. In: STOC (2013)Google Scholar
  7. 7.
    Blum, M.: How to prove a theorem so no one else can claim it. In: Proc. of the International Congress of Mathematicians, pp. 1444–1451 (1986)Google Scholar
  8. 8.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. In: ITCS, pp. 309–325. ACM (2012)Google Scholar
  9. 9.
    Chung, K.M., Ostrovsky, R., Pass, R., Visconti, I.: Simultaneous resettability from one-way functions. In: 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, pp. 60–69. IEEE Computer Society (2013)Google Scholar
  10. 10.
    Chung, K.M., Pass, R., Seth, K.: Non-black-box simulation from one-way functions and applications to resettable security. In: STOC. ACM (2013)Google Scholar
  11. 11.
    Di Crescenzo, G., Persiano, G., Visconti, I.: Improved setup assumptions for 3-round resettable zero knowledge. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 530–544. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: STOC 1990, pp. 416–426 (1990)Google Scholar
  13. 13.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178. ACM (2009)Google Scholar
  14. 14.
    Goldreich, O.: Foundations of Cryptography — Basic Tools. Cambridge University Press (2001)Google Scholar
  15. 15.
    Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for NP. Journal of Cryptology 9(3), 167–190 (1996)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems. In: STOC 1985, pp. 291–304. ACM (1985), http://doi.acm.org/10.1145/22145.22178
  18. 18.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Goyal, V., Jain, A., Ostrovsky, R., Richelson, S., Visconti, I.: Constant-round concurrent zero knowledge in the bounded player model. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 21–40. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Lin, H., Pass, R.: Constant-round non-malleable commitments from any one-way function. In: STOC, pp. 705–714 (2011)Google Scholar
  21. 21.
    Merkle, R.C.: A digital signature based on a conventional encryption function. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 369–378. Springer, Heidelberg (1988)Google Scholar
  22. 22.
    Micali, S.: Computationally sound proofs. SIAM Journal on Computing 30(4), 1253–1298 (2000)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: STOC 1989, pp. 33–43 (1989)Google Scholar
  24. 24.
    Ostrovsky, R., Visconti, I.: Simultaneous resettability from collision resistance. Electronic Colloquium on Computational Complexity (ECCC) 19, 164 (2012)Google Scholar
  25. 25.
    Ostrovsky, R., Wigderson, A.: One-way fuctions are essential for non-trivial zero-knowledge. In: ISTCS, pp. 3–17 (1993)Google Scholar
  26. 26.
    Pass, R., Rosen, A.: New and improved constructions of non-malleable cryptographic protocols. In: STOC 2005, pp. 533–542 (2005)Google Scholar
  27. 27.
    Pass, R., Tseng, W.L.D., Wikström, D.: On the composition of public-coin zero-knowledge protocols. SIAM J. Comput. 40(6), 1529–1553 (2011)CrossRefMATHMathSciNetGoogle Scholar
  28. 28.
    Rompel, J.: One-way functions are necessary and sufficient for secure signatures (1990)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Kai-Min Chung
    • 1
  • Rafail Ostrovsky
    • 2
  • Rafael Pass
    • 3
  • Muthuramakrishnan Venkitasubramaniam
    • 4
  • Ivan Visconti
    • 5
  1. 1.Academia SinicaTaiwan
  2. 2.UCLALos AngelesUSA
  3. 3.Cornell UniversityIthacaUSA
  4. 4.University of RochesterRochesterUSA
  5. 5.University of SalernoItaly

Personalised recommendations