Non-malleable Statistically Hiding Commitment from Any One-Way Function

  • Zongyang Zhang
  • Zhenfu Cao
  • Ning Ding
  • Rong Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5912)


We give a construction of non-malleable statistically hiding commitments based on the existence of one-way functions. Our construction employs statistically hiding commitment schemes recently proposed by Haitner and Reingold [1], and special-sound WI proofs. Our proof of security relies on the message scheduling technique introduced by Dolev, Dwork and Naor [2], and requires only the use of black-box techniques.


  1. 1.
    Haitner, I., Reingold, O.: Statistically-hiding commitment from any one-way function. In: Johnson, D.S., Feige, U. (eds.) STOC, pp. 1–10. ACM, New York (2007)Google Scholar
  2. 2.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30, 391–437 (2000)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fischlin, M., Fischlin, R.: Efficient non-malleable commitment schemes. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 413–431. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Di Crescenzo, G., Ishai, Y., Ostrovsky, R.: Non-interactive and non-malleable commitment. In: STOC, pp. 141–150 (1998)Google Scholar
  5. 5.
    Boyar, J., Kurtz, S.A., Krentel, M.W.: A discrete logarithm implementation of perfect zero-knowledge blobs. J. Cryptology 2, 63–76 (1990)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Brassard, G., Chaum, D., Crépeau, C.: Minimum disclosure proofs of knowledge. J. Comput. Syst. Sci. 37(2), 156–189 (1988)MATHCrossRefGoogle Scholar
  7. 7.
    Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17, 281–308 (1988)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for NP. J. Cryptology 9, 167–190 (1996)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Damgård, I., Pedersen, T.P., Pfitzmann, B.: On the existence of statistically hiding bit commitment schemes and fail-stop signatures. J. Cryptology 10, 163–194 (1997)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Naor, M., Ostrovsky, R., Venkatesan, R., Yung, M.: Perfect zero-knowledge arguments for NP using any one-way permutation. J. Cryptology 11, 87–108 (1998)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Haitner, I., Horvitz, O., Katz, J., Koo, C.Y., Morselli, R., Shaltiel, R.: Reducing complexity assumptions for statistically-hiding commitment. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 58–77. Springer, Heidelberg (2005)Google Scholar
  12. 12.
    Nguyen, M.H., Ong, S.J., Vadhan, S.P.: Statistical zero-knowledge arguments for NP from any one-way function. In: FOCS, pp. 3–14. IEEE Computer Society, Los Alamitos (2006)Google Scholar
  13. 13.
    Di Crescenzo, G., Katz, J., Ostrovsky, R., Smith, A.: Efficient and non-interactive non-malleable commitment. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 40–59. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Pass, R., Rosen, A.: New and improved constructions of nonmalleable cryptographic protocols. SIAM J. Comput. 38, 702–752 (2008)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Lin, H., Pass, R., Venkitasubramaniam, M.: Concurrent non-malleable commitments from any one-way function. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 571–588. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: STOC, pp. 416–426. ACM, New York (1990)Google Scholar
  17. 17.
    Blum, M.: How to prove a theorem so no one else can claim it. In: Proceedings of the International Congress of Mathematicians, pp. 1444–1451 (1986)Google Scholar
  18. 18.
    Naor, M.: Bit commitment using pseudorandomness. J. Cryptology 4, 151–158 (1991)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Goldreich, O.: The Foundations of Cryptography, vol. 1. Cambridge University Press, UK (2001)Google Scholar
  20. 20.
    Feige, U.: Alternative Models for Zero Knowledge Interactive Proofs. PhD thesis, The Weizmann Institute of Science, Rehovot, Israel (1990)Google Scholar
  21. 21.
    Feige, U., Lapidot, D., Shamir, A.: Multiple noninteractive zero knowledge proofs under general assumptions. SIAM J. Comput. 29, 1–28 (1999)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    MacKenzie, P., Yang, K.: On simulation-sound trapdoor commitments. Cryptology ePrint Archive, Report 2003/252 (2003),

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Zongyang Zhang
    • 1
  • Zhenfu Cao
    • 1
  • Ning Ding
    • 1
  • Rong Ma
    • 1
  1. 1.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityP.R. China

Personalised recommendations