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.


Security Parameter Commitment Scheme Interactive Proof Auxiliary Input Common Reference String 
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.
    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)zbMATHCrossRefMathSciNetGoogle 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)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Brassard, G., Chaum, D., Crépeau, C.: Minimum disclosure proofs of knowledge. J. Comput. Syst. Sci. 37(2), 156–189 (1988)zbMATHCrossRefGoogle 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)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for NP. J. Cryptology 9, 167–190 (1996)zbMATHCrossRefMathSciNetGoogle 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)zbMATHCrossRefMathSciNetGoogle 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)zbMATHCrossRefMathSciNetGoogle 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)zbMATHCrossRefMathSciNetGoogle 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)zbMATHCrossRefMathSciNetGoogle 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

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