A Practical Solution to the (t, n) Threshold Untraceable Signature with (k, l) Verification Scheme

  • Jen-Ho Yang
  • Chin-Chen Chang
  • Chih-Hung Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4159)


The (t, n) threshold signature scheme can delegate the signing capability to all n participants in a group, and at least t participants can cooperatively sign a message on behalf of the group, where tv. For the group communication in the real society, the verification site also needs to be restricted in its associated access privileges. Therefore, this paper proposes a practical solution to the (t, n) threshold untraceable signature with (k, l) verification scheme, which requires that k out of l verifiers or more can verify the threshold signature on behalf of the verification group. Compared with the previous works, such as Wang et al.’s scheme and Chang et al.’s scheme, our proposed scheme is more practical and expansible. Our scheme allows each group to be both a signing party and a verification party, and the shadows of all group members are no need to be redistributed after the initialization has been finished. In addition, the share distribution center (SDC) is not required in our scheme.


Threshold Signature Signature Scheme Group Manager Verification Scheme Digital Signature Scheme 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sharmir, A.: How to Share a Secret. Communications of the ACM 22, 612–613 (1979)CrossRefGoogle Scholar
  2. 2.
    Fiat, A., Shamir, A.: How to prove yourself. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–199. Springer, Heidelberg (1987)Google Scholar
  3. 3.
    Wnag, C.T., Chang, C.C., Lin, C.H.: Generalization of Threshold Signature and Authenticated Encryption for Group Communications. IEICE Transactions on Fundamental of Electronics Communications and Computing, E83-A 6, 1228–1237 (2000)Google Scholar
  4. 4.
    Ohta, K., Okamoto, T.: A Modification of the Fiat-Shamir Scheme. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 232–243. Springer, Heidelberg (1990)Google Scholar
  5. 5.
    Harn, L.: Group-Oriented (t, n) Threshold Signature Scheme and Digital Multisignature. IEE Proceedings on Computer Digital Technology 141(5), 307–313 (1994)MATHCrossRefGoogle Scholar
  6. 6.
    Lee, N.Y., Hwang, T., Li, C.M.: (t, n) Threshold Untraceable Signatures. Journal of Information Science and Engineering 16, 835–846 (2000)MathSciNetGoogle Scholar
  7. 7.
    Rivest, R.L., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of the ACM 21(2), 120–126 (1978)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Elgamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information IT-31, 469–472 (1985)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Chang, T.Y., Yang, C.C., Hwang, M.S.: Threshold Untraceable Signature for Group Communications. IEE Proceedings on Communications 151(2), 179–184 (2004)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Desmedt, Y., Frankel, Y.: Shared Generation of Authenticators. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 457–469. Springer, Heidelberg (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jen-Ho Yang
    • 1
  • Chin-Chen Chang
    • 1
    • 2
  • Chih-Hung Wang
    • 3
  1. 1.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayiTaiwan
  2. 2.Department of Information Engineering and Computer ScienceFeng Chia UniversityTaichungTaiwan
  3. 3.Department of Computer Science and Information EngineeringNational Chiayi UniversityChiayiTaiwan

Personalised recommendations