Threshold Cryptography Based on Asmuth-Bloom Secret Sharing

  • Kamer Kaya
  • Ali Aydın Selçuk
  • Zahir Tezcan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4263)


In this paper, we investigate how threshold cryptography can be conducted with the Asmuth-Bloom secret sharing scheme and present two novel function sharing schemes, one for the RSA signature and the other for the ElGamal decryption functions, based on the Asmuth-Bloom scheme. To the best of our knowledge, these are the first threshold cryptosystems realized using the Asmuth-Bloom secret sharing. The proposed schemes compare favorably to the earlier function sharing schemes in performance as well as in certain theoretical aspects.


Secret Sharing Sharing Scheme Secret Sharing Scheme Chinese Remainder Theorem Function Sharing 
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.
    Asmuth, C., Bloom, J.: A modular approach to key safeguarding. IEEE Trans. Information Theory 29(2), 208–210 (1983)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Blakley, G.: Safeguarding cryptographic keys. In: Proc. of AFIPS National Computer Conference (1979)Google Scholar
  3. 3.
    Desmedt, Y.: Some recent research aspects of threshold cryptography. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 158–173. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)Google Scholar
  5. 5.
    Desmedt, Y., Frankel, Y.: Homomorphic zero-knowledge threshold schemes over any finite abelian group. SIAM Journal on Discrete Mathematics 7(4), 667–679 (1994)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Robust threshold dss signatures. Inf. Comput. 164(1), 54–84 (2001)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    De Santis, A., Desmedt, Y., Frankel, Y., Yung, M.: How to share a function securely? In: Proc. of STOC 1994, pp. 522–533 (1994)Google Scholar
  8. 8.
    Shamir, A.: How to share a secret. Comm. ACM 22(11), 612–613 (1979)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kamer Kaya
    • 1
  • Ali Aydın Selçuk
    • 1
  • Zahir Tezcan
    • 1
  1. 1.Department of Computer EngineeringBilkent UniversityAnkaraTurkey

Personalised recommendations