Skip to main content
Springer Nature Link
Log in

Robust Threshold Schemes Based on the Chinese Remainder Theorem

  • Conference paper
Progress in Cryptology – AFRICACRYPT 2008 (AFRICACRYPT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5023))

Included in the following conference series:

  • 2370 Accesses

Abstract

Recently, Chinese Remainder Theorem (CRT) based function sharing schemes are proposed in the literature. In this paper, we investigate how a CRT-based threshold scheme can be enhanced with the robustness property. To the best of our knowledge, these are the first robust threshold cryptosystems based on a CRT-based secret sharing.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Asmuth, C., Bloom, J.: A modular approach to key safeguarding. IEEE Trans. Information Theory 29(2), 208–210 (1983)

    Article  MathSciNet  Google Scholar 

  2. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proc. of First ACM Conference on Computer and Communications Security, pp. 62–73 (1993)

    Google Scholar 

  3. Blakley, G.: Safeguarding cryptographic keys. In: Proc. of AFIPS National Computer Conference (1979)

    Google Scholar 

  4. Boudot, F., Traoré, J.: Efficient publicly verifiable secret sharing schemes with fast or delayed recovery. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 87–102. Springer, Heidelberg (1999)

    Google Scholar 

  5. Chaum, D., Evertse, J.H., Van De Graaf, J.: An improved protocol for demonstrating possesion of discrete logarithm and some generalizations. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 127–141. Springer, Heidelberg (1988)

    Google Scholar 

  6. Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)

    Google Scholar 

  7. Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. ACM Trans. Inf. Syst. Secur. 3(3), 161–185 (2000)

    Article  Google Scholar 

  8. Desmedt, Y.: Some recent research aspects of threshold cryptography. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 158–173. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  9. Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)

    Google Scholar 

  10. Desmedt, Y., Frankel, Y.: Shared generation of authenticators and signatures. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 457–469. Springer, Heidelberg (1992)

    Google Scholar 

  11. Desmedt, Y., Frankel, Y.: Homomorphic zero-knowledge threshold schemes over any finite abelian group. SIAM Journal on Discrete Mathematics 7(4), 667–679 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ding, C., Pei, D., Salomaa, A.: Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography. World Scientific, Singapore (1996)

    MATH  Google Scholar 

  13. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Information Theory 31(4), 469–472 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kaya, K., Selçuk, A.A.: Threshold cryptography based on Asmuth–Bloom secret sharing. Information Sciences 177(19), 4148–4160 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lysyanskaya, A., Peikert, C.: Adaptive security in the threshold setting: From cryptosystems to signature schemes. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 331–350. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  16. Paillier, P.: Public key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)

    Google Scholar 

  17. Poupard, G., Stern, J.: Security analysis of a practical on the fly authentication and signature generation. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 422–436. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  18. Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Comm. ACM 21(2), 120–126 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  19. 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 

  20. Shamir, A.: How to share a secret? Comm. ACM 22(11), 612–613 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  21. Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  22. Wei, W., Trung, T., Magliveras, S., Hoffman, F.: Cryptographic primitives based on groups of hidden order. Tatra Mountains Mathematical Publications 29, 147–155 (2004)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Bilkent University, Ankara, 06800, Turkey

    Kamer Kaya & Ali Aydın Selçuk

Authors
  1. Kamer Kaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Aydın Selçuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Serge Vaudenay

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kaya, K., Selçuk, A.A. (2008). Robust Threshold Schemes Based on the Chinese Remainder Theorem. In: Vaudenay, S. (eds) Progress in Cryptology – AFRICACRYPT 2008. AFRICACRYPT 2008. Lecture Notes in Computer Science, vol 5023. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68164-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-68164-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68159-5

  • Online ISBN: 978-3-540-68164-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics