Wireless Personal Communications

, Volume 78, Issue 1, pp 271–282 | Cite as

Multipartite Secret Sharing Based on CRT

  • Ching-Fang Hsu
  • Lein Harn


Secure communication has become more and more important for system security. Since avoiding the use of encryption one by one can introduce less computation complexity, secret sharing scheme (SSS) has been used to design many security protocols. In SSSs, several authors have studied multipartite access structures, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. Access structures realized by threshold secret sharing are the simplest multipartite access structures, i.e., unipartite access structures. Since Asmuth–Bloom scheme based on Chinese remainder theorem (CRT) was presented for threshold secret sharing, recently, threshold cryptography based on Asmuth–Bloom secret sharing were firstly proposed by Kaya et al. In this paper, we extend Asmuth–Bloom and Kaya schemes to bipartite access structures and further investigate how SSSs realizing multipartite access structures can be conducted with the CRT. Actually, every access structure is multipartite and, hence, the results in this paper can be seen as a new construction of general SSS based on the CRT. Asmuth–Bloom and Kaya schemes become the special cases of our scheme.


Secret sharing schemes Multipartite access structures  Chinese remainder theorem Asmuth–Bloom secret sharing 


  1. 1.
    Blakley, G. R. (1979). Safeguarding cryptographic keys. In Proceedings of AFIPs I979 national computer conference, New York (Vol. 48, pp. 313–317).Google Scholar
  2. 2.
    Shamir, A. (1979). How to share a secret. Communication of the ACM, 22(11), 612–613.CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Guo, C., & Chang, C.-C. (2012). An authenticated group key distribution protocol based on the generalized Chinese remainder theorem. International Journal of Communication System. doi: 10.1002/dac.2348.
  4. 4.
    He, D., Chen, C., Ma, M., Chan, S., & Bu, J. (2011). A secure and efficient password-authenticated group key exchange protocol for mobile ad hoc networks. International Journal of Communication System. doi: 10.1002/dac.1355.
  5. 5.
    Xie, Q. (2012). A new authenticated key agreement for session initiation protocol. International Journal of Communication System, 25, 47–54. doi: 10.1002/dac.1286.CrossRefGoogle Scholar
  6. 6.
    Chang, C.-C., Cheng, T.-F., & Wu, H.-L. (2012). An authentication and key agreement protocol for satellite communications. International Journal of Communication System. doi: 10.1002/dac.2448.
  7. 7.
    Li, J.-S., & Liu, K.-H. (2011). A hidden mutual authentication protocol for low-cost RFID tags. International Journal of Communication System, 24, 1196–1211. doi: 10.1002/dac.1222.CrossRefGoogle Scholar
  8. 8.
    Asmuth, C., & Bloom, J. (1983). A modular approach to key safeguarding. IEEE Transactions on Information Theory, 29(2), 208–210.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Bloom, J. R. (1981). Threshold schemes and error-correcting codes. In Abstract of papers presented to America Mathematical Society (Vol. 2, p. 230).Google Scholar
  10. 10.
    McEliece, R. J., & Sarwate, D. V. (1981). On sharing secret and Reed–Solomon codes. Communication ACM, 24, 583–584.CrossRefMathSciNetGoogle Scholar
  11. 11.
    Kaya, K., & Selçuk, A. A. (2007). Threshold cryptography based on Asmuth–Bloom secret sharing. Information Sciences, 177, 4148–4160.CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Kaya, K., & Selçuk, A. A. (2008). Robust threshold schemes based on the Chinese remainder Ttheorem. In Advances in cryptography—AFRICACRYPT 2008. Lecture notes in computer sciences (Vol. 5023, pp. 94–108).Google Scholar
  13. 13.
    Iftene, S. (2007). General secret sharing based on the Chinese remainder theorem with applications in e-voting. Electronic Notes in Theoretical Computer Science, 186, 67–84.CrossRefMathSciNetGoogle Scholar
  14. 14.
    Harn, L., Fuyou, M., & Chang, C. C. (2013). Verifiable secret sharing based on the Chinese remainder theorem. Security and Communication Networks. doi: 10.1002/sec.807.
  15. 15.
    Liu, Y., Harn, L., & Chang, C.-C. (2014). An authenticated group key distribution Mechanism using theory of numbers. International Journal of Communication Systems.Google Scholar
  16. 16.
    Morillo, P., Padro, C., Saez, G., & Villar, J. L. (1999). Weighted threshold secret sharing schemes. Information Processing Letters, 70, 211–216.CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Padro, C., & Saez, G. (2000). Secret sharing schemes with bipartite access structure. IEEE Transactions on Information Theory, 46, 2596–2604.CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Beimel, A., Tassa, T., & Weinreb, E. (2005). Characterizing ideal weighted threshold secret sharing. In Second theory of cryptography conference, TCC 2005. Lecture notes in computer science (Vol. 3378, pp. 600–619).Google Scholar
  19. 19.
    Brickell, E. F. (1989). Some ideal secret sharing schemes. Journal of Combinatorial Mathematics and Combinatorial Computing, 9, 105–113.MathSciNetGoogle Scholar
  20. 20.
    Simmons, G. J. (1990). How to (really) share a secret. In Advances in cryptology CRYPTO ’88. Lecture notes in computer science (Vol. 403, pp. 390–448).Google Scholar
  21. 21.
    Herranz, J., & Sáez, G. (2006). New results on multipartite access structures. IEE Proceedings-Information Security, 153(4), 153–162.Google Scholar
  22. 22.
    Ng, S.-L. (2006). Ideal secret sharing schemes with multipartite access structures. IEE Proceedings-Communications, 153, 165–168.CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Tassa, T. (2004). Hierarchical threshold secret sharing. In First theory of cryptography conference, TCC 2004. Lecture notes in computer science (Vol. 2951, pp. 473–490).Google Scholar
  24. 24.
    Tassa, T., & Dyn, N. (2006). Multipartite secret sharing by bivariate interpolation. In 33rd international colloquium on automata, languages and programming, ICALP 2006. Lecture notes in computer science (Vol. 4052, pp. 288–299).Google Scholar
  25. 25.
    Ng, S.-L. (2003). A representation of a family of secret sharing matroids. Designs, Codes and Cryptography, 30, 5–19.CrossRefzbMATHGoogle Scholar
  26. 26.
    Ng, S.-L., & Walker, M. (2001). On the composition of matroids and ideal secret sharing schemes. Designs, Codes and Cryptography, 24, 49–67.CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Collins, M. J. (2002). A note on ideal tripartite access structures. IACR Cryptology ePrint Archive, 2002, 193.Google Scholar
  28. 28.
    Farràs, O., Martí-Farré, J., & Padró, C. (2012). Ideal multipartite secret sharing schemes. Journal of Cryptology, 25(3), 434–463.CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Mignotte, M. (1983). How to share a secret. In T. Beth (Ed.), Cryptography-proceedings of the workshop on cryptography, Burg Feuerstein, 1982. Lecture notes in computer science (Vol. 149, pp. 371–375).Google Scholar
  30. 30.
    Chaum, D., Crépeau, C., & Damgard, I. (1998). Multiparty unconditionally secure protocols[C]. In Proceedings of the twentieth annual ACM symposium on theory of computing (pp. 11–19). ACM.Google Scholar
  31. 31.
    Cohen, H. (2000). A course in computational algebraic number theory, 4th ed., Ser. Graduate texts in mathematics. Berlin: Springer.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Computer SchoolCentral China Normal UniversityWuhanChina
  2. 2.Department of Computer Science Electrical EngineeringUniversity of MissouriKansas CityUSA

Personalised recommendations