Efficient Computation Method of Participants’ Weights in Shamir’s Secret Sharing

  • Long Li
  • Tianlong Gu
  • Liang Chang
  • Jingjing LiEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 895)


Shamir’s secret sharing is an important means to realize data protection. Since participants in a specific weighted secret sharing scheme have different weights, these weights need to be computed and allocated in advance. In [15], a weight calculation method is proposed based on Karnaugh map, but this method has certain application bottlenecks and the algorithm efficiency is not efficient enough. To solve the above problems, this paper proposes a novel weight calculation method based on ordered binary decision diagrams. The new method can calculate weights for any number of participants, and the algorithm has lower space-time complexity. Theoretical analysis shows that the proposed scheme is feasible and effective.


Secret sharing Weight computation Karnaugh map Ordered binary decision diagram 



This work was supported in part by the Natural Science Foundation of China (U1711263, U1501252, 11603041), in part by the Key Research and Development Program of Guangxi (AC16380014, AA17202048, AA17202033), and in part by the Natural Science Foundation of Guangxi Province (2017GX NSFAA198283).


  1. 1.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of AFIPS 1979 National Computer Conference, pp. 313–317. AFIPS Press, Montvale (1979)Google Scholar
  3. 3.
    McEliece, R.J., Sarwate, D.V.: On sharing secrets and reed solomon codes. Commun. ACM 24(8), 583–584 (1981)MathSciNetGoogle Scholar
  4. 4.
    Asmuth, A., Bloom, J.: A modular approach to key safeguarding. IEEE Trans. Inf. Theory 30(2), 208–210 (1983)MathSciNetGoogle Scholar
  5. 5.
    Benaloh, J.C.: Secret sharing homomorphisms: keeping shares of a secret. In: Proceedings of CRYPTO 1986, pp. 412–417. Springer, Berlin (1986)Google Scholar
  6. 6.
    Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing general access structure. In: Proceedings of the IEEE Global Telecommunications Conference, pp. 99–102. IEEE Press, Globecom (1987)Google Scholar
  7. 7.
    Hsu, C.F., Cheng, Q., Tang, X., Zeng, B.: An ideal multi-secret sharing scheme based on MSP. Inf. Sci. 181(7), 1403–1409 (2011)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Liu, Y., Zhang, F., Zhang, J.: Attacks to some verifiable multi-secret sharing schemes and two improved schemes. Inf. Sci. 329(1), 524–539 (2016)zbMATHGoogle Scholar
  9. 9.
    Lu, H.C., Fu, H.L.: New bounds on the average information rate of secret-sharing schemes for graph-based weighted threshold access structures. Inf. Sci. 240(11), 83–94 (2013)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: Proceedings of 26 IEEE Symposium on Foundations of Computer Science, Portland, pp. 383–395. IEEE Press (1985)Google Scholar
  11. 11.
    He, J., Dawson, E.: Multistage secret sharing based on one-way function. Electron. Lett. 30(19), 1591–1592 (1994)Google Scholar
  12. 12.
    Kumar, P.S., Ashok, M.S., Subramanian, R.: A publicly verifiable dynamic secret sharing protocol for secure and dependable data storage in cloud computing. Int. J. Cloud Appl. Comput. 2(3), 1–25 (2017)Google Scholar
  13. 13.
    Traverso, G,. Demirel, D., Buchmann, J.: Dynamic and verifiable hierarchical secret sharing. In: Proceedings on International Conference on Information Theoretic Security, pp. 24–43. Springer, Cham (2016)Google Scholar
  14. 14.
    Huang, W., Langberg, M., Kliewer, J., Bruck, J.: Communication efficient secret sharing. IEEE Trans. Inf. Theory 62(12), 7195–7206 (2016)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Harn, L., Hsu, C., Zhang, M., He, T., Zhang, M.: Realizing secret sharing with general access structure. Inf. Sci. 367–368, 209–220 (2016)Google Scholar
  16. 16.
    Prasad, V.C.: Generalized Karnaugh map method for Boolean functions of many variables. IETE J. Educ. 58(1), 1–9 (2017)Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Guangxi Key Laboratory of Trusted SoftwareGuilin University of Electronic TechnologyGuilinChina
  2. 2.School of Information and CommunicationGuilin University of Electronic TechnologyGuilinChina

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