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An Ideal Multi-secret Sharing Scheme Based on Connectivity of Graphs

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Abstract

Secure communication has become more and more important for many modern communication applications. In a secure communication, every pair of users need to have a secure communication channel (each channel is controlled by a server) In this paper, using monotone span programs we devise an ideal linear multi-secret sharing scheme based on connectivity of graphs. In our proposed scheme, we assume that every pair of users, \(p\) and \(q\), use the secret key \(s_{pq} \) to communicate with each other and every server has a secret share such that a set of servers can recover \(s_{pq} \) if the channels controlled by the servers in this set can connect users, \(p\) and \(q\). The multi-secret sharing scheme can provide efficiency for key management. We also prove that the proposed scheme satisfies the definition of a perfect multi-secret sharing scheme. Our proposed scheme is desirable for secure and efficient secure communications.

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References

  1. Shamir, A. (1979). How to share a secret. Communications of the ACM, 22(11), 612–613.

    Article  MATH  MathSciNet  Google Scholar 

  2. Blakley, G. R. (June 1979). Safeguarding cryptographic keys. In Proceedings AFIPS 1979 national computer conference (pp. 313–317).

  3. Karnin, E. D., Greene, J. W., & Hellman, M. E. (1983). On secret sharing systems. IEEE Transactions on Information Theory, 29(1), 35–41.

    Article  MATH  MathSciNet  Google Scholar 

  4. Simmons, G. J. (1991). An introduction to shared secret and/or shared control schemes and their applications. Contemporary Cryptology, 441–497; IEEE Press, New York.

  5. Chan, C. W., & Chang, C. C. (2005). A scheme for threshold multi-secret sharing. Applied Mathematics and Computation, 166(1), 1–14.

    Article  MATH  MathSciNet  Google Scholar 

  6. Dehkordi, M. H., & Mashhadi, S. (2008). An efficient threshold verifiable multi-secret sharing. Computer Standards & Interfaces, 30(3), 187–190.

    Article  Google Scholar 

  7. Dehkordi, M. H., & Mashhadi, S. (2008). New efficient and practical verifiable multi-secret sharing schemes. Information Sciences, 178(9), 2262–2274.

    Article  MATH  MathSciNet  Google Scholar 

  8. Pang, L. J., & Wang, Y. M. (2005). A new (\(t, n)\) multi-secret sharing scheme based on Shamir’s secret sharing. Applied Mathematics and Computation, 167, 840–848.

    Article  MATH  MathSciNet  Google Scholar 

  9. Shao, J., & Cao, Z. F. (2005). A new efficient (\(t, n)\) verifiable multi-secret sharing (VMSS) based on YCH scheme. Applied Mathematics and Computation, 168, 135–140.

    Article  MATH  MathSciNet  Google Scholar 

  10. Zhao, J., Zhang, J., & Zhao, R. (2007). A practical verifiable multi-secret sharing scheme. Computer Standards & Interfaces, 29(1), 138–141.

    Article  Google Scholar 

  11. Jackson, W.-A., Martin, K. M., & O’Keefe, C. M. (1994). Multisecret threshold schemes. In Advances in cryptology—CRYPTO ’93, Lecture Notes in Computer Science (Vol. 773, pp. 126–135). Berlin: Springer.

  12. Jackson, W.-A., Martin, K. M., & O’Keefe, C. M. (1996). A construction for multisecret threshold schemes. Design, Codes and Cryptography, 9(3), 287–303.

    MATH  MathSciNet  Google Scholar 

  13. Blundo, C., De Santis, A., & Vaccaro, U. (1993). Efficient sharing of many secrets. In Proceedings of STACS ’93 (10th symposium on theoretical aspects of computer science), Lecture Notes in Computer Science (Vol. 665, pp. 692–703). Berlin: Springer.

  14. Jackson, W.-A., Martin, K. M., & O’Keefe, C. M. (1995). On sharing many secrets. In Advances in cryptology—ASIACRYPT ’94, Lecture Notes in Computer Science (Vol. 917, pp. 42–54). Berlin: Springer.

  15. Blundo, C., De Santis, A., Di Crescenzo, G., Giorgio Gaggia, A., Vaccaro, U. (1994). Multi-secret sharing schemes. In Advances in cryptology—CRYPTO ’94, Lecture Notes in Computer Science (Vol. 839, pp. 150–163). Berlin: Springer.

  16. Jackson, W.-A., Martin, K. M., & O’Keefe, C. M. (1996). Ideal secret sharing schemes with multiple secrets. Journal of Cryptology, 9, 233–250.

    Article  MATH  MathSciNet  Google Scholar 

  17. Liu, M., Xiao, L., & Zhang, Z. (2006). Linear multi-secret sharing schemes based on multi-party computation. Finite Fields and Their Applications, 12, 704–713.

    Article  MATH  MathSciNet  Google Scholar 

  18. Xiao, L., & Liu, M. (2005). Linear multi-secret sharing schemes. Science in China Series F: Information Sciences, 48(1), 125–136.

    Article  MATH  MathSciNet  Google Scholar 

  19. Hsu, C. F., Cui, G. H., Cheng, Q., & Chen, J. (2011). A novel linear multi-secret sharing scheme for group communication in wireless mesh networks. Journal of Network and Computer Applications, 34(2), 464–468.

    Article  Google Scholar 

  20. Hsu, C. F., Cheng, Q., Tang, X. M., & Zeng, B. (2011). An ideal linear multi-secret sharing scheme based on MSP. Information Sciences, 181(7), 1403–1409.

    Article  MATH  MathSciNet  Google Scholar 

  21. Stinson, D. R. (1992). An explication of secret sharing schemes. Design, Codes, and Cryptography, 2, 357–390.

    Article  MATH  MathSciNet  Google Scholar 

  22. Beimel, A. (1996). Secure schemes for secret sharing and key distribution, Ph.D. dissertation. Technion–Israel Inst. Technol., Haifa, Israel.

  23. Karchmer, M., & Wigderson, A. (May 1993). On span programs. In Proceedings of the 8th annual conference structure in complexity (pp. 102–111), San Diego, CA.

  24. De Santis, A., & Masucci, B. (1999). Multiple ramp schemes. IEEE Transactions on Information Theory, 45(5), 1720–1728.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Computer School, Central China Normal University, Wuhan, 430079, China

    Ching-Fang Hsu

  2. Department of Computer Science Electrical Engineering, University of Missouri-Kansas City, Kansas City, MO, 64110, USA

    Lein Harn

  3. College of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Guohua Cui

Authors
  1. Ching-Fang Hsu
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  2. Lein Harn
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  3. Guohua Cui
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Corresponding author

Correspondence to Ching-Fang Hsu.

Additional information

This work has been supported by the National Natural Science Foundation of China (No: 61100221, 61272405, 61272451).

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Hsu, CF., Harn, L. & Cui, G. An Ideal Multi-secret Sharing Scheme Based on Connectivity of Graphs. Wireless Pers Commun 77, 383–394 (2014). https://doi.org/10.1007/s11277-013-1511-3

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