Abstract
Recently, Chang et al. proposed a multi-stage (t, n)-threshold secret sharing scheme based on the one-way function. For k secrets shared among n participants, each participant has to keep one secret shadow; but there are a total of kn public values. In this paper, a new multi-stage (t, n)-threshold secret sharing scheme was proposed, which is an alternative implementation of Chang etal.’s scheme. Each participant needs to keep only one secret shadow in sharing multiple secrets without updating each participant’s secret shadow. For k secrets shared among n participants, there are only a total of k(n-t+1) public values. Analyses show that the proposed scheme is a computationally secure and efficient scheme. The implementation of the proposed scheme becomes very attractive, especially when the threshold value t is very close to the number of participants n.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chang, T.-Y., Yang, C.-C., Hwang, M.-S.: Threshold Untraceable Signature for Group communications. IEE Proceedings-Communications 151, 179–184 (2004)
Hwang, M.-S., Lee, C.-C., Chang, T.-Y.: Broadcasting Cryptosystem in Computer Networks Using Geometric Properties of Lines. Journal of Information Science and Engineering 18, 373–378 (2002)
Crescenzo, G.D.: Sharing One Secret vs. Sharing Many Secret. Theoretical Computer Science 295, 123–140 (2003)
Shamir, A.: How to Share a Secret. Communications of the ACM 22, 612–613 (1979)
Blakley, G.: Safeguarding Cryptographic Key. In: Smith, M., Zanca, J.T. (eds.) Proc. AFIPS 1979 Natl. Conf., pp. 313–317. AFIPS Press, New York (1979)
Chien, H.Y., Jan, J.K., Tseng, Y.M.: A Practical (t, n) Multi-secret Sharing Scheme. IEICE Transactions on Fundamentals E83-A (12), 2762–2765 (2000)
Pang, L.J., Wang, Y.M.: A New (t,n) Multi-secret Sharing Scheme Based on Shamir’s Secret Sharing. Submitted to Applied Mathematics and Computation. Accepted and in Press, Corrected Proof, Available online November 5 (2004)
Yang, C.C., Chang, T.Y., Hwang, M.S.: A (t, n) Multi-secret Sharing Scheme. Applied Mathematics and Computation 151, 483–490 (2004)
He, J., Dawson, E.: Multistage Secret Sharing Based on One-way Function. Electronics Letters 30, 1591–1592 (1994)
Harn, L.: Comment: Multistage Secret Sharing Based on One-way Function. Electronics Letters 31, 262 (1995)
Chang, T.Y., Hwang, M.S., Yang, W.P.: A new Multi-stage Secret Sharing Scheme Using One-way Function. ACM SIGOPS Operating Systems 39, 48–55 (2005)
Jackson, M.-A., Marin, K.M., O’Keefe, C.M.: On Sharing Many Secrets. In: Pieprzyk, J., Safavi-Naini, R. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 42–54. Springer, Heidelberg (1995)
Crescenzo, G.D.L.: Sharing One Secret vs. Sharing Many Secrets: Tight Bounds on the Average Improvement Ratio. In: Proc. of 11th Annu. ACM-SIAM Symp. On Discrete Algorithms. Society for Industrial and Applied Mathematics, San Francisco, California, pp. 273–274 (2000)
ElGamal, T.: A Public-key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory IT-31, 469–472 (1985)
Rivest, R.L., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of the ACM 21, 120–126 (1978)
Wu, T.C., Wu, T.S.: Cheating Detection and Cheater Identification in Secret Sharing Schemes. IEE Proceedings-Computers and Digital Techniques 142, 367–369 (1995)
Tan, K.J., Zhu, H.W., Gu, S.J.: Cheater Identification in (t, n) Threshold Scheme. Computer Communications 22, 762–765 (1999)
Chang, C.C., Hwang, R.J.: Efficient Cheater Identification Method for Threshold Schemes. IEE Proceedings-Computers and Digital Techniques 144, 23–27 (1997)
Aho, A., Hopcroft, J., Ullman, J.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)
Knuth, D.: The Art of Computer Programming. Seminumerical Algorithms, vol. 2. Addison-Wesley, Reading (1969)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, HX., Cheng, CT., Pang, LJ. (2005). An Improved Multi-stage (t, n)-Threshold Secret Sharing Scheme. In: Fan, W., Wu, Z., Yang, J. (eds) Advances in Web-Age Information Management. WAIM 2005. Lecture Notes in Computer Science, vol 3739. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11563952_24
Download citation
DOI: https://doi.org/10.1007/11563952_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29227-2
Online ISBN: 978-3-540-32087-6
eBook Packages: Computer ScienceComputer Science (R0)