Abstract
In a (k,n) Shamir’s threshold scheme, if one or more of the n shares are fake, then the secret may not be reconstructed correctly by some sets of k shares. Supposing that at most t of the n shares are fake, Rees et al. (1999) described two algorithms to determine consistent sets of shares so that the secret can be reconstructed correctly from k shares in any of these consistent sets. In their algorithms, no honest participant can be absent and at least n-t shares should be pooled during the secret reconstruction phase. In this paper, we propose a modified algorithm for this problem so that the number of participants taking part in the secret reconstruction can be reduced to k+2t and the shares need to be pooled can be reduced to, in the best case, k+t, and less than or equal to k+2t in the others. Its efficiency is also investigated.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Blakley, G.R.: Safeguarding cryptographic keys. In: AFIPS Conf. Proceed., vol. 48, pp. 313–317 (1979)
Brickell, E.F., Stinson, D.R.: The detection of cheaters in threshold schemes. SIAM J. Discrete Math. 4, 502–510 (1991)
Harn, L.: Efficient sharing (broadcasting) of multiple secrets. IEE Proc. -Comput. Digit. Tech. 142, 237–240 (1995)
McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed-Solomon codes. Comm. ACM 24, 583–584 (1981)
Ogata, W., Kurosawa, K.: Optimum secret sharing scheme secure against cheating. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 200–211. Springer, Heidelberg (1996)
Rees, R.S., Stinson, D.R., Wei, R., van Rees, G.H.J.: An application of covering designs: determining the maximum consistent set of shares in a threshold scheme. Ars Combin. 53, 225–237 (1999)
Shamir, A.: How to share a secret. Comm. ACM 22, 612–613 (1979)
Tompa, M., Woll, H.: How to share a secret with cheaters. J. Cryptology 1, 133–138 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tso, R., Miao, Y., Okamoto, E. (2004). A New Algorithm for Searching a Consistent Set of Shares in a Threshold Scheme with Cheaters. In: Lim, JI., Lee, DH. (eds) Information Security and Cryptology - ICISC 2003. ICISC 2003. Lecture Notes in Computer Science, vol 2971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24691-6_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-24691-6_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21376-5
Online ISBN: 978-3-540-24691-6
eBook Packages: Springer Book Archive