×

Threshold changeable secret sharing schemes revisited. (English) Zbl 1236.94085

Summary: This paper studies the methods for changing thresholds in the absence of secure channels after the setup of threshold secret sharing schemes. First, we construct a perfect \((t,n)\) threshold scheme that is threshold changeable to \(t^\prime > t\), which is optimal with respect to the share size. This improves the scheme of H. Wang and D. S. Wong [IEEE Trans. Inf. Theory 54, No. 1, 473–480 (2008; Zbl 1237.94118)] by relaxing the requirement from \(q \geq n+v\) to \(q>n\) with the secret-domain \(\mathbb F^v_q\). But these threshold changeable schemes along with most previously known schemes turn out to be insecure under the collusion attack of players holding initial shares. By adding a broadcast enforcement term we enhance the model with collusion security and \(N\) options of threshold change. Then we construct a computationally secure scheme under the enhanced model, which involves much shorter shares and broadcast messages than the perfect schemes. Finally, we discuss how to realize the enrollment and disenrollment of players and, particularly, how to deal with L-fold changes of access polices.

MSC:

94A62 Authentication, digital signatures and secret sharing

Citations:

Zbl 1237.94118
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barwick, S. G.; Jackson, W.-A.; Martin, K. M., Updating the parameters of a threshold scheme by minimal broadcast, IEEE Trans. Inform. Theory, 51, 2, 620-633 (2005) · Zbl 1285.94105
[2] Blakley, B.; Blakley, G. R.; Chan, A. H.; Massey, J. L., Threshold schemes with disenrollment, (Advances in Cryptology-CRYPTO ’92 (Santa Barbara, CA, 1992). Advances in Cryptology-CRYPTO ’92 (Santa Barbara, CA, 1992), Lecture Notes in Computer Science, vol. 740 (1993), Springer: Springer Berlin), 540-548 · Zbl 0809.94016
[3] G.R. Blakley, Safeguarding cryptographic keys, in: Proceedings of the National Computer Conference, American Federation of Information Processing Societies, 1979, pp. 313-317.; G.R. Blakley, Safeguarding cryptographic keys, in: Proceedings of the National Computer Conference, American Federation of Information Processing Societies, 1979, pp. 313-317.
[4] Blundo, C.; Cresti, A.; De Santis, A.; Vaccaro, U., Fully dynamic secret sharing schemes, Theor. Comput. Sci., 165, 2, 407-440 (1996) · Zbl 0872.68034
[5] Charnes, C.; Pieprzyk, J.; Safavi-Naini, R., Conditionally secure secret sharing schemes with disenrollment capability, (CCS’94: Proceedings of the 2nd ACM Conference on Computer and Communications Security (1994), ACM: ACM New York, NY, USA), 89-95
[6] Chen, L.; Gollmann, D.; Mitchell, C. J., Key escrow in mutually mistrusting domains, (Proceedings of the International Workshop on Security Protocols. Proceedings of the International Workshop on Security Protocols, Lecture Notes in Computer Science, vol. 1189 (1997), Springer-Verlag: Springer-Verlag London, UK), 139-153
[7] Chor, B.; Goldwasser, S.; Micali, S.; Awerbuch, B., Verifiable secret sharing and achieving simultaneity in the presence of faults, (FOCS’85: Proceedings of the 26th Annual Symposium on Foundations of Computer Science (1985), IEEE Computer Society: IEEE Computer Society Washington, DC, USA), 383-395
[8] Y. Desmedt, S. Jajodia, Redistributing secret shares to new access structures and its applications, Tech. Rep. ISSE-TR-97-01, George Mason University, Fairfax, Virginia, 1997.; Y. Desmedt, S. Jajodia, Redistributing secret shares to new access structures and its applications, Tech. Rep. ISSE-TR-97-01, George Mason University, Fairfax, Virginia, 1997.
[9] Goldreich, O., Foundations of Cryptography II: Basic Applications (2004), Cambridge University Press · Zbl 1068.94011
[10] Krawczyk, H., Secret sharing made short, (Advances in Cryptology-CRYPTO’93: Proceedings of the 13th Annual International Cryptology Conference. Advances in Cryptology-CRYPTO’93: Proceedings of the 13th Annual International Cryptology Conference, Lecture Notes in Computer Science, vol. 773 (1993), Springer), 136-146 · Zbl 0871.94034
[11] M. Li, R. Poovendran, Broadcast-enforced disnrollment in threshold schemes, SAC 2003, Lecture Notes in Comput. Sci., vol. 3006, pp. 101-116.; M. Li, R. Poovendran, Broadcast-enforced disnrollment in threshold schemes, SAC 2003, Lecture Notes in Comput. Sci., vol. 3006, pp. 101-116. · Zbl 1081.94551
[12] Maeda, A.; Miyaji, A.; Tada, M., Efficient and unconditionally secure verifiable threshold changeable scheme, (ACISP 2001: Proceedings of the 6th Australasian Conference on Information Security and Privacy. ACISP 2001: Proceedings of the 6th Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science, vol. 2119 (2001), Springer), 403-416 · Zbl 1005.94536
[13] Martin, K. M., Untrustworthy participants in secret sharing schemes, (Ganley, M. J., Cryptography and Coding III (1993), Oxford University Press), 255-264 · Zbl 0814.94015
[14] K.M. Martin, Dynamic access policies for unconditionally secure secret sharing schemes, in: Proceedings of IEEE Information Theory Workshop, ITW 05, Awaji Island, Japan, 2005, pp. 61-66.; K.M. Martin, Dynamic access policies for unconditionally secure secret sharing schemes, in: Proceedings of IEEE Information Theory Workshop, ITW 05, Awaji Island, Japan, 2005, pp. 61-66.
[15] Martin, K. M.; Pieprzyk, J.; Safavi-Naini, R.; Wang, H., Changing thresholds in the absence of secure channels, (ACISP’99: Proceedings of the 4th Australasian Conference on Information Security and Privacy. ACISP’99: Proceedings of the 4th Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science, vol. 1587 (1999), Springer), 177-191 · Zbl 0919.94041
[16] Martin, K. M.; Safavi-Naini, R.; Wang, H., Bounds and techniques for efficient redistribution of secret shares to new access structures, Comput. J., 42, 8, 638-649 (1999) · Zbl 0955.68045
[17] Shamir, A., How to share a secret, Commun. ACM, 22, 11, 612-613 (1979) · Zbl 0414.94021
[18] Steinfeld, R.; Pieprzyk, J.; Wang, H., Lattice-based threshold changeability for standard Shamir secret-sharing schemes, IEEE Trans. Inform. Theory, 53, 7, 2542-2559 (2007) · Zbl 1326.94130
[19] Wang, H.; Wong, D. S., On secret reconstruction in secret sharing schemes, IEEE Trans. Inform. Theory, 54, 1, 473-480 (2008) · Zbl 1237.94118
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.