Abstract
In a (t, n)-threshold multi-secret sharing scheme, several secrets are shared among n participants in such a way that any t (or more) of them can reconstruct the secrets while a group of (t − 1) can not obtain any information. Therefore, when such schemes are used to distribute sensitive information over a network, fault tolerance property is achieved since even if n − t of the nodes go out of function, the remaining t nodes suffice to recover the information. In 2009, Wang et al. proposed a verifiable (t, n)-threshold multi-secret sharing scheme (WTS) based on elliptic curves in which the secrets can change periodically [Wireless Pers. Commun., Springer-Verlage, doi:10.1007/s11277-009-9875-0]. In this paper, we propose a verifiable (t, n)-threshold multi-secret sharing scheme based on bilinear maps. Our scheme does not require a secure channel and participants can verify the shares pooled in the reconstruction phase. Our proposed scheme is multi-use such that in order to change the secrets, it is sufficient to renew some public information. Furthermore, the proposed scheme is flexible to the threshold value. Therefore, our proposed scheme has all the merits of (WTS), however, we achieve two major improvements. First when the secrets are to be changed, we require to publish fewer public values. This reduction can be very important in certain applications such as steganographic use of secret sharing schemes. The second is that (WTS) is designed with the assumption that the number of secrets (m) is equal to the threshold t so that the case m > t is handled by repeating the scheme \({\left\lceil \frac{m}{t}\right\rceil}\) times. However, in designing the scheme we do not assume any restrictions on the number of secrets.
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References
Shamir A. (1979) How to share a secret. Communication of the ACM 22: 612–613
Blakley G. (1979) Safeguarding cryptographic keys. AFIPS Conference Proceedings 48: 313–317
Zhao J., Zhang J., Zhao R. (2007) A practical verifiable multi-secret sharing scheme. Computer Standards Interface 29: 138–141
He J., Dawson E. (1994) Multistage secret sharing based on one-way function. Electronics Letters 30(19): 1591–1592
Jackson W. A., Martin K. M., O’keefe C. M. (1994) On sharing many secrets. Asiacrypt 94: 42–54
Chor, B., & Goldwasser, S. (1985). Verifiable secret sharing and achieving simultaneity in the presence of faults [a]. In Proceedings of 26th IEEE Symposium. FOCS, pp. 251–260.
Hwang R.-J., Chang C.-C. (1998) An on-line secret sharing scheme for multi secrets. Computer Communications 21(13): 1170–1176
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
Chen, W., Long, X., Bai, Y. B., & Gao, X. P. (2007). A new dynamic threshold secret sharing scheme from bilinear maps. In International conference on parallel processing workshops, pp. 19–22.
Wang S. J., Tsai Y. R., Shen J. J. (2008) Verifiable threshold scheme in multi-secret sharing distributions upon extensions of ecc, Wireless Pers Commun. Springer, New York, pp 405–410. doi:10.1007/s11277-009-9875-0
Koblitz N. (1993) Introduction to elliptic curves and modular forms. Springer, New York
Washington L. C. (2003) Elliptic curves: Number theory and cryptography. CRC Press, Boca Raton
Boneh D., Franklin M. (2001) Identity-based encryption from the weil pairing. Advances in Cryptology, Lecture Notes on Computer Science 2139: 213–229
Galbraith S. D., Harrison K., Soldera D. (2002) Implementing the tate pairing. Algorithmic Number Theory Symposium ANTS-V, LNCS 2369: 324–337
Lee H.-S. (2004) Self-pairing map and its applications to cryptography. Applied Mathematics and Computation 151: 671–678
Eslami Z., Razzaghi S., Ahmadabadi J. Z. (2010) Secret image sharing based on cellular automata and steganography. Pattern Recognition 43: 397–404
Lin C., Tsai W. (2004) Secret image sharing with steganography and authentication. The Journal of Systems and Software 73: 405–414
Yang C., Chen T., Yu K., Wang C. (2007) Improvements of image sharing with steganography and authentication. The Journal of Systems and Software 80: 1070–1076
Chang C., Hsieh Y., Lin C. (2008) Sharing secrets in stego images with authentication. Pattern Recognition 41: 3130–3137
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Eslami, Z., Kabiri Rad, S. A New Verifiable Multi-secret Sharing Scheme Based on Bilinear Maps. Wireless Pers Commun 63, 459–467 (2012). https://doi.org/10.1007/s11277-010-0143-0
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DOI: https://doi.org/10.1007/s11277-010-0143-0