Abstract
In a secret sharing protocol, a dealer shares the secret such that only the subsets of players in the (monotone) access structure can reconstruct the secret, while subsets of players that are not in the access structure cannot reconstruct the secret. The sharing is perfect if the players of any set not in the access structure have no information about the secret. Non-perfect secret sharing slackens the requirement as: the players of any set not in the access structure can have some information about the secret but cannot reconstruct the secret. All known schemes in the literature for non-perfect secret sharing are directed toward specific classes of the access hierarchy like threshold, ramp, multiple-level hierarchy etc. In this work, we initiate the study of a more general non-perfect secret sharing. We model the access hierarchy via a weighted lattice. We first give a necessary condition and a sufficient condition for the existence of a secret sharing scheme for any given weighted lattice (that defines the access hierarchy). Subsequently, we provide a framework for designing non-perfect secret sharing schemes, using generalized monotone span programs (GenMSPs). We also show how to construct new non-perfect secret sharing schemes by composition of known GenMSPs, and design an exemplary secret sharing algorithm that is based on and illustrates the above framework.
Financial support from Infosys Technologies Limited, India, is acknowledged.
Partially supported by DRDO collaborative project on Communication and Networking Technologies.
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References
P. Beguin and A. Cresti. General short computational secret sharing schemes. In Proceedings of EUROCRYPT’95, volume 921 of LNCS, pages 194–208. Springer-Verlag, 1995.
A. Beimel. Secure Schemes for Secret Sharing and Key Distribution. PhD thesis, Department of Computer Science, Technion-Israel Institute of Technology, 1996.
A. Beimel and Y. Ishai. On the power of nonlinear secret sharing. In Proceedings of the 16th Annual IEEE Structure in Complexity Theory, pages 188–202, 2001.
J. Benaloh and J. Leichter. Generalized secret sharing and monotone functions. In Proceedings of CRYPTO’88, volume 403 of LNCS, pages 27–35. Springer-Verlag, 1988.
J.C. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Proceedings of CRYPTO’86, volume 263 of LNCS, pages 251–260, Springer-Verlag. 1986.
G.R. Blakley. Safeguarding cryptographic keys. In Proceedings of AFIPS 1979 National Computer Conference, pages 313–317. AFIPS, 1979.
G.R. Blakley and C. Meadows. Security of ramp schemes. In Proceedings of CRYPTO’84, volume 196 of LNCS, pages 242–268. Springer Verlag, 1984.
C. Blundo and D.R. Stinson. Anonymous secret sharing schemes. In Discrete Applied Mathematics, volume 77:13–28, 1997.
E. F. Brickell and D.M. Davenport. On the classification of ideal secret sharing scheme. In Journal of Cryptology, pages 123–134, 1991.
B. Chor, S. Goldwasser, S. Micali, and B. Awerbuch. Verifiable secret sharing and achieving simultaneity in the presence of faults. In 26th IEEE FOCS, pages 383–395. 1985.
A. Herzberg, S. Jarecki, H. Krawczyk, and M. Yung. Proactive secret sharing, or: How to cope with perpetual leakage. In Proceedings of CRYPTO’95, volume 963 of LNCS, pages 339–352. Springer-Verlag, 1995.
M. Itoh, A. Saito, and T. Nishizeki. Secret sharing scheme realizing general access structure. In Proc. of IEEE Globecom’87, pages 99–102, 1987.
E.D. Karnin, J.W. Green, and M. E. Hellman. On secret sharing systems. In IEEE Transactions on Information Theory, IT-29, pages 35–41, 1982.
M. Kerchmer and A. Wigderson. On span programs. In Proceedings of the 8th IEEE Structure in Complexity Theory, pages 102–111, 1993.
K. Kurosawa, K. Okada, K. Sakano, W. Ogata, and S. Tsuji. Nonperfect secret sharing schemes and matroids. In Proceedings of EUROCRYPT’93, volume 765 of LNCS, pages 126–141. Springer Verlag, 1993.
W. Ogata and K. Kurosawa. Some basic properties of general nonperfect secret sharing schemes. Journal of Universal Computer Science, 4(8):690–704, 1998.
R. Ostrovsky and M. Yung. How to withstand mobile virus attacks. In Proceedings of the 10th ACM PODC, pages 51–59,1991.
A. Renvall and C. Ding. A nonlinear secret sharing scheme. In ACISP’96, volume 1172 of LNCS, pages 56–66, 1996.
A. Shamir. How to share a secret. Communications of the ACM, 22:612–613, 1979.
M. Tompa and H. Woll. How to share a secret with cheaters. In Proceedings of CRYPTO’86, volume 263 of LNCS, pages 261–265, 1987.
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Srinathan, K., Rajan, N.T., Rangan, C.P. (2002). Non-perfect Secret Sharing over General Access Structures. In: Menezes, A., Sarkar, P. (eds) Progress in Cryptology — INDOCRYPT 2002. INDOCRYPT 2002. Lecture Notes in Computer Science, vol 2551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36231-2_32
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DOI: https://doi.org/10.1007/3-540-36231-2_32
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