Abstract
Secret sharing scheme (SSS) has been extensively studied since SSSs are important not only for secure data storage but also as the fundamental building block for many cryptographic protocols such as multiparty computation (MPC). Although both code efficiency and application of MPC are important for SSSs, it is difficult to satisfy both. There have been many studies about MPC on Shamir’s and replicated SSS while their share size is large, and computationally secure SSS and a ramp scheme have a short share size while there have been few studies concerning their MPC. We propose a new computational SSS, and show how to convert shares of our SSS and a ramp SSS to those of multiparty-friendly SSS such as Shamir’s and replicated SSS. This enables one to secretly-share data compactly and extend secretly-shared data to MPC if needed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: STOC, pp. 1–10 (1988)
Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, vol. 48, pp. 313–317 (1979)
Blakley, G.R., Meadows, C.: Security of ramp schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 242–268. Springer, Heidelberg (1985)
Bogdanov, D., Laur, S., Willemson, J.: Sharemind: A framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008)
Bogdanov, D., Niitsoo, M., Toft, T., Willemson, J.: High-performance secure multi-party computation for data mining applications. Int. J. Inf. Sec. 11(6), 403–418 (2012)
Burkhart, M., Strasser, M., Many, D., Dimitropoulos, X.A.: Sepia: Privacy-preserving aggregation of multi-domain network events and statistics. In: USENIX Security Symposium, pp. 223–240 (2010)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: STOC, pp. 11–19 (1988)
Cramer, R., Damgård, I., de Haan, R.: Atomic secure multi-party multiplication with low communication. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 329–346. Springer, Heidelberg (2007)
Cramer, R., Damgård, I., Ishai, Y.: Share conversion, pseudorandom secret-sharing and applications to secure computation. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 342–362. Springer, Heidelberg (2005)
Cramer, R., Damgård, I., Maurer, U.M.: General secure multi-party computation from any linear secret-sharing scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000)
Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)
Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)
Franklin, M.K., Yung, M.: Communication complexity of secure computation (extended abstract). In: STOC, pp. 699–710 (1992)
Ghodosi, H., Pieprzyk, J., Steinfeld, R.: Multi-party computation with conversion of secret sharing. Des. Codes Cryptography 62(3), 259–272 (2012)
Goldreich, O.: The Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press (2004)
Ito, M., Saito, A., Nishizeki, T.: Secret sharing schemes realizing general access structure. In: Proc. of the IEEE Global Telecommunication Conf., Globecom 1987, pp. 99–102 (1987); Journal version: Multiple assignment scheme for sharing secret. J. of Cryptology 6(1), 15–20 (1993)
Krawczyk, H.: Secret sharing made short. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 136–146. Springer, Heidelberg (1994)
Rabin, M.O.: Efficient dispersal of information for security, load balancing, and fault tolerance. Journal of the ACM 36(2), 335–348 (1989)
Rabin, M.O.: Sequences, pp. 406–419. Springer-Verlag New York, Inc., New York (1990)
Resch, J.K., Plank, J.S.: Aont-rs: Blending security and performance in dispersed storage systems. In: FAST, pp. 191–202 (2011)
Rivest, R.L.: All-or-nothing encryption and the package transform. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 210–218. Springer, Heidelberg (1997)
Rogaway, P., Bellare, M.: Robust computational secret sharing and a unified account of classical secret-sharing goals. In: ACM Conference on Computer and Communications Security, pp. 172–184 (2007)
Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005)
Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)
Yamamoto, H.: Secret sharing system using (k,l,n) threshold scheme. IECE Trans. J68-A(9), 945–952 (1985) (in Japanese); English translation: Electronics and Communications in Japan, Part I, vol. 69(9), pp. 46–54. Scripta Technica, Inc. (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kikuchi, R., Chida, K., Ikarashi, D., Hamada, K., Takahashi, K. (2013). Secret Sharing Schemes with Conversion Protocol to Achieve Short Share-Size and Extendibility to Multiparty Computation. In: Boyd, C., Simpson, L. (eds) Information Security and Privacy. ACISP 2013. Lecture Notes in Computer Science, vol 7959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39059-3_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-39059-3_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39058-6
Online ISBN: 978-3-642-39059-3
eBook Packages: Computer ScienceComputer Science (R0)