Abstract
In Shamir’s (k,n)-threshold secret sharing scheme (threshold scheme), a heavy computational cost is required to make n shares and recover the secret. As a solution to this problem, several fast threshold schemes have been proposed. This paper proposes a new (k,n)-threshold scheme. For the purpose to realize high performance, the proposed scheme uses just EXCLUSIVE-OR(XOR) operations to make shares and recover the secret. We prove that the proposed scheme is a perfect secret sharing scheme, every combination of k or more participants can recover the secret, but every group of less than k participants cannot obtain any information about the secret. Moreover, we show that the proposed scheme is an ideal secret sharing scheme similar to Shamir’s scheme, which is a perfect scheme such that every bit-size of shares equals that of the secret. We also evaluate the efficiency of the scheme, and show that our scheme realizes operations that are much faster than Shamir’s. Furthermore, from the aspect of both computational cost and storage usage, we also introduce how to extend the proposed scheme to a new (k,L,n)-threshold ramp scheme similar to the existing ramp scheme based on Shamir’s scheme.
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
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Blakley, G.R.: Safeguarding cryptographic keys. In: Proc. AFIPS, 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. 242–269. Springer, Heidelberg (1985)
Yamamoto, H.: On secret sharing systems using (k,L,n) threshold scheme. IEICE Trans. Fundamentals (Japanese Edition) J68-A(9), 945–952 (1985)
Kurosawa, K., Okada, K., Sakano, K., Ogata, W., Tsujii, T.: Non perfect secret sharing schemes and matroids. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 126–141. Springer, Heidelberg (1994)
Ogata, W., Kurosawa, K.: Some basic properties of general nonperfect secret sharing schemes. J. Universal Computer Science 4(8), 690–704 (1998)
Okada, K., Kurosawa, K.: Lower bound on the size of shares of nonperfect secret sharing schemes. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 34–41. Springer, Heidelberg (1995)
Ishizu, H., Ogihara, T.: A study on long-term storage of electronic data. In: Proc. IEICE General Conf., vol. D-9-10(1), p. 125 (2004) (in Japanese)
Fujii, Y., Tada, M., Hosaka, N., Tochikubo, K., Kato, T.: A fast (2,n)-threshold scheme and its application. In: Proc. CSS 2005, pp. 631–636 (2005) (in Japanese)
Hosaka, N., Tochikubo, K., Fujii, Y., Tada, M., Kato, T.: (2,n)-threshold secret sharing systems based on binary matrices. In: Proc. SCIS. pp. 2D1–4 (2007) (in Japanese)
Kurihara, J., Kiyomoto, S., Fukushima, K., Tanaka, T.: A fast (3,n)-threshold secret sharing scheme using exclusive-or operations. IEICE Trans. Fundamentals, E91-A(1), 127–138 (2008)
Shiina, N., Okamoto, T., Okamoto, E.: How to convert 1-out-of-n proof into k-out-of-n proof. In: Proc. SCIS 2004, pp. 1435–1440 (2004) (in Japanese)
Kunii, H., Tada, M.: A note on information rate for fast threshold schemes. In: Proc. CSS 2006, pp. 101–106 (2006) (in Japanese)
Karnin, E.D., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Trans. Inform. Theory 29(1), 35–41 (1983)
Capocelli, R.M., De Santis, A., Gargano, L., Vaccaro, U.: On the size of shares for secret sharing schemes. J. Cryptology 6, 35–41 (1983)
Blundo, C., De Santis, A., Gargano, L., Vaccaro, U.: On the information rate of secret sharing schemes. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 149–169. Springer, Heidelberg (1993)
Stinson, D.R.: Decomposition constructions for secret sharing schemes. IEEE Trans. Inform. Theory 40(1), 118–125 (1994)
Stinson, D.R.: Cryptography: Theory and Practice. CRC Press, Florida (1995)
Poettering, B.: SSSS: Shamir’s Secret Sharing Scheme, http://point-at-infinity.org/ssss/
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kurihara, J., Kiyomoto, S., Fukushima, K., Tanaka, T. (2008). A New (k,n)-Threshold Secret Sharing Scheme and Its Extension. In: Wu, TC., Lei, CL., Rijmen, V., Lee, DT. (eds) Information Security. ISC 2008. Lecture Notes in Computer Science, vol 5222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85886-7_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-85886-7_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85884-3
Online ISBN: 978-3-540-85886-7
eBook Packages: Computer ScienceComputer Science (R0)