Abstract
In this paper, we investigate a new concept, called share selectable secret sharing, where no unauthorized set can obtain information of the secret (in the information-theoretic sense) even if shares are selectable as arbitrary values which are independent of the secret. We propose two totally selectable (i.e., all users’ shares are selectable) secret sharing schemes with unanimous structure. We also propose a quasi-selectable (i.e., a part of each user’s share is selectable) secret sharing scheme with certain hierarchical structures which contains special cases of the hierarchical threshold structures introduced by Tamir Tassa in TCC2004 (or its full version (J. Cryptology2007)). If all selectable shares are randomly chosen, then our schemes are perfect. Finally, we discuss the effect of the leakage information of the secret if a weak secret is indicated as a selectable share.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Abdalla, M., Boyen, X., Chevalier, C., Pointcheval, D.: Distributed Public-key Cryptography from Weak Secrets. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 139–159. Springer, Heidelberg (2009)
Attrapadung, N., Libert, B., de Panafieu, E.: Expressive Key-policy Attribute-based Encryption with Constant-size Ciphertexts. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 90–108. Springer, Heidelberg (2011)
Béguin, P., Cresti, A.: General Short Computational Secret Sharing Schemes. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 194–208. Springer, Heidelberg (1995)
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)
Blundo, C., Cresti, A., De Santis, A., Vaccaro, U.: Fully dynamic secret sharing schemes. Theor. Comput. Sci. 165(2), 407–440 (1996)
Blundo, C., De Santis, A., Di Crescenzo, G., Gaggia, A.G., Vaccaro, U.: Multi-secret Sharing Schemes. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 150–163. Springer, Heidelberg (1994)
Boneh, D., Boyen, X., Halevi, S.: Chosen Ciphertext Secure Public Key Threshold Encryption without Random Oracles. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 226–243. Springer, Heidelberg (2006)
Boyen, X., Chevalier, C., Fuchsbauer, G., Pointcheval, D.: Strong Cryptography from Weak Secrets. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 297–315. Springer, Heidelberg (2010)
Brickell, E.F.: Some Ideal Secret Sharing Schemes. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 468–475. Springer, Heidelberg (1990)
Brickell, E.F., Stinson, D.R.: Some improved bounds on the information rate of perfect secret sharing schemes. J. Cryptology 5(3), 153–166 (1992)
Cachin, C.: On-line secret sharing. In: IMA Conf., pp. 190–198 (1995)
Csirmaz, L.: The size of a share must be large. J. Cryptology 10(4), 223–231 (1997)
Csirmaz, L., Tardos, G.: On-line secret sharing. Cryptology ePrint Archive, Report 2011/174 (2011), http://eprint.iacr.org/
Desmedt, Y., Frankel, Y.: Threshold Cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)
Dodis, Y., Wichs, D.: Non-malleable extractors and symmetric key cryptography from weak secrets. In: STOC, pp. 601–610 (2009)
Gennaro, R.: Faster and Shorter Password-authenticated Key Exchange. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 589–606. Springer, Heidelberg (2008)
Gentry, C., MacKenzie, P.D., Ramzan, Z.: Password authenticated key exchange using hidden smooth subgroups. In: ACM Conference on Computer and Communications Security, pp. 299–309 (2005)
Gordon, S.D., Katz, J.: Rational Secret Sharing, Revisited. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 229–241. Springer, Heidelberg (2006)
Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM Conference on Computer and Communications Security, pp. 89–98 (2006)
Halpern, J.Y., Teague, V.: Rational secret sharing and multiparty computation: extended abstract. In: STOC, pp. 623–632 (2004)
Herzberg, A., Jarecki, S., Krawczyk, H., Yung, M.: Proactive Secret Sharing or: How to Cope with Perpetual Leakage. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 339–352. Springer, Heidelberg (1995)
Hwang, R.-J., Chang, C.-C.: An on-line secret sharing scheme for multi-secrets. Computer Communications 21(13), 1170–1176 (1998)
Isshiki, T., Wada, K., Tanaka, K.: A rational secret-sharing scheme based on RSA-OAEP. IEICE Transactions 93-A(1), 42–49 (2010)
Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing general access structure. In: Proceedings IEEE Globecom 1987, pp. 99–102 (1987)
Iwamoto, M., Yamamoto, H., Ogawa, H.: Optimal multiple assignments based on integer programming in secret sharing schemes with general access structures. IEICE Transactions 90-A(1), 101–112 (2007)
Katz, J., Ostrovsky, R., Yung, M.: Efficient Password-authenticated Key Exchange using Human-memorable Passwords. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 475–494. Springer, Heidelberg (2001)
Kol, G., Naor, M.: Games for exchanging information. In: STOC, pp. 423–432 (2008)
Krawczyk, H.: Secret Sharing Made Short. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 136–146. Springer, Heidelberg (1994)
Kurihara, J., Kiyomoto, S., Fukushima, K., Tanaka, T.: A fast (k, L, n)-threshold ramp secret sharing scheme. IEICE Transactions 92-A(8), 1808–1821 (2009)
MacKenzie, P.D., Shrimpton, T., Jakobsson, M.: Threshold password-authenticated key exchange. J. Cryptology 19(1), 27–66 (2006)
Martí-Farré, J., Padró, C.: Secret sharing schemes on access structures with intersection number equal to one. Discrete Applied Mathematics 154(3), 552–563 (2006)
Micali, S., Shelat, A.: Purely Rational Secret Sharing (Extended Abstract). In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 54–71. Springer, Heidelberg (2009)
Nikov, V., Nikova, S.: On Proactive Secret Sharing Schemes. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 308–325. Springer, Heidelberg (2004)
Nishide, T., Yoneyama, K., Ohta, K.: Attribute-based encryption with partially hidden ciphertext policies. IEICE Transactions 92-A(1), 22–32 (2009)
Oba, T., Ogata, W.: Provably secure on-line secret sharing scheme. IEICE Transactions 94-A(1), 139–149 (2011)
Qin, B., Wu, Q., Zhang, L., Domingo-Ferrer, J.: Threshold Public-key Encryption with Adaptive Security and Short Ciphertexts. In: Soriano, M., Qing, S., López, J. (eds.) ICICS 2010. LNCS, vol. 6476, pp. 62–76. Springer, Heidelberg (2010)
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Shin, S., Kobara, K., Imai, H.: Security analysis of two augmented password-authenticated key exchange protocols. IEICE Transactions 93-A(11), 2092–2095 (2010)
Stinson, D.R., Wei, R.: Unconditionally Secure Proactive Secret Sharing Scheme with Combinatorial Structures. In: Heys, H.M., Adams, C.M. (eds.) SAC 1999. LNCS, vol. 1758, pp. 200–214. Springer, Heidelberg (2000)
Sun, H.-M.: On-line multiple secret sharing based on a one-way function. Computer Communications 22(8), 745–748 (1999)
Tassa, T.: Hierarchical Threshold Secret Sharing. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 473–490. Springer, Heidelberg (2004)
Tassa, T.: Hierarchical threshold secret sharing. J. Cryptology 20(2), 237–264 (2007)
Tassa, T., Dyn, N.: Multipartite secret sharing by bivariate interpolation. J. Cryptology 22(2), 227–258 (2009)
Tochikubo, K.: Efficient secret sharing schemes realizing general access structures. IEICE Transactions 87-A(7), 1788–1797 (2004)
Yamada, S., Attrapadung, N., Hanaoka, G., Kunihiro, N.: Generic Constructions for Chosen-ciphertext Secure Attribute Based Encryption. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 71–89. Springer, Heidelberg (2011)
Yoneyama, K.: Does secure password-based authenticated key exchange against leakage of internal states exist? IEICE Transactions 92-A(1), 113–121 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Emura, K., Miyaji, A., Nomura, A., Rahman, M.S., Soshi, M. (2011). Ideal Secret Sharing Schemes with Share Selectability. In: Qing, S., Susilo, W., Wang, G., Liu, D. (eds) Information and Communications Security. ICICS 2011. Lecture Notes in Computer Science, vol 7043. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25243-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-25243-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25242-6
Online ISBN: 978-3-642-25243-3
eBook Packages: Computer ScienceComputer Science (R0)