Publicly verifiable multi‐secret sharing scheme from bilinear pairings
Abstract
In a verifiable multi‐secret sharing (VMSS) scheme, multiple secrets are shared among participants during one sharing process in such a way that some qualified subsets of them can recover these secrets. Verifiable property means that one participant may verify his/her own share, but cannot check the validity of the other participants’ shares. Verifiable property is deficient for some specific applications such as electronic voting and revocable electronic cash. Publicly verifiable property is more applicable than verifiable property because the shares can be verified by any party. In this study, an efficient publicly verifiable multi‐secret sharing (PVMSS) scheme using bilinear pairings is proposed. Under the computational Diffie–Hellman and modified bilinear Diffie–Hellman assumptions, the authors demonstrate that the proposed scheme is a secure PVMSS scheme.
9 References
[1]
Shamir, A.: ‘How to share a secret’, Commun. ACM, 1979, 22, (11), pp. 612–613 (https://doi.org/10.1145/359168.359176)
[2]
Blakey, G.R.: ‘Safeguarding cryptographic keys’. Proc. American Federation of Information Processing Societies, 1979, pp. 313–317
[3]
Feldman, P.: ‘A practical scheme for non‐interactive verifiable secret sharing’. Proc. 28th Annual Symposium on Foundations of Computer Science, 1987, pp. 427–437
[4]
Harn, L., Lin, C.: ‘Strong (n, t, n) verifiable secret sharing scheme’, Inf. Sci., 2010, 180, (16), pp. 3059–3064 (https://doi.org/10.1016/j.ins.2010.04.016)
[5]
Pedersen, T.P.: ‘Non‐interactive and information‐theoretic secure verifiable secret sharing’. Proc. CRYPTO'92, 1992 (LNCS, 576), pp. 129–140
[6]
Fujisaki, E., Okamoto, T.: ‘A practical and provably secure scheme for publicly verifiable secret sharing and its applications’. Proc. EUROCRYPT'98, 1998 (LNCS, 1403), pp. 32–46
[7]
Heidarvand, S., Villar, J.L.: ‘Public verifiability from pairings in secret sharing schemes’. Proc. Selected Areas in Cryptography, 2008, pp. 294–308
[8]
Jhanwar, M.: ‘A practical (non‐interactive) publicly verifiable secret sharing scheme’. Proc. ISPEC2011, 2011 (LNCS, 6672), pp. 273–287
[9]
Schoenmakers, B.: ‘A simple publicly verifiable secret sharing scheme and its application to electronic voting’. Proc. CRYPTO'99, 1999 (LNCS, 1666), pp. 148–164
[10]
Stadler, M.: ‘Public verifiable secret sharing’. Proc. EUROCRYPT'96, 1996 (LNCS, 1070), pp. 190–199
[11]
Tian, Y., Peng, C., Ma, J.: ‘Publicly verifiable secret sharing schemes using bilinear pairings’, Int. J. Netw. Sec., 2012, 14, (3), pp. 142–148
[12]
Wu, T.Y., Tseng, Y.M.: ‘A pairing‐based publicly verifiable secret sharing scheme’, J. Syst. Sci. Complexity, 2011, 24, (1), pp. 186–194 (https://doi.org/10.1007/s11424-011-8408-6)
[13]
Benaloh, J., Yung, M.: ‘Distributing the power of a government to enhance the privacy of voters’. Proc. Fifth Annual ACM Symp. Principles of Distributed Computing, 1986, pp. 52–62
[14]
Cohen, J., Fischer, M.: ‘A robust and verifiable cryptographically secure election scheme’. Proc. 26th Annual Symp. Foundations of Computer Science, 1985, pp. 372–382
[15]
Camenisch, J., Piveteau, J.M., Stadler, M.: ‘An efficient fair payment system’. Proc. Third ACM Conf. Computer and Communications Security, 1996, pp. 88–94
[16]
Jakobsson, M., Yung, M.: ‘Revocable and versatile electronic money’. Proc. Third ACM Conf. on Computer and Communications Security, 1996, pp. 76–87
[17]
Stadler, M., Piveteau, J.M., Camenisch, J.: ‘Fair blind signatures’. Proc. EUROCRYPT'95, 1995 (LNCS, 921), pp. 209–219
[18]
Chien, H.Y., Jan, J.K., Tseng, Y.M.: ‘A practical (t, n) multi‐secret sharing scheme’, IEICE Trans. Fundam., 2000, E83‐A, (12), pp. 2762–2765
[19]
He, J., Dawson, E.: ‘Multi secret‐sharing scheme based on one‐way function’, Electron. Lett., 1995, 30, (19), pp. 1591–1592 (https://doi.org/10.1049/el:19941076)
[20]
Yang, C.C., Chang, T.Y., Hwang, M.S.: ‘A (t, n) multi‐secret sharing scheme’, Appl. Math. Comput., 2004, 151, (2), pp. 483–490 (https://doi.org/10.1016/S0096-3003(03)00355-2)
[21]
Eslami, Z., Ahmadabadi, J.: ‘A verifiable multi‐secret sharing scheme based on cellular automata’, Inf. Sci., 2010, 180, (15), pp. 2889–2894 (https://doi.org/10.1016/j.ins.2010.04.015)
[22]
Shao, J., Cao, Z.: ‘A new efficient (t, n) verifiable multi‐secret sharing (VMSS) based on YCH scheme’, Appl. Math. Comput., 2005, 168, (1), pp. 135–140 (https://doi.org/10.1016/j.amc.2004.08.023)
[23]
Zhao, J., Zhang, J., Zhao, R.: ‘A practical verifiable multi‐secret sharing scheme’, Comput. Stand. and Interfaces, 2007, 29, (1), pp. 138–141 (https://doi.org/10.1016/j.csi.2006.02.004)
[24]
Menezes, A., Okamoto, T., Vanstone, S.: ‘Reducing elliptic curve logarithms to logarithms in a finite field’, IEEE Trans. Inf. Theory, 1993, 39, (5), pp. 1639–1646 (https://doi.org/10.1109/18.259647)
[25]
Joux, A.: ‘A one round protocol for tripartite Diffie–Hellman’, J. Cryptol., 2004, 17, (4), pp. 263–276 (https://doi.org/10.1007/s00145-004-0312-y)
[26]
Boneh, D., Franklin, M.: ‘Identity‐based encryption from the Weil pairing’, SIAM J. Comput., 2003, 32, (3), pp. 586–615 (https://doi.org/10.1137/S0097539701398521)
[27]
Boneh, D., Lynn, B., Shacham, H.: ‘Short signature from the Weil pairing’, J. Cryptol., 2004, 17, (4), pp. 297–319 (https://doi.org/10.1007/s00145-004-0314-9)
[28]
Galbraith, S.D.: ‘Supersingular curves in cryptography’. Proc. ASIACRYPT, 2001 (LNCS, 2248), pp. 495–513
[29]
Rubin, K., Silverberg, A.: ‘Supersingular abelian varieties in cryptology’. Proc. CRYPTO'02, 2002 (LNCS, 2442), pp. 336–353
[30]
Cha, J.C., Cheon, J.H.: ‘An identity‐based signature from gap Diffie–Hellman groups’. Proc. 6th Int. Workshop on Theory and Practice in Public Key Cryptography, 2002 (LNCS, 2567), pp. 18–30
[31]
Chen, L., Cheng, Z., Smart, N.P.: ‘Identity‐based key agreement protocols from pairings’, Int. J. Inf. Secur., 2007, 6, (4), pp. 213–241 (https://doi.org/10.1007/s10207-006-0011-9)
[32]
Tseng, Y.M., Wu, T.Y., Wu, J.D.: ‘An efficient and provably secure ID‐based signature scheme with batch verifications’, Int. J. Innov. Comput. Inf. Control, 2009, 5, (11), pp. 3911–3922
[33]
Wu, T.Y., Tseng, Y.M.: ‘An ID‐based mutual authentication and key exchange protocol for low‐power mobile devices’, Comput. J., 2010, 53, (7), pp. 1062–1070 (https://doi.org/10.1093/comjnl/bxp083)
[34]
Wu, T.Y., Tseng, Y.M.: ‘An efficient user authentication and key exchange protocol for mobile client‐server environment’, Comput. Netw., 2010, 54, (9), pp. 1520–1530 (https://doi.org/10.1016/j.comnet.2009.12.008)
[35]
Wu, T.Y., Tseng, Y.M., Tsai, T.T.: ‘A revocable ID‐based authenticated group key exchange protocol with resistant to malicious participants’, Comput. Netw., 2012, 56, pp. 2994–3006 (https://doi.org/10.1016/j.comnet.2012.05.011)
[36]
Zhang, F., Safavi‐Naini, R., Susilo, W.: ‘An efficient signature scheme from bilinear pairings and its applications’. Proc. Public Key Cryptography (PKC 2004), 2004 (LNCS, 2947), pp. 277–290
[37]
Bellare, M., Rogaway, P.: ‘Random oracles are practical: a paradigm for designing efficient protocols’. Proc. First ACM Conf. Computer and Communications Security’, 1993, pp. 62–73
[38]
Tseng, Y.M.: ‘A robust multi‐party key agreement protocol resistant to malicious participants’, Comput. J., 2005, 48, (4), pp. 480–487 (https://doi.org/10.1093/comjnl/bxh111)
[39]
Wu, S., Chen, K.: ‘An efficient key‐management scheme for hierarchical access control in e‐medicine system’, J. Med. Syst., 2012, 36, pp. 2325–2337 (https://doi.org/10.1007/s10916-011-9700-7)
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© 2020 The Institution of Engineering and Technology.
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Published: 01 September 2013
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