Abstract
As known, multiplicative secret sharing schemes over Abelian groups play an important role in threshold cryptography, such as in threshold RSA signature schemes. In this paper we present a new approach for constructing multiplicative threshold schemes over finite Abelian groups, which generalises a scheme proposed by Blackburn, Burmester, Desmedt and Wild in Eurocrypt’96. Our method is based on a notion of multiple perfect hash families, which we introduce in this paper. We also give several constructions for multiple perfect hash families from resolvable BIBD, difference matrix and error-correcting code.
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References
Alon, N., Naor, M.: Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions. Algorithmica 16, 434–449 (1996)
Atici, M., Magliveras, S.S., Stinson, D.R., Wei, W.D.: Some Recursive Constructions for Perfect Hash Families. Journal of Combinatorial Designs 4, 353–363 (1996)
Benaloh, J.C.: Secret sharing homomorphisms: Keeping shares of a secret secret. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 251–260. Springer, Heidelberg (1987)
Blackburn, S.R.: Combinatorics and Threshold Cryptology. In: Combinatorial Designs and their Applications (Chapman and Hall/CRC Research Notes in Mathematics), pp. 49–70. CRC Press, London (1999)
Blackburn, S.R., Burmester, M., Desmedt, Y., Wild, P.R.: Efficient multiplicative sharing schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 107–118. Springer, Heidelberg (1996)
Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of AFIPS 1979 National Computer Conference, vol. 48, pp. 313–317 (1979)
Czech, Z.J., Havas, G., Majewski, B.S.: Perfect Hashing. Theoretical Computer Science 182, 1–143 (1997)
De Santis, A., Desmedt, Y., Frankel, Y., Yung, M.: How to share a function securely. In: Proc. 26th Annual Symp. on the Theory of Computing, pp. 522–533. ACM, New York (1994)
Desmedt, Y.: Some recent research aspects of threshold cryptography. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 99–114. Springer, Heidelberg (1998)
Desmedt, Y., Di Crescenzo, G., Burmester, M.: Multiplicative non-abelian sharing schemes and their application to threshold cryptography. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 21–32. Springer, Heidelberg (1995)
Desmedt, Y., Frankel, Y.: Homomorphic zero-knowledge threshold schemes over any finite group. SIAM J. Disc. Math. 7, 667–679 (1994)
Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–490. Springer, Heidelberg (1994)
Jackson, W.-A., Martin, K., O’keefe, C.M.: Mutually trusted authority free secret sharing schemes. J. Cryptology 10, 261–289 (1997)
Mehlhorn, K.: Data Structures and Algorithms, vol. 1. Springer, Heidelberg (1984)
Shamir, A.: How to Share a Secret. Communications of the ACM 22, 612–613 (1979)
Stinson, D.R.: An explication of secret sharing schemes. Des. Codes Cryptogr. 2, 357–390 (1992)
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Wang, H., Lam, K.Y., Xiao, GZ., Zhao, H. (2000). On Multiplicative Secret Sharing Schemes. In: Dawson, E.P., Clark, A., Boyd, C. (eds) Information Security and Privacy. ACISP 2000. Lecture Notes in Computer Science, vol 1841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10718964_28
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DOI: https://doi.org/10.1007/10718964_28
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