On Multiplicative Secret Sharing Schemes

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.

[1]  Ueli Maurer,et al.  Advances in Cryptology — EUROCRYPT ’96 , 2001, Lecture Notes in Computer Science.

[2]  Douglas R. Stinson,et al.  Advances in Cryptology — CRYPTO’ 93 , 2001, Lecture Notes in Computer Science.

[3]  G. R. BLAKLEY.  Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[4]  George Havas,et al.  Perfect Hashing , 1997, Theor. Comput. Sci..

[5]  Yvo Desmedt,et al.  Some Recent Research Aspects of Threshold Cryptography , 1997, ISW.

[6]  Douglas R. Stinson,et al.  An explication of secret sharing schemes , 1992, Des. Codes Cryptogr..

[7]  Yvo Desmedt,et al.  Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group , 1994, SIAM J. Discret. Math..

[8]  Giovanni Di Crescenzo,et al.  Multiplicative Non-abelian Sharing Schemes and their Application to Threshold Cryptography , 1994, ASIACRYPT.

[9]  Andrew Odlyzko,et al.  Advances in Cryptology — CRYPTO’ 86 , 2000, Lecture Notes in Computer Science.

[10]  Douglas R Stinson,et al.  Some recursive constructions for perfect hash families , 1996 .

[11]  Moti Yung,et al.  How to share a function securely , 1994, STOC '94.

[12]  Amos Fiat,et al.  Broadcast Encryption , 1993, CRYPTO.

[13]  Josh Benaloh,et al.  Secret Sharing Homomorphisms: Keeping Shares of A Secret Sharing , 1986, CRYPTO.

[14]  Yvo Desmedt,et al.  Efficient Multiplicative Sharing Schemes , 1996, EUROCRYPT.

[15]  Tsutomu Matsumoto,et al.  Incidence structures for key sharing , 1995 .

[16]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[17]  Keith M. Martin,et al.  Mutually Trusted Authority-Free Secret Sharing Schemes , 1997, Journal of Cryptology.

[18]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .