Abstract
In a threshold secret sharing scheme, a dishonest participant can disrupt the operation of the system by submitting junk instead of his/her share. We propose two constructions for threshold secret sharing schemes that allow identification of cheaters where the secret is an element of the ringZ m . The main motivation of this work is to design RSA-based threshold cryptosystems, such as robust threshold RSA signature, in which additive (multiplicative) threshold secret sharing schemes over Abelian groups with cheater identification play the central role. The first construction extends Desmedt-Frankel’s construction of secret sharing over Z m to provide cheater detection, and the second construction uses perfect hash families to construct a robust (t, n) scheme from a (t, t) scheme. We prove security of these schemes and assess their performance.
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
N. Alon and M. Naor, Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions. Algorithmica, 16 (1996), 434–449.
M. Atici, S.S. Magliveras, D. R. Stinson and W.D. Wei, Some Recursive Constructions for Perfect Hash Families. Journal of Combinatorial Designs, 4 (1996), 353–363.
J. C. Benaloh, Secret sharing homomorphisms: Keeping shares of a secret secret. In Advances in Cryptology - Crypto ‘86, LNCS, 263 (1986), 251–260.
S. R. Blackburn, Combinatorics and Threshold Cryptology. In Combinatorial Designs and their Applications (Chapman and Hall/CRC Research Notes in Mathematics), CRC Press, London, 1999,49–70.
S.R. Blackburn, S. Blake-Wilson, M. Burmester and S. Galbraith, Shared generation of shared RSA keys. Tech. Report CORR98–19, University of Waterloo, 1998.
S. R. Blackburn, M. Burmester, Y. Desmedt and P. R. Wild, Efficient multiplicative sharing schemes. In Advances in Cryptology - Eurocrypt ‘86,LNCS, 1070 (1996), 107–118.
G. R. Blakley, Safeguarding cryptographic keys. In Proceedings of AFIPS 1979 National Computer Conference, 48 (1979), 313–317.
D. Boneh and M. Franklin, Efficient generation of shared RSA keys. In Advances in Cryptology - Crypto ‘87,LNCS, 1294 (1997), 425–439.
C. Boyd, Digital multisignatures, In Cryptography and coding,Clarendon Press, 1989, 241–246.
E. Brickell and D. Stinson, The Detection of Cheaters in Threshold Schemes. In Advances in Cryptology - Proceedings of CRYPTO ‘88, LNCS, 403 (1990), 564–577.
Z. J. Czech, G. Havas and B.S. Majewski, Perfect Hashing. Theoretical Computer Science, 182 (1997), 1–143.
C. Cocks, Split knowledge generation of RSA parameters. In Cryptography and Coding, 6th IMA Conference, LNCS, 1355 (1997), 89–95.
Y. Desmedt, Some recent research aspects of threshold cryptography. In Information Security Workshop, Japan (JSW ‘87), LNCS, 1396 (1998), 99–114.
Y. Desmedt, G. Di Crescenzo and M. Burmester, Multiplicative non-abelian sharing schemes and their application to threshold cryptography. InAdvances in Cryptology - Asiacrypt ‘84, LNCS, 917 (1995), 21–32.
Y. Desmedt and Y. Frankel, Homomorphic zero-knowledge threshold schemes over any finite group. SIAM J. Disc. Math., 7 (1994), 667–679.
Y. Desmedt, B. King, W. Kishimoto and K. Kurosawa, A comment on the efficiency of secret sharing scheme over any finite abelian group. In Information Security and Privacy,ACISP’98 (Third Australasian Conference on Information Security and Privacy), LNCS, 1438 (1998), 391–402.
Y. Frankel, A practical protocol for large group oriented networks. In Advances in Cryptology - Eurocrypt ‘89, LNCS, 434 (1989), 56–61.
E. Karnin, J. Greene, and M. Hellman, On Secret Sharing Systems. IEEE Transactions on Information Theory, 29 (1983), 35–41.
K. Mehlhorn, Data Structures and Algorithms. Vol. 1, Springer-Verlag, 1984.
A. Shamir, How to Share a Secret. Communications of the ACM, 22 (1979), 612–613.
G. Simmons, W.-A. Jackson and K. Martin, The Geometry of Shared Secret Schemes. Bulletin of the Institute of Combinatorics and its Applications (ICA), 1 (1991), 71–88.
D.R. Stinson, An explication of secret sharing schemes. Des. Codes Cryptogr., 2 (1992), 357–390.
M. Tompa and H. Woll, How To Share a Secret with Cheaters. Journal of Cryptology, 1 (1988), 133–138.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Safavi-Naini, R., Wang, H. (2001). Robust Additive Secret Sharing Schemes over Z m . In: Lam, KY., Shparlinski, I., Wang, H., Xing, C. (eds) Cryptography and Computational Number Theory. Progress in Computer Science and Applied Logic, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8295-8_26
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8295-8_26
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9507-1
Online ISBN: 978-3-0348-8295-8
eBook Packages: Springer Book Archive