Generalised cumulative arrays in secret sharing

Long, Shoulun, Pieprzyk, Josef, Wang, Huaxiong, & Wong, Duncan S. (2006) Generalised cumulative arrays in secret sharing. Designs, Codes and Cryptography, 40(2), pp. 191-209.

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Cumulative arrays have played an important role in the early development of the secret sharing theory. They have not been subject to extensive study so far, as the secret sharing schemes built on them generally result in much larger sizes of shares, when compared with other conventional approaches. Recent works in threshold cryptography show that cumulative arrays may be the appropriate building blocks in non-homomorphic threshold cryptosystems where the conventional secret sharing methods are generally of no use. In this paper we study several extensions of cumulative arrays and show that some of these extensions significantly improve the performance of conventional cumulative arrays. In particular, we derive bounds on generalised cumulative arrays and show that the constructions based on perfect hash families are asymptotically optimal. We also introduce the concept of ramp perfect hash families as a generalisation of perfect hash families for the study of ramp secret sharing schemes and ramp cumulative arrays.

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4 citations in Scopus
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3 citations in Web of Science®

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ID Code: 73455
Item Type: Journal Article
Refereed: Yes
Keywords: Secret sharing, Cumulative array, Perfect hash family
DOI: 10.1007/s10623-006-0007-5
ISSN: 1573-7586
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2006 Springer
Deposited On: 07 Jul 2014 23:07
Last Modified: 14 Jul 2014 06:39

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