An optimal class of symmetric key generation systems
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Elements of information theory
Elements of information theory
An explication of secret sharing schemes
Designs, Codes and Cryptography
Geometric secret sharing schemes and their duals
Designs, Codes and Cryptography
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
On Some Methods for Unconditionally Secure Key Distributionand Broadcast Encryption
Designs, Codes and Cryptography - Special issue: selected areas in cryptography I
Communications of the ACM
Cryptography: Theory and Practice
Cryptography: Theory and Practice
On the Key Predistribution System: A Practical Solution to the Key Distribution Problem
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Perfectly-Secure Key Distribution for Dynamic Conferences
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
A new authenticated group key transfer protocol for actual network environment
International Journal of Ad Hoc and Ubiquitous Computing
On the security of an authenticated group key transfer protocol based on secret sharing
ICT-EurAsia'13 Proceedings of the 2013 international conference on Information and Communication Technology
A New Secure Authenticated Group Key Transfer Protocol
Wireless Personal Communications: An International Journal
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In a key predistribution scheme a trusted authority distributes pieces of information among a set of users in such a way that users belonging to a specified privileged subset can compute individually a secret key common to this subset. In such a scheme, a family of forbidden subsets of users cannot obtain any information about the value of the secret. In this paper, we present a new construction of a key predistribution scheme using a family of vector space secret sharing schemes. The set of privileged users and the family of forbidden subsets is described in terms of the family of vector space access structures. A generalization using linear secret sharing schemes is given. We show that a particular case of this construction is any key predistribution scheme in which pieces of information and secrets are linear combinations of random numbers. Using this result, we show explicitly that the most important key predistribution schemes can be seen as a particular case of this construction. For this construction, the question of when given secrets can be predistributed is discussed.