A characterisation of ideal weighted secret sharing schemes

Journal of mathematical cryptology

article

Ali Hameed¹  Arkadii Slinko¹ 

[1] Department of Mathematics, The University of Auckland, Private Bag 92019

关键词: Secret sharing scheme;    access structure;    simple game;    composition of games;   

DOI  :  10.1515/jmc-2015-0002

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Beimel, Tassa and Weinreb [SIAM J. Discrete Math. 22 (2008), 360–397] and Farràs and Padró [Lecture Notes in Comput. Sci. 5978, Springer, 2010, 219–236] partially characterised access structures of ideal weighted secret sharing schemes in terms of the operation of composition. They proved that any weighted ideal access structure is a composition of indecomposable ones. Farràs and Padró gave a list of seven classes of access structures – one unipartite, three bipartite and three tripartite – to which all weighted ideal indecomposable access structures may belong. In this paper we determine exactly which access structures from those classes are indecomposable. We also determine which compositions of indecomposable weighted access structures are again weighted and obtain an if-and-only-if characterisation of ideal weighted secret sharing schemes. We use game-theoretic techniques to achieve this.

【 授权许可】

CC BY|CC BY-NC-ND