This paper proposes a new construction of the visual secret sharing scheme for the (n, n)-threshold access structure applicable to color images. The construction uses matrices with n rows that can be identified with homogeneous polynomials of degree n. It is shown that, if we find a set of homogeneous polynomials of degree n satisfying a certain system of simultaneous partial differential equat...

In a ciphertext policy attribute based encryption system, a user’s private key is associated with a set of attributes (describing the user) and an encrypted ciphertext will specify an access policy over attributes. A user will be able to decrypt if and only if his attributes satisfy the ciphertext’s policy. In this work, we present the first construction of a ciphertext-policy attribute based e...

This paper is an explication of secret sharing schemes, emphasizing combinatorial construction methods. The main problem we consider is the construction of perfect secret sharing schemes, for specified access structures, with the maximum possible information rate. In this paper, we present numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean...

In this thesis, we explain linear secret sharing schemes, in particular multiplicative threshold linear secret sharing schemes, over fields and rings in a compact and concise way. We explain two characterisations of linear secret sharing schemes, and in particular, we characterise threshold linear secret sharing schemes. We develop an algorithm to generate all multiplicative (t+ 1)-out-of-n thr...

In this paper we introduce the class of composite access structures for secret sharing. We also provide secret sharing schemes realizing these structures and study their information rates. As a particular case of this construction, we present the subclass of iterated threshold schemes, a large class of ideal secret sharing schemes.

How to construct an ideal multi-secret sharing scheme for general access structures is difficult. In this paper, we solve an open problem proposed by Spiez et al.recently [Finite Fields and Their Application, 2011(17) 329-342], namely to design an algorithm of privileged coalitions of any length if such coalitions exist. Furthermore, in terms of privileged coalitions, we show that most of the e...

In this paper we provide upper and lower bounds on the randomness required by the dealer to set up a secret sharing scheme for innnite classes of access structures. Lower bounds are obtained using entropy arguments. Upper bounds derive from a decomposition construction based on combinatorial designs (in particular, t-(v; k;) designs). We prove a general result on the randomness needed to constr...

In this paper we study anonymous secret sharing schemes. Informally, in an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In such schemes the computation of the secret can be carried out by giving the shares to a black box that does not know the identities of the participants holding those shares. Phillips and Phillips ...

The physical theory of phase transition explains sudden changes of phase in materials that undergo gradual changes of some parameter like temperature. There are analogs of phase transition in the theory of random graphs, initiated by ErdGs and Renyi. This paper gives a nontechnical but precise account, without proofs, of some of the beautiful discoveries of Erdijs and RCnyi about threshold phen...