FUNCTION AND SECRET SHARING EXTENSIONS FOR BLAKLEY AND ASMUTH-BLOOM SECRET SHARING SCHEMES İlker Nadi Bozkurt M.S. in Computer Engineering Supervisor: Assist. Prof. Dr. Ali Aydın Selçuk August, 2009 Threshold cryptography deals with situations where the authority to initiate or perform cryptographic operations is distributed amongst a group of individuals. Usually in these situations a secret s...

The aim of a secret sharing scheme is to share a secret among a group of participants in such a way that while authorized subsets of participants are able to recover the secret, non-authorized subsets of them obtain no information about it. Multi-secret sharing is the natural generalization of secret sharing for situations in which the simultaneous protection of more than one secret is required...

Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorised subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct numbers, usually positive...

A t-out-of-n secret-sharing scheme allows an honest dealer D to distribute a secret s among n players, such that any subset of t players has no information about s, but every set of t + 1 players can collaboratively reconstruct the secret. The most famous secret-sharing scheme is Shamir’s Sharing Scheme [Sha79] (cf. Section 8.1.2). It uses polynomials to obtain the desired properties. Before pr...

A t-out-of-n secret-sharing scheme allows an honest dealer D to distribute a secret s among n players, such that any subset of t players has no information about s, but every set of t + 1 players can collaboratively reconstruct the secret. The most famous secret-sharing scheme is Shamir’s Sharing Scheme [Sha79] (cf. Section 7.1.2). It uses polynomials to obtain the desired properties. Before pr...

A proactive secret sharing scheme is a method of sharing a secret among a set of participants. And, the corresponding shadows can be periodically renewed under the premise of never changing the shared secret. However, in the most existing proactive secret sharing schemes, only one secret can be shared during one secret sharing process. The proposed scheme describes PMSS, a new way to share mult...

A simple secret sharing scheme for secure visual communications is presented in this paper. Secret sharing schemes allow a group of participants at different locations to share a secret (i.e., an image) among them by splitting it into n pieces (“shares” or “shadows”). In case of the (k, n) secret sharing scheme only a group of k qualified participants among n (where k ≤ n) can reconstruct the s...

In this paper, we attempt to construct practical secret sharing schemes, which scheme has smaller share size and can detect cheating with high probability. We de ne two secure ramp schemes, secure ramp scheme and strongly secure ramp scheme. Then, we propose two constructions of secure ramp scheme. These schemes both have small share size and the cheating can be detected with high probability. ...

In 2004, C.-C. Yang, T.-Y. Chang and M.-S. Hwang proposed an efficient multi-secret sharing scheme based on two-variable one-way function and Shamir's secret sharing. In order to add the verifiable property into previous scheme, J. Shao and Z. Cao proposed an efficient (t,n) verifiable multi-secret sharing based on YCH [C.-C. Yang, T.-Y. Chang, M.-S. Hwang, A (t,n) multi-secret sharing scheme, ...

In a (t,n) secret sharing scheme, a mutually trusted dealer divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret, but fewer than t shares cannot reconstruct the secret. When there is no mutually trusted dealer, a (n,t,n) secret sharing scheme can be used to set up a (t,n) secret sharing because each shareholder also acts as a dealer to decide ...