Secret sharing schemes perform an important role in protecting se-cret by sharing it among multiple participants. In 1979, (t; n) threshold secret sharing schemes were proposed by Shamir and Blakley independently. In a (t; n) threshold secret sharing scheme a secret can be shared among n partic-ipants such that t or more participants can reconstruct the secret, but it can not be reconstructed b...

‎In a (t,n)-threshold secret sharing scheme‎, ‎a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together‎, ‎but no group of fewer than t participants can do‎. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao‎, ‎and the intractability of the elliptic curve discrete logar...

A threshold scheme is a system that protects a secret (key) among a group of participants in such a way that it can only be reconstructed from the joint information held by some predetermined number of these participants. In this paper we extend this problem to one where there is more than one secret that participants can reconstruct using the information that they hold. In particular we consid...

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...

A secret sharing scheme derives from a given secret certain shares (or shadows) which are distributed to users. The secret can be recovered only by certain predetermined groups. In the first secret sharing schemes only the number of the participants in the reconstruction phase was important for recovering the secret. Such schemes have been referred to as threshold secret sharing schemes. In the...

(t, n)-threshold secret sharing was first introduced by Shamir and Blakley separately in 1979. Apart from this, there are threshold secret sharing schemes which use the Chinese Remainder Theorem (CRT). The above mentioned are three of the most extensively researched tools used for designing a (t, n)-threshold secret sharing scheme. In this paper we propose a scheme for Multilevel Threshold Secr...

A , (m  ) n threshold secret sharing scheme is a method for distributing a secret amongst a group of participants. In a , (m  ) n threshold secret sharing scheme any m participants recover the secret, but no ) 1 (  m participants can [6]. Each of participants is allocated a share of the secret. The secret can only be reconstructed when the shares are combined together [2]. In this paper, we ...

A (k, n) threshold secret image sharing scheme, abbreviated as (k, n)-TSISS, splits a secret image into n shadow images in such a way that any k shadow images can be used to reconstruct the secret image exactly. In 2002, for (k, n)-TSISS, Thien and Lin reduced the size of each shadow image to 1 k of the original secret image. Their main technique is by adopting all coefficients of a (k − 1)-deg...

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...