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...

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 a threshold scheme, the sensitivity of the secret as well as the number of players may fluctuate due to various reasons, e.g., mutual trust may vary or the structure of the players’ organization might be changed. A possible solution to this problem is to modify the threshold and/or change the secret. Moreover, a common problem with almost all secret sharing schemes is that they are “one-time...

An (m, n) threshold scheme is to decompose the master key K into n secret shadows in such a way that the master key K cannot be reclaimed unless any m shadows are collected. However, any m 1 or fewer shadows provide absolutely no information about K. In 1989, Laih et al. proposed the concept of dynamic threshold schemes which allow the master key to be updated without changing the secret shadow...

In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure by an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop a...

By using a recently introduced framework for non-perfect secret sharing, several known results on perfect secret sharing are generalized. Specifically, we discuss about ideal secret sharing schemes, constructions of efficient linear secret sharing schemes, and the search for lower bounds on the length of the shares. Similarly to perfect secret sharing, matroids and polymatroids are very useful ...

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...

For a secret sharing scheme, two parameters dmin and dcheat are defined in [1] and [2]. These two parameters measure the errorcorrecting capability and the secret-recovering capability of the secret sharing scheme against cheaters. Some general properties of the parameters have been studied in [1-3]. The MDS secret-sharing scheme is defined in [2] and it is proved that MDS perfect secret sharin...

Terrorist fraud is a class of relay attacks against distancebounding (DB) protocols in which a distant malicious prover colludes with an attacker located in a verifier’s proximity when authenticating. Existing DB protocols resisting such attacks are designed to be lightweight and thus symmetric, relying on a secret shared by the prover and the verifier. Recently, several asymmetric distance-bou...

A multi{secret sharing scheme is a protocol to share a number of (arbitrarily related) secrets among a set of participants in such a way that only quali ed sets of participants can recover the secrets, whereas non-quali ed sets of participants might have partial information about them. In this paper we analyze the amount of randomness needed by multi{secret sharing schemes. Given an m-tuple of ...