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A secret sharing scheme is a system designed to share a piece of information or the secret among a group of people such that only authorized people can reconstruct the secret from their shares. Since Blakley and Shamir proposed threshold secret sharing schemes in 1979 independently, many secret sharing schemes have been constructed. In this paper, we present several threshold schemes that are generalizations of Shamir's secret sharing scheme.

In principle, every linear code can be used to construct a secret sharing scheme. However, determining the access structure of the scheme is a very difficult problem. In this paper, we study MacDonald codes over the finite non-chain ring ${\mathbb{F}}_p+v{\mathbb{F}}_p$, where p is a prime and $v^2=v$. We provide a method to construct a class of two-weight linear codes over the ring. Then, we determine the access structure of secret sharing schemes based on these codes.

This paper firstly provides a formal definition of the n out of n extended color visual cryptography scheme (ECVCS) based on the XOR cipher, where a color secret image and k color cover images are encoded into n shares in such a way that the n shares present cover images individually and any n shares and above will recover the secret image while any less than n shares, will not reveal any information about the secret image. The proposed scheme in the paper has no extra expansion and it can easily trade the visual quality of the recovery image with the visual quality of shares by changing the value of a certain parameter in the scheme. The validity of the proposed scheme is verified by formal proofs, and its feasibility is demonstrated by computer simulations.