It is well-known that the linear secret-sharing scheme (LSSS) can be constructed from linear error-correcting codes (Brickell [1], R.J. McEliece and D.V.Sarwate [2],Cramer, el.,[3]). The theory of linear codes from algebraic-geometric curves (algebraic-geometric (AG) codes or geometric Goppa code) has been well-developed since the work of V.Goppa and Tsfasman, Vladut, and Zink( see [17], [18] a...

Secret sharing schemes are methods for distributing a secret among n participants in such a way that any qualified subsets of participants can recover the secret, and unqualified participants can not. In 1979, secret sharing schemes were first independently introduced by Blakley and Shamir. In 1987, Feldman proposed a verifiable secret sharing scheme based on Shamir’s Scheme, that every partici...

Secret image sharing, as an extension of secret sharing, has attracted the attention of many scholars in recent years. Multi-secret image sharing is an extension of traditional secret image sharing in which only one secret image can be shared among one group. In order to extend the utility of the mechanism, we propose an innovative (n, n) secret image sharing scheme based on matrix transformati...

An efficient threshold scheme is proposed in this paper. It overcomes the weakness of Asmuth et al.’s scheme. The (r, n)-threshold scheme proposed below only takes O(r) operations to recover the shared secret while Shamir’s scheme takes O(rlogr) operations. We show that our scheme is perfect. Further, we also propose a method to generate a pairwise relatively prime integer set which satisfies t...

A novel multi secret sharing scheme is proposed in this paper. In the scheme, n secret images are firstly encrypted by hyper-chaos whose initial values are hash of the image itself. Then the encrypted images are shuffled into n confused images; lastly, the confused images are used to generate n sharing images using the random grid method. The proposed scheme has the advantage such that it can l...

A non-interactive (t,n)-publicly veriable secret sharing scheme (non-interactive (t,n)-PVSS scheme) is a (t,n)-secret sharing scheme in which anyone, not only the participants of the scheme, can verify the correctness of the produced shares without interacting with the dealer and participants. The (t,n)-PVSS schemes have found a lot of applications in cryptography because they are suitable for<...

In [3] Damgard and Thorbek proposed the linear integer secret sharing (LISS) scheme. In this note we show that the LISS scheme can be made proactive.