This paper first reviews some basic properties of cryptographic hash function, secret sharing scheme, and Latin square. Then we discuss why Latin square or its critical set is a good choice for secret representation and its relationship with secret sharing scheme. Further we enumerate the limitations of Latin square in a secret sharing scheme. Finally we propose how to apply cryptographic hash ...

We propose efficient secret sharing schemes realizing general access structures. Our proposed schemes are perfect secret sharing schemes and include Shamir’s (k, n)-threshold schemes as a special case. Furthermore, we show that a verifiable secret sharing scheme for general access structures is realized by one of the proposed schemes. key words: (k, n)-threshold scheme, general access structure...

In 1979, secret sharing schemes were first proposed by Blakley and Shamir. In a secret sharing scheme, each participant receives a share of a secret in such a way that only authorized subsets can reconstruct the secret. Later, Wu and He proposed a (t, n)-threshold scheme for sharing a secret based on a hyperspherical function (HS-TS). Their scheme give a practical algorithm to solve the problem...

In the visual secret sharing scheme proposed by Naor and Shamir [3], a secret image is encoded into shares, of which size is larger than that of the secret image and the shares are decoded by stacking them without performing any cryptographic computation. In this paper we propose a (k, n) visual secret sharing scheme to encode a black-and-white image into the same size shares as the secret imag...

In Shamir’s (t, n) threshold secret sharing scheme, one secret s is divided into n shares by a dealer and all shares are shared among n shareholders, such that knowing t or more than t shares can reconstruct this secret; but knowing fewer than t shares cannot reveal any information about the secret s. The secret reconstruction phase in Shamir’s (t, n) threshold secret sharing is very simple and...

Secret Sharing techniques are now the building blocks of several security protocols. A (t, n) threshold secret sharing scheme is one in which t or more participant can join together to retrieve the secret.Traditional single secret sharing schemes are modified and generalized to share multiple secrets.Use of elliptic curve and pairing in secret sharing is gaining more importance.In this paper we...

We introduce and formally define polynomial commitment schemes, and provide two efficient constructions. A polynomial commitment scheme allows a committer to commit to a polynomial with a short string that can be used by a verifier to confirm claimed evaluations of the committed polynomial. Although the homomorphic commitment schemes in the literature can be used to achieve this goal, the sizes...

A secret sharing scheme is a method to distribute a secret among a set of participants, such that only qualified subsets of the participants can recover the secret. A secret sharing scheme is perfect if any unqualified subset obtains no information regarding the master key. The collection of qualified subsets is called access structure. In a hypergraph, if the size of edges is equal to r, the h...