This article documents some of the known constructions for secret sharing schemes. It includes a discussion of the mathematical structures which have been used to model secret sharing schemes, the establishment of secret sharing schemes which do not require the existence of a trusted authority to administer them, variations which can be incorporated into these schemes to increase their flexibil...

A rational secret sharing scheme is a game in which each party responsible for reconstructing a secret tries to maximize his utility by obtaining the secret alone. Quantum secret sharing schemes, either derived from quantum teleportation or from quantum error correcting code, do not succeed when we assume rational participants. This is because all existing quantum secret sharing schemes conside...

In this paper, we attempt to construct practical secret sharing schemes, which scheme has smaller share size and can detect cheating with high probability. We de ne two secure ramp schemes, secure ramp scheme and strongly secure ramp scheme. Then, we propose two constructions of secure ramp scheme. These schemes both have small share size and the cheating can be detected with high probability. ...

Verifiable secret sharing is a cryptographic primitive used in many distributed applications. To engineer realistic applications, it is beneficial to have dynamically changing shares and shareholder groups. Proactive secret sharing schemes deal with dynamically changing shares. Secret redistribution schemes solve issues of both dynamically changing shares and shareholder groups. In this dissert...

A secret sharing scheme is a cryptographic protocol by means of which a dealer shares a secret among a set of participants in such a way that it can be subsequently reconstructed by certain qualiied subsets. The setting we consider is the following: in a rst phase, the dealer gives in a secure way a piece of information, called a share, to each participant. Then, participants belonging to a qua...

We show a general connection between various types of statistical zero-knowledge (SZK) proof systems and (unconditionally secure) secret sharing schemes. Viewed through the SZK lens, we obtain several new results on secret-sharing: • Characterizations: We obtain an almost-characterization of access structures for which there are secret-sharing schemes with an efficient sharing algorithm (but no...

Secret sharing allows a dealer to distribute a secret among multiple parties such that authorized coalitions can reconstruct the secret. Traditionally, the dealer knows the exact share each user holds. Grigoriev and Shpilrain recently considered secret sharing systems for which the dealer does not know the share of a particular party and introduced a construction for the special case of all-or-...

A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this en...

Secret sharing schemes for classical secrets can be classified into secret and quantum schemes. Classical has been known to able distribute some shares before a given secret. On the other hand, mechanics extends capabilities of beyond those sharing. We propose with in designing access structures more flexibly realizing higher efficiency sharing, that