The algebraic setting for threshold secret sharing scheme can vary, dependent on the application. This algebraic setting can limit the number of participants of an ideal secret sharing scheme. Thus it is important to know for which thresholds one could utilize an ideal threshold sharing scheme and for which thresholds one would have to use nonideal schemes. The implication is that more than one...

Due to the rapid growth of the next generation networking and system technologies, computer networks require new design and management. In this context, security, and more specifically, access structures have been one of the major concerns. As such, in this article, sequential secret sharing (SQS), as an application of dynamic threshold schemes, is introduced. In this new cryptographic primitiv...

Quantum secret sharing is a scheme for encoding a quantum state (the secret) into multiple shares and distributing them among several participants. If a sufficient number of shares are put together, then the secret can be fully reconstructed. If an insufficient number of shares are put together however, no information about the secret can be revealed. In quantum ramp secret sharing, partial inf...

Lee and Hwang proposed a multi-stage (t, n) secret sharing scheme which has fewer public values than pervious schemes. In their scheme, a group of participants share multiple secrets stage-by-stage, and only one secret share should been kept by each participant. However, in this article, we will show that multiple secrets cannot, in fact, be reconstructed stage-by-stage by the secret holder’s d...

A well-known fact in the theory of secret sharing schemes is that shares must be of length at least as the secret itself. However, the proof of this lower bound uses the notion of information theoretic secrecy. A natural (and very practical) question is whether one can do better for secret sharing if the notion of secrecy is computational, namely, against resource bounded adversaries. In this n...

We define the notion of an arithmetic codex (or codex, for short), and as a special case, arithmetic secret sharing. This notion encompasses as well as generalizes, in a single mathematical framework, all known types of specialized secret sharing schemes from the area of secure multi-party computation, i.e., the so-called (strongly) multiplicative linear secret sharing schemes. These schemes we...

Recently, verifiable secret sharing schemes have been proposed to keep participants from providing fake or illegal stego-images. However, the schemes do not consider the recovery mechanism when parts of the information in stego-images are lost or incidentally modified during the transmission process. This paper presents a novel verifiable and reversible secret sharing scheme based on Shamir’s s...

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) p...

In anonymous secret sharing schemes, the secret can be reconstructed without knowledge of which participants hold which shares. In this paper, we derive a tighter lower bound on the size of the shares than the bound of Blundo and Stinson for anonymous (k, n)threshold schemes with 1 < k < n. Our bound is tight for k = 2. We also show a close relationship between optimum anonymous (2, n)threshold...

Protocols for Generalized Oblivious Transfer(GOT) were introduced by Ishai and Kushilevitz [10]. They built it by reducing GOT protocols to standard 1-out-of-2 oblivious transfer protocols based on private protocols. In our protocols, we provide alternative reduction by using secret sharing schemes instead of private protocols. We therefore show that there exist a natural correspondence between...