Related papers: Randomness Requirements for Three-Secret Sharing
We consider a secret-sharing model where a dealer distributes the shares of a secret among a set of participants with the constraint that only predetermined subsets of participants must be able to reconstruct the secret by pooling their…
In this paper, we study an information-theoretic secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the following constraints: (i) authorized sets of users can recover the secret by…
We consider a distributed secret sharing system that consists of a dealer, $n$ storage nodes, and $m$ users. Each user is given access to a certain subset of storage nodes, where it can download the stored data. The dealer wants to securely…
In this paper, we consider the case that sharing many secrets among a set of participants using the threshold schemes. All secrets are assumed to be statistically independent and the weak secure condition is focused on. Under such…
A dealer aims to share a secret with participants so that only predefined subsets can reconstruct it, while others learn nothing. The dealer and participants access correlated randomness and communicate over a one-way, public, rate-limited…
The motivation for extending secret sharing schemes to cases when either the set of players is infinite or the domain from which the secret and/or the shares are drawn is infinite or both, is similar to the case when switching to abstract…
Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…
We consider the problem of secret key extraction when $n$ honest parties and an eavesdropper share correlated information. We present a family of probability distributions and give the full characterization of its distillation properties.…
I present a variety of results on the theory of quantum secret sharing. I show that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantum…
There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access…
The evolving $k$-threshold secret sharing scheme allows the dealer to distribute the secret to many participants such that only no less than $k$ shares together can restore the secret. In contrast to the conventional secret sharing scheme,…
Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in…
In quantum secret sharing, a quantum secret state is mapped to multiple shares such that shares from qualified sets can recover the secret state and shares from other forbidden sets reveal nothing about the secret state; we study the…
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of…
Threshold secret sharing schemes do not prevent any malicious behavior of the dealer or shareholders and so we need verifiable secret sharing, to detect and identify the cheaters, to achieve fair reconstruction of a secret. The problem of…
Sharing a secret efficiently amongst a group of participants is not easy since there is always an adversary / eavesdropper trying to retrieve the secret. In secret sharing schemes, every participant is given a unique share. When the desired…
For the multiterminal secret key agreement problem, new single-letter lower bounds are obtained on the public discussion rate required to achieve any given secret key rate below the secrecy capacity. The results apply to general source…
Secret sharing is the well-known problem of splitting a secret into multiple shares, which are distributed to shareholders. When enough or the correct combination of shareholders work together the secret can be restored. We introduce two…
A novel information theoretic approach is proposed to solve the secret sharing problem, in which a dealer distributes one or multiple secrets among a set of participants that for each secret only qualified sets of users can recover it by…
Shamir's celebrated secret sharing scheme provides an efficient method for encoding a secret of arbitrary length $\ell$ among any $N \leq 2^\ell$ players such that for a threshold parameter $t$, (i) the knowledge of any $t$ shares does not…