Related papers: MDS Ideal Secret Sharing Scheme from AG-codes on E…
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,…
A Homomorphic Secret Sharing (HSS) scheme is a secret-sharing scheme that shares a secret $x$ among $s$ servers, and additionally allows an output client to reconstruct some function $f(x)$, using information that can be locally computed by…
This paper investigates the construction of efficient quantum secret sharing schemes for quantum access structures based on hypergraphs with three hyperedges. We prove that hypercycles with three hyperedges are quantum access structures if…
The secret sharing schemes are the important tools in cryptography that are used as building blocks in many secured protocols. It is a method used for distributing a secret among the participants in a manner that only the threshold number…
New families of maximum distance separable (MDS) codes are constructed from elliptic curves by exploiting their group structures. In contrast to classical constructions based on divisors supported at a single rational point, the proposed…
We consider a distributed multi-user secret sharing (DMUSS) setting in which there is a dealer, $n$ storage nodes, and $m$ secrets. Each user demands a $t$-subset of $m$ secrets. Earlier work in this setting dealt with the case of $t=1$; in…
A common approach of system identification and machine learning is to generate a model by using training data to predict the test data instances as accurate as possible. Nonetheless, concerns about data privacy are increasingly raised, but…
Motivated by the application of high-density data storage technologies, symbol-pair codes are proposed to protect against pair-errors in symbol-pair channels, whose outputs are overlapping pairs of symbols. The research of symbol-pair codes…
Shamir's (n, k) threshold secret sharing is an important component of several cryptographic protocols, such as those for secure multiparty-computation and key management. These protocols typically assume the presence of direct communication…
This paper introduces the first two-dimensional XOR-based secret sharing scheme for layered multipath communication networks. We present a construction that guarantees successful message recovery and perfect privacy when an adversary…
Recently, an information theoretical model for Quantum Secret Sharing (QSS) schemes was introduced. By using this model, we prove that pure state Quantum Threshold Schemes (QTS) can be constructed from quantum MDS codes and vice versa. In…
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…
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…
This paper considers the problem of outsourcing the multiplication of two private and sparse matrices to untrusted workers. Secret sharing schemes can be used to tolerate stragglers and guarantee information-theoretic privacy of the…
This paper addresses the problem of constructing secure exact-repair regenerating codes at the MSR point for all feasible values of the parameters. The setting involves a passive eavesdropper who is allowed to observe the stored contents…
Binary maximum distance separable (MDS) array codes are a special class of erasure codes for distributed storage that not only provide fault tolerance with minimum storage redundancy but also achieve low computational complexity. They are…
We consider the problem of private distributed multi-party multiplication. It is well-established that Shamir secret-sharing coding strategies can enable perfect information-theoretic privacy in distributed computation via the celebrated…
A (t,n)-threshold secret sharing scheme is a method to distribute a secret among n participants in such a way that any t participants can recover the secret, but no t-1 participants can. In this paper, we propose two secret sharing schemes…
In this paper, we propose a class of threshold secret sharing schemes with repairing function between shares without the help of the dealer, that we called repairable threshold secret sharing schemes. Specifically, if a share fails, such as…
A linear code with parameters of the form $[n, k, n-k+1]$ is referred to as an MDS (maximum distance separable) code. A linear code with parameters of the form $[n, k, n-k]$ is said to be almost MDS (i.e., almost maximum distance separable)…