Related papers: Linear Secret Sharing from Algebraic-Geometric Cod…
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer…
In coding theory, a common question is to understand the threshold rates of various local properties of codes, such as their list decodability and list recoverability. A recent work Levi, Mosheiff, and Shagrithaya (FOCS 2025) gave a novel…
With the rapid development of MANET, secure and practical authentication is becoming increasingly important. The existing works perform the research from two aspects, i.e., (a)secure key division and distributed storage, (b)secure…
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…
The problem of providing privacy, in the private information retrieval (PIR) sense, to users requesting data from a distributed storage system (DSS), is considered. The DSS is coded by an $(n,k,d)$ Maximum Distance Separable (MDS) code to…
Transversal gates play a crucial role in suppressing error propagation in fault-tolerant quantum computation, yet they are intrinsically constrained: any nontrivial code encoding a single logical qubit admits only a finite subgroup of…
In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical…
Quantum secret sharing is a method for sharing a secret quantum state among a number of individuals such that certain authorized subsets of participants can recover the secret shared state by collaboration and other subsets cannot. In this…
The main aim of this paper is to construct a multi-secret sharing scheme for general access structure in a trusted dealer model using suitable hash function and Lagrange's interpolation method. Even though, the proposed scheme is a…
Recent results of Cascudo, Cramer, and Xing on the construction of arithmetic secret sharing schemes are improved by using some new bounds on the torsion limits of algebraic function fields. Furthermore, new bounds on the torsion limits of…
This paper considers distributed storage systems (DSSs) from a graph theoretic perspective. A DSS is constructed by means of the path decomposition of a 3- regular graph into P4 paths. The paths represent the disks of the DSS and the edges…
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…
In recent years there has been a great deal of work done on secret sharing scehemes. Secret Sharing Schemes allow for the division of keys so that an authorised set of users may access information. In this paper we wish to present a…
A novel technique for construction of minimum storage regenerating (MSR) codes is presented. Based on this technique, three explicit constructions of MSR codes are given. The first two constructions provide access-optimal MSR codes, with…
We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive…
This paper introduces a methodology based on Euclidean information theory to investigate local properties of secure communication over discrete memoryless wiretap channels. We formulate a constrained optimization problem that maximizes a…
In a secret sharing scheme, shares of a secret are distributed to participants in such a way that only certain predetermined sets of participants are qualified to reconstruct the secret. An access structure on a set of participants…
This work introduces the \emph{Secure and Private Structured-Subset Retrieval (SPSSR)} problem. In SPSSR, a user wishes to retrieve one subset from an arbitrary family of size-$D$ subsets from $K$ messages replicated across $N$…
The correspondence between linear codes and representable matroids is well known. But a similar correspondence between quantum codes and matroids is not known. We show that representable symplectic matroids over a finite field…
The Stealth Address Protocol (SAP) allows users to receive assets through stealth addresses that are unlinkable to their stealth meta-addresses. The most widely used SAP, Dual-Key SAP (DKSAP), and the most performant SAP, Elliptic Curve…