Related papers: Secret sharing schemes based on additive codes ove…
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…
We present Modular Polynomial (MP) Codes for Secure Distributed Matrix Multiplication (SDMM). The construction is based on the observation that one can decode certain proper subsets of the coefficients of a polynomial with fewer evaluations…
Publicly verifiable secret sharing (PVSS) allows a dealer to share a secret among a set of shareholders so that the secret can be reconstructed later from any set of qualified participants. In addition, any public verifier should be able to…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
This paper presents a recursive computational multi-secret sharing technique that hides k-2 secrets of size b each into n shares of a single secret S of size b, such that any k of the n shares suffice to recreate the secret S as well as all…
This paper presents a recursive hiding scheme for 2 out of 3 secret sharing. In recursive hiding of secrets, the user encodes additional information about smaller secrets in the shares of a larger secret without an expansion in the size of…
We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect "ramp" secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical…
Recently, codes in the sum-rank metric attracted attention due to several applications in e.g. multishot network coding, distributed storage and quantum-resistant cryptography. The sum-rank analogs of Reed-Solomon and Gabidulin codes are…
Secret sharing is a fundamental primitive in cryptography, and it can be achieved even with perfect security. However, the distribution of shares requires computational assumptions, which can compromise the overall security of the protocol.…
Data security and availability for operational use are frequently seen as conflicting goals. Research on searchable encryption and homomorphic encryption are a start, but they typically build from encryption methods that, at best, provide…
An ideal secret sharing scheme is a method of sharing a secret key in some key space among a finite set of participants in such a way that only the authorized subsets of participants can reconstruct the secret key from their shares which…
Reed-Solomon (RS) codes over GF$(2^m)$ have traditionally been the most popular non-binary codes in almost all practical applications. The distance properties of RS codes result in excellent performance under hard-decision bounded-distance…
Sometimes it is possible to embed an algebraic trapdoor into a block cipher. Building on previous research, in this paper we investigate an especially dangerous algebraic structure, which is called a hidden sum and which is related to some…
Homomorphic secret sharing (HSS) allows multiple input clients to secretly share their private inputs to a function among several servers such that each server can homomorphically compute the function over its share to produce a share of…
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…
At the beginning some results from the field of graph theory are presented. Next we show how to share a secret that is proper n-coloring of the graph, with the known structure. The graph is described and converted to the form, where colors…
In (k, n) visual secret sharing (VSS) scheme, secret image can be visually reconstructed when k or more participants printing theirs shares on transparencies and stack them together. No secret is revealed with fewer than k shares. The…
Subspace codes were introduced by K\"otter and Kschischang for error control in random linear network coding. In this paper, a layered type of subspace codes is considered, which can be viewed as a superposition of multiple component…
We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing…