Related papers: Secret sharing with a class of minimal linear code…
Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyun {\em et al.} Building upon their research, in this paper more linear codes over the ring $\mathbb{Z}_4$ are…
Traditional threshold secret sharing cannot realizing all access structures of secret sharing. So, Ito introduced the concept of Secret sharing scheme realizing general access structure. But Its scheme has to send multiple shares to each…
Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…
We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension $q$, as well as explicit decoding operations for quantum secret sharing based on…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
We study a secret sharing problem with three secrets where the secrets are allowed to be related to each other, i.e., only certain combinations of the three secrets are permitted. The dealer produces three shares such that every pair of…
Nowadays, the utilization of the ever expanding amount of data has made a huge impact on web technologies while also causing various types of security concerns. On one hand, potential gains are highly anticipated if different organizations…
We generalize secret-sharing models that rely on correlated randomness and public communication, originally designed for a fixed access structure, to support a sequence of dynamic access structures, which we term an Additive Access…
In this article we present a class of codes with few weights arising from special type of linear sets. We explicitly show the weights of such codes, their weight enumerator and possible choices for their generator matrices. In particular,…
Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is…
The two-terminal key agreement problem with biometric or physical identifiers is considered. Two linear code constructions based on Wyner-Ziv coding are developed. The first construction uses random linear codes and achieves all points of…
Information leakage to a guessing adversary in index coding is studied, where some messages in the system are sensitive and others are not. The non-sensitive messages can be used by the server like secret keys to mitigate leakage of the…
Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the non-local operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
Private data analysis suffers a costly curse of dimensionality. However, the data often has an underlying low-dimensional structure. For example, when optimizing via gradient descent, the gradients often lie in or near a low-dimensional…
A general theory for constructing linear secret sharing schemes over a finite field $\Fq$ from toric varieties is introduced. The number of players can be as large as $(q-1)^r-1$ for $r\geq 1$. We present general methods for obtaining the…
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…