Related papers: Direct Construction of Recursive MDS Diffusion Lay…
The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. Consequently, various methods have been proposed for designing MDS matrices, including search…
This article presents a new algorithm to find MDS matrices that are well suited for use as a diffusion layer in lightweight block ciphers. Using an recursive construction, it is possible to obtain matrices with a very compact description.…
The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. However, in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch numbers…
Many recent block ciphers use Maximum Distance Separable (MDS) matrices in their diffusion layer. The main objective of this operation is to spread as much as possible the differences between the outputs of nonlinear Sboxes. So they…
Maximum-distance-separable (MDS) codes are a class of erasure codes that are widely adopted to enhance the reliability of distributed storage systems (DSS). In (n, k) MDS coded DSS, the original data are stored into n distributed nodes in…
Ciphers get their strength from the mathematical functions of confusion and diffusion, also known as substitution and permutation. These were the basics of classical cryptography and they are still the basic part of modern ciphers. In block…
MDS matrices play a critical role in the design of diffusion layers for block ciphers and hash functions due to their optimal branch number. Involutory and orthogonal MDS matrices offer additional benefits by allowing identical or nearly…
In AES-like ciphers, diffusion layers are commonly instantiated using MDS matrices, since their optimal branch number yields strong diffusion guarantees and underpins classical resistance arguments against differential and linear…
Maximum Distance Profile (MDP) convolutional codes are an important class of channel codes due to their maximal delay-constrained error correction capabilities. The design of MDP codes has attracted significant attention from the research…
In recent years, the Substitution-Permutation Network has emerged as a crucial structure for constructing symmetric key ciphers. Composed primarily of linear matrices and nonlinear S-boxes, it offers a robust foundation for cryptographic…
The present paper focuses on the construction of a set of submatrices of a circulant matrix such that it is a smaller set to verify that the circulant matrix is an MDS (maximum distance separable) one, comparing to the complete set of…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
Maximum distance separable (MDS) matrices play a crucial role not only in coding theory but also in the design of block ciphers and hash functions. Of particular interest are involutory MDS matrices, which facilitate the use of a single…
Array codes have been widely used in communication and storage systems. To reduce computational complexity, one important property of the array codes is that only XOR operation is used in the encoding and decoding process. In this work, we…
In this paper we introduce a novel MDS array code with lowest density. In contrast to existing codes, this one has no restrictions on the size or the number of erasures it can correct. It is based on a simple matrix construction involving…
Maximum distance separable convolutional codes are the codes that present best performance in error correction among all convolutional codes with certain rate and degree. In this paper, we show that taking the constant matrix coefficients…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said…
Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing and minimizing the computational load. Such codes have been constructed via Reed-Solomon codes…
A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion…