This paper proposes a new, large diffusion layer for the AES block cipher. This new layer replaces the ShiftRows and MixColumns operations by a new involutory matrix in every round. The objective is to provide complete diffusion in a single round, thus sharply improving the overall cipher security. Moreover, the new matrix elements have low Hamming-weight in order to provide equally good perfor...

We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to each submatrix. For this scheme, we prove that up to a given number of partitions the communication load and the computational delay (not including the encoding...

We use the formalism of the Riordan group to study a one-parameter family of lower-triangular matrices related to the weight distribution of maximum distance separable codes. We obtain factorization results for these matrices. We then derive alternative expressions for the weight distribution of MDS codes. We define related weight ratios and show that they satisfy a certain linear recurrence.

Isomap [4] is a manifold learning algorithm, which extends classical multidimensional scaling (MDS) by considering approximate geodesic distance instead of Euclidean distance. The approximate geodesic distance matrix can be interpreted as a kernel matrix, which implies that Isomap can be solved by a kernel eigenvalue problem. However, the geodesic distance kernel matrix is not guaranteed to be ...

Blind choice and parameterization of data mining tools often yield vague or completely misleading results. Interactive visualization enables not only extensive exploration of data but also better matching of clustering/classification schemes to the type of data being analyzed. The multidimensional scaling (MDS), which employs particle dynamics to the error function minimization, is a good candi...

Maximum distance separable (MDS) codes have the maximum branch number in cryptography, and they are generally used diffusion layers of symmetric ciphers. The layer Advanced Encryption Standard (AES) uses circulant MDS matrix with row element {2;3;1;1} F28. It is simplest F2n4, recorded as A=Circ(2;3;1;1). In this paper, we study more extensive constructions A F2n4. By transforming multiplicatio...

MaximumDistance Separable (MDS) andMaximumDistance Binary Linear (MDBL) codes are used as diffusion layers in the design of the well-known block ciphers like the Advanced Encryption Standard, Khazad, Camellia, and ARIA. The reason for the use of these codes in the design of block ciphers is that they provide optimal diffusion effect to meet security of a round function of a block cipher. On the...

Let Fq be a finite field of order q with characteristic p. An arc in Fq is an ordered family of at least k vectors in which every subfamily of size k is a basis of Fq . The MDS conjecture, which was posed by Segre in 1955, states that if k 6 q, then an arc in Fq has size at most q + 1, unless q is even and k = 3 or k = q − 1, in which case it has size at most q + 2. We propose a conjecture whic...

When the coordinates of a set of points are known, the pairwise Euclidean distances among the points can be easily computed. Conversely, if the Euclidean distance matrix is given, a set of coordinates for those points can be computed through the well known classical Multi-Dimensional Scaling (MDS). In this paper, we consider the case where some of the distances are far from being accurate (cont...

Myelodysplastic syndrome (MDS), is a group of heterogeneous disorders of hematopoietic stem cell colonies which is determined by incomplete hematopoiesis in one or more cell lines. The incidence increases with age and it has less been reported among patients under 50 years of age. The commonest form of MDS is sporadic, and familial occurrence of MDS is rare. Patients with familial MDS are young...