A transversal design of order n and block size k, or TD(k; n), is a triple (X, G, B ), where X is a set of kn elements. G 5 hG1 , . . . , Gkj is a partition of X into k sets each of size n; each class of the partition is a group. B is a set of k-subsets of X, with the property that each B [ B satisfies uB > Giu 5 1 for each 1 # i # k; sets in B are blocks. Finally, each unordered pair of elemen...

A defining set of a t-(v, k, λ) design is a subcollection of its blocks which is contained in no other t-design with the given parameters, on the same point set. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M | | M is a minimal defining set of D}. We show that if a t-(v, k, λ) de...

We present constructions and results about GDDs with two groups and block size five in which each block has Configuration (s, t), that is, in which each block has exactly s points from one of the two groups and t points from the other. After some results for a general k, s and t, we consider the (2, 3) case for block size 5. We give new necessary conditions for this family of GDDs and give mini...

Let Vn(q) denote a vector space of dimension n over the field with q elements. A set P of subspaces of Vn(q) is a partition of Vn(q) if every nonzero vector in Vn(q) is contained in exactly one subspace in P. A uniformly resolvable design is a pairwise balanced design whose blocks can be resolved in such a way that all blocks in a given parallel class have the same size. A partition of Vn(q) co...

We complete the solution of the existence problem for generalized Bhaskar Rao designs of block size 3 over groups of order 12. In particular we prove that if G is a group of order 12 which is cyclic or dicyclic, then a generalized Bhaskar Rao design, GBRD(v, 3, λ = 12t;G) exists for all v ≥ 3 when t is even and for all v ≥ 4 when t is odd.

Fast mode decision algorithms in video intra coding are very useful and necessary for implementing practical real-time performance of the encoder. It can reduce the computational complexity by excluding impossible modes from candidate set. Anyway, most of these algorithms may give rise to the remarkable quality degradation, especially for the all intra coding scenario. In order to improve the e...

In this paper we propose a new family of very efficient hardware oriented block ciphers. The family contains six block ciphers divided into two flavors. All block ciphers share the 80-bit key size and security level. The first flavor, KATAN, is composed of three block ciphers, with 32, 48, or 64-bit block size. The second flavor, KTANTAN, contains the other three ciphers with the same block siz...

PAGES is block cipher family based on the design of Speck, see [1]. However, some intriguing design details of Speck were not used in the design of PAGES. PAGES has block size of 256 bit and comes in three version: PAGES-512, PAGES-768, and PAGES-1024, were the number denotes the key length. The number of rounds is 64, 96, or 128, respectively. PAGES uses variables of 128 bit, that is half the ...

The cipher CTC (Courtois Toy Cipher) described in [4] has been designed to demonstrate that it is possible to break on a PC a block cipher with good diffusion and very small number of known (or chosen) plaintexts. It has however never been designed to withstand all known attacks on block ciphers and Dunkelman and Keller have shown [13] that a few bits of the key can be recovered by Linear Crypt...