A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine spaces over various finite fields. Then algebro-geometric transformations on those spaces is transported back to provide encryption. For a specific block size <...

We introduce, for block size 3, the problem of minimal enclosings of GDDs with u groups of size g into GDDs with u groups of size g + 1. We prove the necessary conditions are sufficient for the embedding of any GDD with group size 1, i.e., a BIBD(v, 3, λ), into a GDD with v groups of size 2. Minimal faithful enclosings of GDDs are given for group size 2 with any index into GDDs with group size ...

Each parallel class of a uniformly resolvable design (URD) contains blocks of only one block size. AURDwith v points andwith block sizes three and fourmeans that at least one parallel class has block size three and at least one has block size four. Danziger [P. Danziger, Uniform restricted resolvable designs with r = 3, ARS Combin. 46 (1997) 161–176] proved that for all v ≡ 12 (mod 24) there ex...

The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007

A novel methodology to quantify displacements and strain in musculoskeletal ultrasound sequences is presented. We extend the principles of 2D interframe displacements produced by our earlier work using hierarchical variable block size matching, to quantify displacement trajectories. We provide novel solutions for probe motion, quantification of objects moving in the 3D volume traversing the 2D ...

In this paper, we employ the known recursive construction methods to obtain some new existence results for large sets of t-designs of prime sizes. We also present a new recursive construction which leads to more comprehensive theorems on large sets of sizes two and three. As an application, we show that for infinitely many values of block size, the trivial necessary conditions for the existence...

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v, 4, λ)-BIBDs have been determined for λ = 2, 3, 4 and 6. When λ = 5, the necessary conditions of such a d...

Effective Boltzmannians in the sense of the block spin renormalization group are computed for the 2D Ising model. The blocking is done with majority and Kadanoff rules for blocks of size 2 by 2. Transfer matrix techniques allow the determination of the effective Boltzmannians as polynomials in u = exp(4β) for lattices of up to 4 by 4 blocks. The zeroes of these polynomials are computed for all ...

Curupira is a 96-bit block cipher, with keys of 96, 144 or 192 bits, and variable number of rounds, an algorithm described at SBRC 2007. This paper1 presents impossible-differential, boomerang and higher-order multiset attacks on reduced-round versions of Curupira, that were not previously considered in the security analysis by its designers. Also, we provide security analyses based solely on t...