This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n, n) Springer variety. The results build on Khovanov’s work with crossingless matchings and the cohomology of the (n, n) Springer variety. We also give a formula for comultiplication in the Bar-Natan skein module for this specific three-ma...

This work analyzes the statistical properties of the SHA-3 candidate cryptographic hash algorithms CubeHash and Skein to try to find nonrandom behavior. Cube tests were used to probe each algorithm’s internal polynomial structure for a large number of choices of the polynomial input variables. The cube test data were calculated on a 40-core hybrid SMP cluster parallel computer. The cube test da...

In this study, the buckling behavior of moderately thick Carbon Nano-Tube (CNT)-reinforced spherical composite panels subjected to both uniaxial and biaxial loads is examined. The uniform and various kinds of functionally graded distributions of the CNT are considered. The mechanical properties of the nanocomposite panels are estimated using the modified rule of mixture. Based on the first-orde...

We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read–Rezayi state whose effective theory is the SU(2)K Chern–Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we prop...

The objective of the research is to study and compare response surface designs: Central composite designs (CCD), BoxBehnken designs (BBD), Small composite designs (SCD), Hybrid designs, and Uniform shell designs (USD) over sets of reduced models when the design is in a spherical region for 3 and 4 design variables. The two optimality criteria ( D and G ) are considered which larger values imply...

Shielding radiation from both x-rays and gamma-rays is important for personnel in medical fields e.g. interventional radiology, nuclear power stations, and other inspection facilities where radiation is involved. Lead is known for its effective shielding property against these high energy radiations, however heaviness and toxicity are its main drawback. In this study effectiveness of non-lead p...

This work1 provides a detailed study of two finalists of the SHA-3 competition from the sidechannel analysis point of view. For both functions when used as a MAC, this paper presents detected strategies for performing a power analysis. Besides the classical HMAC mode, two additionally proposed constructions, the envelope MAC for Grøstl and the Skein-MAC for Skein, are analyzed. Consequently, ex...

In this paper we study boomerang attacks in the chosen-key setting. This is particularly relevant to hash function analysis, since many boomerang attacks have been described against ARX-based designs. We present a new way to combine message modifications, or auxiliary differentials, with the boomerang attack. We show that under some conditions, we can combine three independent paths instead of ...

The hash function Skein is one of the five finalists of the NIST SHA-3 competition; it is based on the block cipher Threefish which only uses three primitive operations: modular addition, rotation and bitwise XOR (ARX). This paper studies the boomerang attacks on Skein-512. Boomerang distinguishers on the compression function reduced to 32 and 36 rounds are proposed, with complexities 2 and 2 r...