The SHA-3 competition organized by NIST [1] aims to find a new hash standard as a replacement of SHA-2. Till now, 14 submissions have been selected as the second round candidates, including Skein and BLAKE, both of which have components based on modular addition, rotation and bitwise XOR (ARX). In this paper, we propose improved near-collision attacks on the reduced-round compression functions ...

Algebra Situs is a branch of mathematics which has its roots in Jones' construction of his polynomial invariant of links and Drinfeld's work on quantum groups. It encompasses the theory of quantum invariants of knots and 3-manifolds, algebraic topology based on knots, operads, planar algebras, q-deformations, quantum groups, and overlaps with algebraic geometry, non-commutative geometry and sta...

This paper relates skein spaces based on the Kauffman bracket and spin structures. A spin structure on an oriented 3-manifold provides an isomorphism between the skein space for parameter A and the skein space for parameter −A. There is an application to Penrose’s binor calculus, which is related to the tensor calculus of representations of SU(2). The perspective developed here is that this ten...

This paper presents an exact analytical solution for two-dimensional conductive heat transfer in spherical composite pressure vessels .The vessels are in spherical shape and fibers are winded in circumferential direction. The analytical solution is obtained under the general boundary conditions which consist of convection, conduction and radiation inside/outside of vessel. The heat transfer equ...

We introduce higher skein modules of links generalizing the Conway skein module. We show that these modules are closely connected to the HOMFLY polynomial.

We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A ±1 ] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z 2-homology of the manifold, we determine that they are linearly independent.

Skein is a submission to the NIST SHA-3 hash function competition which has been optimized towards implementation in modern 64-bit processor architectures. This paper investigates the performance characteristics of a high-speed hardware implementation of Skein with a 0.18 μm standard-cell library and on different modern FPGAs. The results allow a first comparison of the hardware performance fig...

Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of quantum topology. Our results can be considered as weak extensions to all orientable 3-manifolds of classical results by Turaev and Goldman concerning intersectio...

The E6 state sum invariant is a topological invariant of closed 3manifolds constructed by using the 6j-symbols of the E6 subfactor. In this paper, we introduce the E6 linear skein as a certain vector space motivated by E6 subfactor planar algebra, and develop its linear skein theory by showing many relations in it. By using this linear skein, we give an elementary self-contained construction of...