Abstract We give a new, algebraically computable formula for skein modules of closed 3-manifolds via Heegaard splittings. As an application, we prove that are finite-dimensional, resolving in the affirmative conjecture Witten.

Abstract Morrison, Walker, and Wedrich used the blob complex to construct a generalization of Khovanov–Rozansky homology links in boundary 4-manifold. The degree zero part their theory, called skein lasagna module, admits an elementary definition terms certain diagrams We give description module for 4-manifolds without 1- 3-handles, present some explicit calculations disk bundles over <m:math x...

For any n ≥ 2 we define an isotopy invariant, 〈Γ〉n , for a certain set of n-valent ribbon graphs Γ in R, including all framed oriented links. We show that our bracket coincides with the Kauffman bracket for n = 2 and with the Kuperberg’s bracket for n = 3. Furthermore, we prove that for any n, our bracket of a link L is equal, up to normalization, to the SUn quantum invariant of L. We show a nu...

The 256-bit versions of the SHA-3 finalist candidate hash functions—BLAKE, Grøstl, JH, Keccak, and Skein—were subjected to statistical tests to attempt to disprove the hypothesis that the output bits are uniformly distributed, independent, binary random variables. The hash functions were also subjected to cube tests to attempt to disprove the hypothesis that the superpoly bits are uniformly dis...

An SLn-character of a groupG is the trace of an SLn-representation of G.We show that all algebraic relations between SLn-characters of G can be visualized as relations between graphs (resembling Feynman diagrams) in any topological space X, with π1(X) = G. We also show that all such relations are implied by a single local relation between graphs. In this way, we provide a topological approach t...

We extend and improve biclique attacks, which were recently introduced for the cryptanalysis of block ciphers and hash functions. While previous attacks required a primitive to have a key or a message schedule, we show how to mount attacks on the primitives with these parameters fixed, i.e. on permutations. We introduce the concept of sliced bicliques, which is a translation of regular biclique...

This paper describes SPARKSkein – a new reference implementation of the Skein algorithm, written and verified using the SPARK language and toolset. This paper is aimed at readers familiar with the Skein algorithm and its existing reference implementation, but who might not be familiar with SPARK. The new implementation is readable, completely portable to a wide-variety of machines of differing ...