46 research outputs found
Anomalous diffusion in polymers: long-time behaviour
We study the Dirichlet boundary value problem for viscoelastic diffusion in
polymers. We show that its weak solutions generate a dissipative semiflow. We
construct the minimal trajectory attractor and the global attractor for this
problem.Comment: 13 page
Fast Near Collision Attack on the Grain v1 Stream Cipher
Modern stream ciphers often adopt a large internal state to resist various
attacks, where the cryptanalysts have to deal with a large number of variables
when mounting state recovery attacks. In this paper, we propose a general new
cryptanalytic method on stream ciphers, called fast near collision attack, to
address this situation. It combines a near collision property with the
divide-and-conquer strategy so that only subsets of the internal state,
associated with different keystream vectors, are recovered first and merged
carefully later to retrieve the full large internal state. A self-contained
method is introduced and improved to derive the target subset of the internal
state from the partial state difference efficiently. As an application, we
propose a new key recovery attack on Grain v1, one of the finalists
selected by the eSTREAM project, in the single-key setting. Both the
pre-computation and the online phases are tailored according to its internal
structure, to provide an attack for any fixed IV in cipher ticks
after the pre-computation of cipher ticks, given -bit memory
and about keystream bits. Practical experiments on Grain v1 itself
whenever possible and on a 80-bit reduced version confirmed our results
Strong trajectory and global W 1,p -attractors for the damped-driven Euler system in R 2.
We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solutions satisfy the energy and enstrophy equality. It is shown that this system has a strong global and a strong trajectory attractor in the Sobolev space H1. A similar result on the strong attraction holds in the spaces H1 ∩ {u : k curl ukLp < ∞} for p ≥ 2