Cryptanalysis of a computer cryptography scheme based on a filter bank

This paper analyzes the security of a recently-proposed signal encryption scheme based on a filter bank. A very critical weakness of this new signal encryption procedure is exploited in order to successfully recover the associated secret key.Comment: 6 pages, 1 figur

A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations

We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and Green-Naghdi equation and discuss the problem of their validity as asymptotic models for the water-waves equations

Mass-radius constraints for compact stars and a critical endpoint

We present two types of models for hybrid compact stars composed of a quark core and a hadronic mantle with an abrupt first order phase transition at the interface which are in accordance with the latest astrophysical measurements of two 2 M_sun pulsars. While the first is a schematic one, the second one is based on a QCD motivated nonlocal PNJL model with density-dependent vector coupling strength. Both models support the possibility of so called twin compact stars which have the same mass but different radius and internal structure at high mass (~2 M_sun), provided they exhibit a large jump \Delta \epsilon in the energy density of the first order phase transition fulfilling \Delta \epsilon/\epsilon_crit > 0.6. We conclude that the measurement of high-mass twin stars would support the existence of a first order phase transition in symmetric matter at zero temperature entailing the existence of a critical end point in the QCD phase diagram.Comment: 7 pages, 2 figures, 1 table, prepared for the Proceedings of the 8th International Workshop on "Critical Point and Onset of Deconfinement",March 11 to 15, 2013, Napa, California, US

Spin and abelian electromagnetic duality on four-manifolds

We investigate the electromagnetic duality properties of an abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling constants. The true partition function is invariant under the full modular group but the generalised partition function exhibits more complicated behaviour depending on topological properties of the four-manifold concerned. It is already known that there may be "modular weights" which are linear combinations of the Euler number and Hirzebruch signature of the four-manifold. But sometimes the partition function transforms only under a subgroup of the modular group (the Hecke subgroup). In this case it is impossible to define real spinor wave functions on the four-manifold. But complex spinors are possible provided the background magnetic fluxes are appropriately fractional rather that integral. This gives rise to a second partition function which enables the full modular group to be realised by permuting the two partition functions, together with a third. Thus the full modular group is realised in all cases. The demonstration makes use of various constructions concerning integral lattices and theta functions that seem to be of intrinsic interest.Comment: 29 pages, Plain Te