Practical Relativistic Zero-Knowledge for NP

In a Multi-Prover environment, how little spatial separation is sufficient to assert the validity of an NP statement in Perfect Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability problem that use two (local) provers or three (entangled) provers and only require exchanging one edge and two bits with two trits per prover. This greatly improves the ability to prove Zero-Knowledge statements on very short distances with very basic communication gear

Practical Relativistic Zero-Knowledge for NP

In this work we consider the following problem: in a Multi-Prover environment, how close can we get to prove the validity of an NP statement in Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability problem that use two (local) provers or three (entangled) provers and only require them to reply two trits each. This greatly improves the ability to prove Zero-Knowledge statements on very short distances with very minimal equipment.Comment: Submitted to ITC 202

Off shell behaviour of the in medium nucleon-nucleon cross section

The properties of nucleon-nucleon scattering inside dense nuclear matter are investigated. We use the relativistic Brueckner-Hartree-Fock model to determine on-shell and half off-shell in-medium transition amplitudes and cross sections. At finite densities the on-shell cross sections are generally suppressed. This reduction is, however, less pronounced than found in previous works. In the case that the outgoing momenta are allowed to be off energy shell the amplitudes show a strong variation with momentum. This description allows to determine in-medium cross sections beyond the quasi-particle approximation accounting thereby for the finite width which nucleons acquire in the dense nuclear medium. For reasonable choices of the in-medium nuclear spectral width, i.e. $\Gamma\leq 40$ MeV, the resulting total cross sections are, however, reduced by not more than about 25% compared to the on-shell values. Off-shell effect are generally more pronounced at large nuclear matter densities.Comment: 31 pages Revtex, 12 figures, typos corrected, to appear in Phys. Rev.

A proposal for founding mistrustful quantum cryptography on coin tossing

A significant branch of classical cryptography deals with the problems which arise when mistrustful parties need to generate, process or exchange information. As Kilian showed a while ago, mistrustful classical cryptography can be founded on a single protocol, oblivious transfer, from which general secure multi-party computations can be built. The scope of mistrustful quantum cryptography is limited by no-go theorems, which rule out, inter alia, unconditionally secure quantum protocols for oblivious transfer or general secure two-party computations. These theorems apply even to protocols which take relativistic signalling constraints into account. The best that can be hoped for, in general, are quantum protocols computationally secure against quantum attack. I describe here a method for building a classically certified bit commitment, and hence every other mistrustful cryptographic task, from a secure coin tossing protocol. No security proof is attempted, but I sketch reasons why these protocols might resist quantum computational attack.Comment: Title altered in deference to Physical Review's fear of question marks. Published version; references update

Constraining mean-field models of the nuclear matter equation of state at low densities

An extension of the generalized relativistic mean-field (gRMF) model with density dependent couplings is introduced in order to describe thermodynamical properties and the composition of dense nuclear matter for astrophysical applications. Bound states of light nuclei and two-nucleon scattering correlations are considered as explicit degrees of freedom in the thermodynamical potential. They are represented by quasiparticles with medium-dependent properties. The model describes the correct low-density limit given by the virial equation of state (VEoS) and reproduces RMF results around nuclear saturation density where clusters are dissolved. A comparison between the fugacity expansions of the VEoS and the gRMF model provides consistency relations between the quasiparticles properties, the nucleon-nucleon scattering phase shifts and the meson-nucleon couplings of the gRMF model at zero density. Relativistic effects are found to be important at temperatures that are typical in astrophysical applications. Neutron matter and symmetric matter are studied in detail.Comment: 50 pages, 21 figure