38 research outputs found
Group theory in cryptography
This paper is a guide for the pure mathematician who would like to know more
about cryptography based on group theory. The paper gives a brief overview of
the subject, and provides pointers to good textbooks, key research papers and
recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
Cryptanalysis of three matrix-based key establishment protocols
We cryptanalyse a matrix-based key transport protocol due to Baumslag, Camps,
Fine, Rosenberger and Xu from 2006. We also cryptanalyse two recently proposed
matrix-based key agreement protocols, due to Habeeb, Kahrobaei and Shpilrain,
and due to Romanczuk and Ustimenko.Comment: 9 page
Cryptanalysis of the MST_3 Public Key Cryptosystem
In this paper we describe a cryptanalysis of MST_3, a public key
cryptosystem based on non-commutative groups recently proposed by
Lempken, Magliveras, van Trung and Wei
Graphene hot-electron light bulb: incandescence from hBN-encapsulated graphene in air
The excellent electronic and mechanical properties of graphene allow it to
sustain very large currents, enabling its incandescence through Joule heating
in suspended devices. Although interesting scientifically and promising
technologically, this process is unattainable in ambient environment, because
graphene quickly oxidises at high temperatures. Here, we take the performance
of graphene-based incandescent devices to the next level by encapsulating
graphene with hexagonal boron nitride (hBN). Remarkably, we found that the hBN
encapsulation provides an excellent protection for hot graphene filaments even
at temperatures well above 2000 K. Unrivalled oxidation resistance of hBN
combined with atomically clean graphene/hBN interface allows for a stable light
emission from our devices in atmosphere for many hours of continuous operation.
Furthermore, when confined in a simple photonic cavity, the thermal emission
spectrum is modified by a cavity mode, shifting the emission to the visible
range spectrum. We believe our results demonstrate that hBN/graphene
heterostructures can be used to conveniently explore the technologically
important high-temperature regime and to pave the way for future optoelectronic
applications of graphene-based systems
Giant magnetoresistance of Dirac plasma in high-mobility graphene
The most recognizable feature of graphene's electronic spectrum is its Dirac
point around which interesting phenomena tend to cluster. At low temperatures,
the intrinsic behavior in this regime is often obscured by charge inhomogeneity
but thermal excitations can overcome the disorder at elevated temperatures and
create electron-hole plasma of Dirac fermions. The Dirac plasma has been found
to exhibit unusual properties including quantum critical scattering and
hydrodynamic flow. However, little is known about the plasma's behavior in
magnetic fields. Here we report magnetotransport in this quantum-critical
regime. In low fields, the plasma exhibits giant parabolic magnetoresistivity
reaching >100% in 0.1 T even at room temperature. This is orders of magnitude
higher than magnetoresistivity found in any other system at such temperatures.
We show that this behavior is unique to monolayer graphene, being underpinned
by its massless spectrum and ultrahigh mobility, despite frequent
(Planckian-limit) scattering. With the onset of Landau quantization in a few T,
where the electron-hole plasma resides entirely on the zeroth Landau level,
giant linear magnetoresistivity emerges. It is nearly independent of
temperature and can be suppressed by proximity screening, indicating a
many-body origin. Clear parallels with magnetotransport in strange metals and
so-called quantum linear magnetoresistance predicted for Weyl metals offer an
interesting playground to further explore relevant physics using this
well-defined quantum-critical 2D system.Comment: 8 pages, 3 figure
Long-range ballistic transport of Brown-Zak fermions in graphene superlattices
In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational (p/q) fractions of the magnetic flux quantum per superlattice unit cell. Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 106 cm2 V−1 s−1 and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are 4q times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1 K. We also found negative bend resistance at 1/q fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field