Understanding the Related-Key Security of Feistel Ciphers from a Provable Perspective

We initiate the provable related-key security treatment for models of practical Feistel ciphers. In detail, we consider Feistel networks with four whitening keys $w_i(k)$ ($i=0,1,2,3$) and round-functions of the form $f(\gamma_i(k)\oplus X)$, where $k$ is the main-key, $w_i$ and $\gamma_i$ are efficient transformations, and $f$ is a public ideal function or permutation that the adversary is allowed to query. We investigate conditions on the key-schedules that are sufficient for security against XOR-induced related-key attacks up to $2^{n/2}$ adversarial queries. When the key-schedules are non-linear, we prove security for 4 rounds. When only affine key-schedules are used, we prove security for 6 rounds. These also imply secure tweakable Feistel ciphers in the Random Oracle model. By shuffling the key-schedules, our model unifies both the DES-like structure (known as Feistel-2 scheme in the cryptanalytic community, a.k.a. key-alternating Feistel due to Lampe and Seurin, FSE 2014) and the Lucifer-like model (previously analyzed by Guo and Lin, TCC 2015). This allows us to derive concrete implications on these two (more common) models, and helps understanding their differences---and further understanding the related-key security of Feistel ciphers.Comment: The technical part is the same as the submission (only modify to fit into the double column). In "Related Work" comparison with [72] is added: in short, these two works focus on very different goals, and their general results aren't comparabl

On algebraic Riccati equations associated with M-Matrices

We consider the algebraic Riccati equation for which the four coefficient matrices form an M-matrix K. When K is a nonsingular M-matrix or an irreducible singular M-matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M-matrix. Under a regularity assumption on the M-matrix K, we show that the Riccati equation still has a minimal nonnegative solution. We also study the properties of this particular solution and explain how the solution can be found by existing methods.Comment: 16 page

A note on algebraic Riccati equations associated with reducible singular M-matrices

We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the minimal nonnegative solutions

3D Prominence-hosting Magnetic Configurations: Creating a Helical Magnetic Flux Rope

The magnetic configuration hosting prominences and their surrounding coro- nal structure is a key research topic in solar physics. Recent theoretical and observational studies strongly suggest that a helical magnetic flux rope is an es- sential ingredient to fulfill most of the theoretical and observational requirements for hosting prominences. To understand flux rope formation details and obtain magnetic configurations suitable for future prominence formation studies, we here report on three-dimensional isothermal magnetohydrodynamic simulations including finite gas pressure and gravity. Starting from a magnetohydrostatic corona with a linear force-free bipolar magnetic field, we follow its evolution when introducing vortex flows around the main polarities and converging flows towards the polarity inversion line near the bottom of the corona. The con- verging flows bring feet of different loops together at the polarity inversion line and magnetic reconnection and flux cancellation happens. Inflow and outflow signatures of the magnetic reconnection process are identified, and the thereby newly formed helical loops wind around pre-existing ones so that a complete flux rope grows and ascends. When a macroscopic flux rope is formed, we switch off the driving flows and find that the system relaxes to a stable state containing a helical magnetic flux rope embedded in an overlying arcade structure. A major part of the formed flux rope is threaded by dipped field lines which can stably support prominence matter, while the total mass of the flux rope is in the order of 4-5.e14 g

Two-dimensional group delay in graphene probed by spin precession measurements

We take graphene as an example to demonstrate that the present widely adopted expression is only the scattering component of a true 2D group delay in the condensed matter context, in which the spatial Goos-H\"{a}nchen (GH) shift along an interface contributes an intrinsic component. We relate the dwell time to spin precession and derive a relation between the 2D group delay and dwell time, whereby we for the first time reveal that, the group delay for 2D ballistic electronic systems can be directly observed by measuring a conductance difference in a weak-field spin precession experiment. This physical observable not only implies the group delay being a relevant quantity even in the condensed matter context, but also provides an experimental evidence for the intrinsic effect of the GH shift. Finally, we revisit the 2D Hartman effect, a central issue of the group delay, by analytically solving it via the vested relation and calculating the proposed observable at the Dirac point.Comment: 12 preprint pages and 6 figure

Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids

By using Bogoliubov transformations to construct the ground states of fermionic Bardeen-Cooper-Schrieffer (BCS) superfluids and weakly-interacting Bose gases supporting Bose Einstein Condensation (BEC), their algebraic structures and implications can be analyzed in detail. Both ground states are generalized squeezed coherent states saturating a generalized Heisenberg uncertainty relation, and they acquire quantized Berry phases when the corresponding systems are transported along a closed path in their parameter spaces. While the Berry phase of the BCS ground state depends on the total particle number, the Berry phase of the BEC ground state depends only on the particles outside the BEC. The Berry phases are associated with magnetic monopoles in the parameter spaces and we found that the Dirac quantization condition is satisfied. Moreover, both ground states are entangled states of the fermion or boson quanta and we found the entanglement entropy quantifying the internal correlations. A fixed particle-number approach of fermionic superfluids does not saturate the generalized uncertainty relation, exhibits internal entanglement, and gives corresponding Berry phase. In addition, the algebraic structures of the ground states can be classified by the $q$-deformed Hopf algebra, $\bigoplus_{\mathbf{k}}h_{q_{\mathbf{k}}}(1)$ for bosons and $q$-deformed Hopf superalgebra $\bigoplus_{\mathbf{k}}h_{q_{\mathbf{k}}}(1|1)$ for fermions, respectively.Comment: 14 pages, no figure, revised versio

Negative differential resistances with back gate-controlled lowest operation windows in graphene double barrier resonant tunneling diodes

We theoretically investigate negative differential resistance (NDR) of massless and massive Dirac Fermions in double barrier resonant tunneling diodes based on sufficiently short and wide graphene strips. The current-voltage characteristics calculated in a rotated pseudospin space show that, the NDR feature only presents with appropriate structural parameters for the massless case and the peak-to-valley current ratio can be enhanced exponentially by a tunable band gap. Remarkably, the lowest NDR operation window is nearly structure-free and can be almost solely controlled by a back gate, which may have potential applications in NDR devices with the operation window as a crucial parameter.Comment: 5 pages, 5 figure

Establishing the Presence of Coherence in Atomic Fermi Superfluids: Spin-Flip and Spin-Preserving Bragg Scattering at Finite Temperatures

We show how the difference between the finite temperature T structure factors, called S_-, associated with spin and density, can be used as a indication of superfluidity in ultracold Fermi gases. This observation can be exploited in two photon Bragg scattering experiments on gases which undergo BCS- Bose Einstein condensation crossover. Essential to our calculations is a proper incorporation of spin and particle number conservation laws which lead to compatibility at general T with two f-sum rules. Because it is applicable to general scattering lengths, a measurement of S- can be a useful, direct approach for establishing where superfluidity occurs

Relativistic BCS-BEC crossover of a two-species Fermi gas with number density asymmetry at zero temperature

We systematically study relativistic two-species fermions with tunable attractive interactions and number-density asymmetry at zero temperature. In general, a Bardeen-Cooper-Schrieffer (BCS) - Bose-Einstein Condensation (BEC) - relativistic BEC (RBEC) crossover is observed. A generalized BCS ground state and its stability are analyzed. The homogeneous superfluid phase can become unstable and we consider phase separation in real space for neutral systems. In the nonrelativistic limit, our results are consistent with well-known results. In addition to a BCS-BEC crossover similar to that in the nonrelativistic case, in the strongly attractive regime gapless excitations of antifermions and a RBEC state are observed. We address how different phases respond to number density asymmetry and present predictive phase diagrams of BCS-BEC-RBEC crossover.Comment: 18 pages, 6 figure

Investigating the quark flavor dependence of the chiral magnetic effect with a multiphase transport model

Because the properties of the QCD phase transition and the chiral magnetic effect (CME) depend on the number of quark flavors ($N_{f}$) and quark mass, relativistic heavy-ion collisions provide a natural environment to investigate the flavor features if quark deconfinement occurs. We introduce an initial two-flavor or three-flavor dipole charge separation into a multiphase transport (AMPT) model to investigate the flavor dependence of the CME. By taking advantage of the recent ALICE data of charge azimuthal correlations with identified hadrons, we attempt to disentangle two-flavor and three-flavor CME scenarios in Pb+Pb collisions at 2.76 TeV. We find that the experimental data show a certain potential to distinguish the two scenarios, therefore we further suggest to collect more data to clarify the possible flavor dependence in future experiments.Comment: 12 pages, 4 figures; final published versio