Enabling Privacy-preserving Auctions in Big Data

We study how to enable auctions in the big data context to solve many upcoming data-based decision problems in the near future. We consider the characteristics of the big data including, but not limited to, velocity, volume, variety, and veracity, and we believe any auction mechanism design in the future should take the following factors into consideration: 1) generality (variety); 2) efficiency and scalability (velocity and volume); 3) truthfulness and verifiability (veracity). In this paper, we propose a privacy-preserving construction for auction mechanism design in the big data, which prevents adversaries from learning unnecessary information except those implied in the valid output of the auction. More specifically, we considered one of the most general form of the auction (to deal with the variety), and greatly improved the the efficiency and scalability by approximating the NP-hard problems and avoiding the design based on garbled circuits (to deal with velocity and volume), and finally prevented stakeholders from lying to each other for their own benefit (to deal with the veracity). We achieve these by introducing a novel privacy-preserving winner determination algorithm and a novel payment mechanism. Additionally, we further employ a blind signature scheme as a building block to let bidders verify the authenticity of their payment reported by the auctioneer. The comparison with peer work shows that we improve the asymptotic performance of peer works' overhead from the exponential growth to a linear growth and from linear growth to a logarithmic growth, which greatly improves the scalability

Landau level states on a topological insulator thin film

We analyze the four-dimensional Hamiltonian proposed to describe the band structure of the single-Dirac-cone family of topological insulators in the presence of a uniform perpendicular magnetic field. Surface Landau level(LL) states appear, decoupled from the bulk levels and following the quantized energy dispersion of a purely two-dimensional surface Dirac Hamiltonian. A small hybridization gap splits the degeneracy of the central n=0 LL with dependence on the film thickness and the field strength that can be obtained analytically. Explicit calculation of the spin and charge densities show that surface LL states are localized within approximately one quintuple layer from the surface termination. Some new surface-bound LLs are shown to exist at a higher Landau level index.Comment: 8 pages, 4 figure

Search Me If You Can: Privacy-preserving Location Query Service

Location-Based Service (LBS) becomes increasingly popular with the dramatic growth of smartphones and social network services (SNS), and its context-rich functionalities attract considerable users. Many LBS providers use users' location information to offer them convenience and useful functions. However, the LBS could greatly breach personal privacy because location itself contains much information. Hence, preserving location privacy while achieving utility from it is still an challenging question now. This paper tackles this non-trivial challenge by designing a suite of novel fine-grained Privacy-preserving Location Query Protocol (PLQP). Our protocol allows different levels of location query on encrypted location information for different users, and it is efficient enough to be applied in mobile platforms.Comment: 9 pages, 1 figure, 2 tables, IEEE INFOCOM 201

Classification of flat bands according to the band-crossing singularity of Bloch wave functions

We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular flat band, its Bloch wave function possesses immovable discontinuities generated by the band-crossing with other bands, and thus the vector bundle associated with the flat band cannot be defined. This singularity precludes the compact localized states from forming a complete set spanning the flat band. Once the degeneracy at the band crossing point is lifted, the singular flat band becomes dispersive and can acquire a finite Chern number in general, suggesting a new route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave function of a nonsingular flat band has no singularity, and thus forms a vector bundle. A nonsingular flat band can be completely isolated from other bands while preserving the perfect flatness. All one-dimensional flat bands belong to the nonsingular class. We show that a singular flat band displays a novel bulk-boundary correspondence such that the presence of the robust boundary mode is guaranteed by the singularity of the Bloch wave function. Moreover, we develop a general scheme to construct a flat band model Hamiltonian in which one can freely design its singular or nonsingular nature. Finally, we propose a general formula for the compact localized state spanning the flat band, which can be easily implemented in numerics and offer a basis set useful in analyzing correlation effects in flat bands.Comment: 23 pages, 13 figure

Searching for topological density wave insulators in multi-orbital square lattice systems

We study topological properties of density wave states with broken translational symmetry in two-dimensional multi-orbital systems with a particular focus on t$_{2g}$ orbitals in square lattice. Due to distinct symmetry properties of d-orbitals, a nodal charge or spin density wave state with Dirac points protected by lattice symmetries can be achieved. When an additional order parameter with opposite reflection symmetry is introduced to a nodal density wave state, the system can be fully gapped leading to a band insulator. Among those, topological density wave (TDW) insulators can be realized, when an effective staggered on-site potential generates a gap to a pair of Dirac points connected by the inversion symmetry which have the same topological winding numbers. We also present a mean-field phase diagram for various density wave states, and discuss experimental implications of our results.Comment: 15 pages, 10 figures, 7 table

Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle

We show that the Wannier obstruction and the fragile topology of the nearly flat bands in twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two-dimensional real wave functions characterized by the Euler class. To prove this, we examine the generic band topology of two dimensional real fermions in systems with space-time inversion $I_{ST}$ symmetry. The Euler class is an integer topological invariant classifying real two band systems. We show that a two-band system with a nonzero Euler class cannot have an $I_{ST}$-symmetric Wannier representation. Moreover, a two-band system with the Euler class $e_{2}$ has band crossing points whose total winding number is equal to $-2e_2$. Thus the conventional Nielsen-Ninomiya theorem fails in systems with a nonzero Euler class. We propose that the topological phase transition between two insulators carrying distinct Euler classes can be described in terms of the pair creation and annihilation of vortices accompanied by winding number changes across Dirac strings. When the number of bands is bigger than two, there is a $Z_{2}$ topological invariant classifying the band topology, that is, the second Stiefel Whitney class ($w_2$). Two bands with an even (odd) Euler class turn into a system with $w_2=0$ ($w_2=1$) when additional trivial bands are added. Although the nontrivial second Stiefel-Whitney class remains robust against adding trivial bands, it does not impose a Wannier obstruction when the number of bands is bigger than two. However, when the resulting multi-band system with the nontrivial second Stiefel-Whitney class is supplemented by additional chiral symmetry, a nontrivial second-order topology and the associated corner charges are guaranteed.Comment: 23 pages, 13 figure