Query-Efficient Locally Decodable Codes of Subexponential Length

We develop the algebraic theory behind the constructions of Yekhanin (2008) and Efremenko (2009), in an attempt to understand the ``algebraic niceness'' phenomenon in $\mathbb{Z}_m$. We show that every integer $m = pq = 2^t -1$, where $p$, $q$ and $t$ are prime, possesses the same good algebraic property as $m=511$ that allows savings in query complexity. We identify 50 numbers of this form by computer search, which together with 511, are then applied to gain improvements on query complexity via Itoh and Suzuki's composition method. More precisely, we construct a $3^{\lceil r/2\rceil}$-query LDC for every positive integer $r<104$ and a $\left\lfloor (3/4)^{51}\cdot 2^{r}\right\rfloor$-query LDC for every integer $r\geq 104$, both of length $N_{r}$, improving the $2^r$ queries used by Efremenko (2009) and $3\cdot 2^{r-2}$ queries used by Itoh and Suzuki (2010). We also obtain new efficient private information retrieval (PIR) schemes from the new query-efficient LDCs.Comment: to appear in Computational Complexit

An Efficient Method for Realizing Contractions of Access Structures in Cloud Storage

In single-cloud storage, ciphertext-policy attribute-based encryption (CP-ABE) allows one to encrypt any data under an access structure to a cloud server, specifying what attributes are required to decrypt. In multi-cloud storage, a secret sharing scheme (SSS) allows one to split any data into multiple shares, one to a single server, and specify which subset of the servers are able to recover the data. It is an interesting problem to remove some attributes/servers but still enable the remaining attributes/servers in every authorized set to recover the data. The problem is related to the contraction problem of access structures for SSSs. In this paper, we propose a method that can efficiently transform a given SSS for an access structure to SSSs for contractions of the access structure. We show its applications in solving the attribute removal problem in the CP-ABE based single-cloud storage and the data relocating problem in multi-cloud storage. Our method results in solutions that require either less server storage or even no additional server storage.Comment: IEEE Transactions on Services Computin

One-way cloak based on nonreciprocal photonic crystal

We propose a physical concept of non-reciprocal transformation optics, by which a one-way invisible cloak is designed. The one-way invisible cloak is made of a coordinate-transformed nonreciprocal photonic crystal, showing a perfect cloaking for wave incident from one direction but acting as a perfect reflector for wave from the counter direction. The proposed design shows a high promise of applications in military, as protecting the own information to be detected but efficiently grabbing the information from the “enemy” side

Probing Half-odd Topological Number with Cold Atoms in a Non-Abelian Optical Lattice

We propose an experimental scheme to probe the contribution of a single Dirac cone to the Hall conductivity as half-odd topological number sequence. In our scheme, the quantum anomalous Hall effect as in graphene is simulated with cold atoms trapped in an optical lattice and subjected to a laser-induced non-Abelian gauge field. By tuning the laser intensity to change the gauge flux, the energies of the four Dirac points in the first Brillouin zone are shifted with each other and the contribution of the single Dirac cone to the total atomic Hall conductivity is manifested. We also show such manifestation can be experimentally probed with atomic density profile measurements.Comment: 5 pages, 3 figure