Traditional protocols for secure multi-party computation among n parties communicate at least a linear (in n) number of bits, even when computing very simple functions. In this work we investigate the feasibility of protocols with sublinear communication complexity. Concretely, we consider two clients, one of which may be corrupted, who wish to perform some “small” joint computation using n ser...

We consider wideband wireless communication over a multiple-input, multiple-output (MIMO) Rayleigh fading channel where the transmitter has no channel state information (CSI). We study the channel with perfect receiver CSI (coherent channel) versus the channel with no CSI at the receiver (non-coherent channel). A channel with partial CSI at the receiver has a capacity between the coherent and n...

Schemes for encrypted search face inherent trade-offs between efficiency and privacy guarantees. Whereas search in plaintext can leverage efficient structures to achieve sublinear query time in the data size, similar performance is harder to achieve for secure search. Oblivious RAM (ORAM) techniques can provide the desired efficiency for simple look-ups, but do not address the needs of complex ...

Consider real reductive group G, as defined in [Wal88]. Let Π be an irreducible admissible representation of G with the distribution character ΘΠ, [Har51]. Denote by uΠ the lowest term in the asymptotic expansion of ΘΠ, [BV80]. This is a finite linear combination of Fourier transforms of nilpotent coadjoint orbits, uΠ = ∑ O cOμ̂O. As shown by Rossmann, [Ros95], the closure of the union of the ni...

Private Information Retrieval (PIR) allows a client to obtain data from a public database without disclosing the locations accessed. Traditionally, the stress is on preserving sublinear work for the client, while the server’s work is taken to inevitably be at least linear in the database size. Beimel, Ishai and Malkin (JoC 2004) show PIR schemes where, following a linear-work preprocessing stag...

We describe a new succinct zero-knowledge argument protocol with the following properties. The prover commits to a large dataset M , and can thereafter prove many statements of the form ∃w : Ri(M,w) = 1, where Ri is a public function. The protocol is succinct in the sense that the cost for the verifier (in computation & communication) does not depend on |M |, not even in any initialization phas...

This paper presents a new taxonomy of sublinear (multiple) keyword pattern matching algorithms. Based on an earlier taxonomy by Watson and Zwaan [WZ96, WZ95], this new taxonomy includes not only suffix-based algorithms related to the Boyer-Moore, CommentzWalter and Fan-Su algorithms, but factorand factor oracle-based algorithms such as Backward DAWG Matching and Backward Oracle Matching as well...

When dealing with massive data sets, standard algorithms may easily “run out of memory”. In this thesis, we design efficient algorithms in space-conscious models. In particular, in-place algorithms, multi-pass algorithms, read-only algorithms, and stream-sort algorithms are studied, and the focus is on fundamental geometric problems, such as 2D convex hulls, 3D convex hulls, Voronoi diagrams an...

Sufficient conditions for the existence of at least one solution of anti-periodic boundary value problems for nonlinear functional difference equations are established. We allow f to be at most linear, superlinear or sublinear in obtained results.

We study conditions under which the silhouette of a polyhedron is guaranted to be sublinear, either on average or in the worst case, and give some counter-examples when not.