Communication complexity

About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.

Secure quantum private information retrieval using phase-encoded queries

Abstract: We propose a quantum solution to the classical private information retrieval (PIR) problem, which allows one to query a database in a private manner. The protocol offers privacy thresholds and allows the user to obtain information from a database in a way that offers the potential adversary, in this model the database owner, no possibility of deterministically establishing the query contents. This protocol may also be viewed as a solution to the symmetrically private information retrieval problem in that it can offer database security (inability for a querying user to steal its contents). Compared to classical solutions, the protocol offers substantial improvement in terms of communication complexity. In comparison with the recent quantum private queries [Phys. Rev. Lett. 100, 230502 (2008)] protocol, it is more efficient in terms of communication complexity and the number of rounds, while offering a clear privacy parameter. We discuss the security of the protocol and analyze its strengths and conclude that using this technique makes it challenging to obtain the unconditional (in the information-theoretic sense) privacy degree; nevertheless, in addition to being simple, the protocol still offers a privacy level. The oracle used in the protocol is inspired both by the classical computational PIR solutionsmore » as well as the Deutsch-Jozsa oracle.« less

Joint encryption and message-efficient secure computation

Abstract: This paper addresses the message complexity of secure computation in the (passive adversary) privacy setting. We show that O(nC) encrypted bits of communication suffice for n parties to evaluate any boolean circuit of size C privately, under a specific cryptographic assumption. This work establishes a connection between secure distributed computation and group-oriented cryptography, i.e., cryptographic methods in which subsets of individuals can act jointly as single agents. Our secure computation protocol relies on a new group-oriented probablistic public-key encryption scheme with useful algebraic properties.

Lower bounds in communication complexity based on factorization norms

Abstract: We introduce a new method to derive lower bounds on randomized and quantum communication complexity. Our method is based on factorization norms, a notion from Banach Space theory. This approach gives us access to several powerful tools from this area such as normed spaces duality and Grothendiek's inequality. This extends the arsenal of methods for deriving lower bounds in communication complexity. As we show, our method subsumes most of the previously known general approaches to lower bounds on communication complexity. Moreover, we extend all (but one) of these lower bounds to the realm of quantum communication complexity with entanglement. Our results also shed some light on the question how much communication can be saved by using entanglement. It is known that entanglement can save one of every two qubits, and examples for which this is tight are also known. It follows from our results that this bound on the saving in communication is tight almost always. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009

The Partition Bound for Classical Communication Complexity and Query Complexity

Abstract: We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the partition bound is stronger than both the rectangle/corruption bound and the γ2/generalized discrepancy bounds. In the model of query complexity we show that the partition bound is stronger than the approximate polynomial degree and classical adversary bounds. We also exhibit an example where the partition bound is quadratically larger than the approximate polynomial degree and adversary bounds.

Rectangle size bounds and threshold covers in communication complexity

Abstract: We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, with respect to arbitrary distributions on the inputs. While it is known that the 0-error version of this bound is polynomially tight for deterministic communication, nothing in this direction is known for constant error and randomized communication complexity. We first study a one-sided version of this bound and obtain that its value lies between the MA- and AM- complexities of the considered function. Hence the lower bound actually works for a (communication) complexity class between MA/spl cap/co - MA and AM/spl cap/co - AM, and allows to show that the MA-complexity of the disjointness problem is /spl Omega/(/spl radic/n). Following this we consider the conjecture that the lower bound method is polynomially tight for randomized communication complexity. First we disprove a distributional version of this conjecture. Then we give a combinatorial characterization of the value of the lower bound method, in which the optimization over all distributions is absent. This characterization is done by what we call a bounded error uniform threshold cover, and reduces showing tightness of the bound to the construction of an efficient protocol for a specific communication problem. We then study relaxations of bounded error uniform threshold covers, namely approximate majority covers and majority covers, and exhibit exponential separations between them. Each of these covers captures a lower bound method previously used for randomized communication complexity.