Communication complexity

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

Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication

Abstract: We study whether information complexity can be used to attack the long-standing open problem of proving lower bounds against Arthur{Merlin (AM) communication protocols. Our starting point is to show that|in contrast to plain randomized communication complexity|every boolean function admits an AM communication protocol where on each yes- input, the distribution of Merlin's proof leaks no information about the input and moreover, this proof is unique for each outcome of Arthur's randomness. We posit that these two properties of zero information leakage and unambiguity on yes-inputs are interesting in their own right and worthy of investigation as new avenues toward AM.Zero-information protocols (ZAM). Our basic ZAM protocol uses exponential communication for some functions, and this raises the question of whether more efficient protocols exist. We prove that all functions in the classical space-bounded complexity classes NL and L have polynomial-communication ZAM protocols. We also prove that ZAM complexity is lower bounded by conondeterministic communication complexity.Unambiguous protocols (UAM). Our most technically substantial result is a (n) lower bound on the UAM complexity of the NP-complete set-intersection function; the proof uses information complexity arguments in a new, indirect way and overcomes the \zero-information barrier" described above. We also prove that in general, UAM complexity is lower bounded by the classic discrepancy bound, and we give evidence that it is not generally lower bounded by the classic corruption bound.

Precise BER Computation for Binary Data Detection in Bandlimited White Laplace Noise

Abstract: Investigation into the characteristics and behaviours of Laplace noise is of crucial importance for evaluating the performance of communication systems operating in impulsive noise, as well as for ultra-wideband wireless systems operating in the presence of multi-user interference. The bit error rate performances of a binary data communication system operating in the presence of additive bandlimited white Laplace noise is analyzed theoretically. A theoretical expression for the average bit error rate is derived using the Beaulieu series for the optimal soft-limiting detector and the matched-filter detector when arbitrary pulse shapes are used. The bit error rate performance of a reduced complexity version of the optimal detector, the hard-limiting detector, and a reduced complexity version of the matched-filter detector, the sum-of-samples detector, are also analyzed. The analytical expressions for the bit error rate are validated by numerical examples.

Private inference control

Abstract: Access control can be used to ensure that database queries pertaining to sensitive information are not answered. This is not enough to prevent users from learning sensitive information though, because users can combine non-sensitive information to discover something sensitive. Inference control prevents users from obtaining sensitive information via such "inference channels", however, existing inference control techniques are not private - that is, they require the server to learn what queries the user is making in order to deny inference-enabling queries.We propose a new primitive - private inference control (PIC) -which is a means for the server to provide inference control without learning what information is being retrieved. PIC is a generalization of private and symmetrically-private information retrieval (PIR/SPIR). While it is straightforward to implement access control using PIR (simply omit sensitive information from the database), it is nontrivial to implement inference control efficiently. We measure the efficiency of a PIC protocol in terms of its communication complexity, its round complexity, and the work the server performs per query. Under existing cryptographic assumptions, we give a PIC scheme which is simultaneously optimal, up to logarithmic factors, in the work the server performs per query, the total communication complexity, and the number of rounds of interaction. We also present a scheme requiring more communication but sufficient storage of state by the server to facilitate private user revocation. Finally, we present a generic reduction which shows that one can focus on designing PIC schemes for which the inference channels take a particularly simple threshold form.

Communication Complexity of Approximate Maximum Matching in Distributed Graph Data

Abstract: We consider the problem of computing an approximate maximum matching in a graph that consists of n vertices whose edges are stored partitioned across k distributed sites in a data center. We are interested in characterizing the communication complexity of this problem which is of primary concern in data centers where communication bandwidth is a scarce resource. Our main result is that any algorithm that finds an α-approximate maximum matching has a communication complexity of Ω(α2 k n). Perhaps surprisingly, we show that this lower bound matches an upper bound of a simple sequential algorithm, showing that no benefits can be obtained with respect to the communication cost despite the full flexibility allowed by the underlying computation model. Our lower bound for matching also implies lower bounds for other important graph problems in the distributed computation setting, including max-flow and graph sparsification. Other main contribution of this paper is a new technique for multi-party randomized communication complexity that is of wide applicability.

Essentially Optimal Universally Composable Oblivious Transfer

Abstract: Oblivious transfer is one of the most important cryptographic primitives, both for theoretical and practical reasons and several protocols were proposed during the years. We propose a protocol which is simultaneously optimal on the following list of parameters: Security: it has universal composition. Trust in setup assumptions: only one of the parties needs to trust the setup (and some setup is needed for UC security). Trust in computational assumptions: only one of the parties needs to trust a computational assumption. Round complexity: it uses only two rounds. Communication complexity: it communicates $\mathcal{O}(1)$ group elements to transfer one out of two group elements. The Big-O notation hides 32, meaning that the communication is probably not optimal, but is essentially optimal in that the overhead is at least constant. Our construction is based on pairings, and we assume the presence of a key registration authority.