Communication complexity

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

Efficient and secure protocols for privacy-preserving set operations

Abstract: Many applications require performing set operations without publishing individual datesets. In this article, we address this problem for five fundamental set operations including set intersection, cardinality of set intersection, element reduction, overthreshold set-union, and subset relation. Our protocols are obtained in the universally composable security framework, in the assumption of the probabilistic polynomial time bounded adversary, which actively controls a fixed set of t parties and the assumption of an authenticated broadcast channel. Our constructions utilize building blocks of nonmalleable NonInteractive Zero-Knowledge (NIZK) arguments, which are based on a (t + 1,N)-threshold version (N is the number of parties in the protocol) of the boneh-goh-nissim (BGN) cryptosystem whose underlying group supports bilinear maps, in the assumption that the public key and shares of the secret key have been generated by a trusted dealer. The previous studies were all based on the stand-alone model with the same assumptions on the adversary, broadcast channel, and key generation. For the first four operations, we propose protocols that improve the previously known results by an O(N) factor in the computation and communication complexities. For the subset relation, our protocol is the first one secure against the active adversary. Our constructions of NIZK have independent interest in that, though also mentioned as building blocks, the previous work did not illustrate how to construct them. We construct these NIZK with an additional nonmalleable property, the same complexity as claimed in the previous work, and also an improvement on the communication complexity.

Labeled PSI from Fully Homomorphic Encryption with Malicious Security.

Abstract: Private Set Intersection (PSI) allows two parties, the sender and the receiver, to compute the intersection of their private sets without revealing extra information to each other. We are interested in the unbalanced PSI setting, where (1) the receiver's set is significantly smaller than the sender's, and (2) the receiver (with the smaller set) has a low-power device. Also, in a Labeled PSI setting, the sender holds a label per each item in its set, and the receiver obtains the labels from the items in the intersection. We build upon the unbalanced PSI protocol of Chen, Laine, and Rindal (CCS~2017) in several ways: we add efficient support for arbitrary length items, we construct and implement an unbalanced Labeled PSI protocol with small communication complexity, and also strengthen the security model using Oblivious Pseudo-Random Function (OPRF) in a pre-processing phase. Our protocols outperform previous ones: for an intersection of 220 and $512$ size sets of arbitrary length items our protocol has a total online running time of just $1$~second (single thread), and a total communication cost of 4 MB. For a larger example, an intersection of 228 and 1024 size sets of arbitrary length items has an online running time of $12$ seconds (multi-threaded), with less than 18 MB of total communication.

Las Vegas Versus Determinism for One-way Communication Complexity, Finite Automata, and Polynomial-time Computations

Abstract: The study of the computational power of randomized computations is one of the central tasks of complexity theory. The main aim of this paper is the comparison of the power of Las Vegas computation and deterministic respectively nondeterministic computation. An at most polynomial gap has been established for the combinational complexity of circuits and for the communication complexity of two-party protocols. We investigate the power of Las Vegas computation for the complexity measures of one-way communication, finite automata and polynomialtime relativized Turing machine computation. (i) For the one-way communication complexity of two-party protocols we show that Las Vegas communication can save at most one half of the deterministic one-way communication complexity. We also present a language for which this gap is tight. (ii) For the size (i.e., the number of states) of finite automata we show that the size of Las Vegas finite automata recognizing a language L is at least the root of the size of the minimal deterministic finite automaton recognizing L. Using a specific language we verify the optimality of this lower bound.

Prioritized token-based mutual exclusion for distributed systems

Abstract: A number of solutions have been proposed for the problem of mutual exclusion in distributed systems. Some of these approaches have since been extended to a prioritized environment suitable for real-time applications but impose a higher message passing overhead than our approach. We present a new protocol for prioritized mutual exclusion in a distributed environment. Our approach uses a token-based model working on a logical tree structure, which is dynamically modified. In addition, we utilize a set of local queues whose union would resemble a single global queue. Furthermore, our algorithm is designed for out-of-order message delivery, handles messages asynchronously and supports multiple requests from one node for multi-threaded nodes. The prioritized algorithm has an average overhead of O(log(n)) messages per request for mutual exclusion with a worst-case overhead of O(n), where n represents the number of nodes in the system. Thus, our prioritized algorithm matches the message complexity of the best non-prioritized algorithms while previous prioritized algorithms have a higher message complexity, to our knowledge. Our concept of local queues can be incorporated into arbitrary token-based protocols with or without priority support to reduce the amount of messages. Performance results indicate that the additional functionality of our algorithm comes at the cost of 30% longer response times within our test environment for distributed execution when compared with an unprioritized algorithm. This result suggests that the algorithm should be used when strict priority ordering is required.

Solving narrow banded systems on ensemble architectures

Abstract: We present concurrent algorithms for the solution of narrow banded systems on ensemble architectures, and analyze the communication and arithmetic complexities of the algorithms. The algorithms consist of three phases. In phase 1, a block tridiagonal system of reduced size is produced through largely local operations. Diagonal dominance is preserved. If the original system is positive, definite, and symmetric, so is the reduced system. It is solved in a second phase, and the remaining variables obtained through local back substitution in a third phase. With a sufficient number of processing elements, there is no first and third phase. We investigate the arithmetic and communicationcomplexity of Gaussian elimination and block cyclic reduction for the solution of the reduced system on boolean cubes, perfect shuffle and shuffle-exchange networks, binary trees, and linear arrays.With an optimum number of processors, the minimum solution time on a linear array is of an order that ranges from O(m2√Nm) to O(m3 + m3log2(N/m)) depending on the bandwidth, the dimension of the problem, and the times for communication and arithmetic. For boolean cubes, cube-connected cycles, prefect shuffle and shuffle-exchange networks, and binary trees, the minimum time is O(m3+m3log2(N/m)) including the communication complexity