Related papers: Finding Collisions in Interactive Protocols -- Tig…
Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful…
Searching for collisions in random functions is a fundamental computational problem, with many applications in symmetric and asymmetric cryptanalysis. When one searches for a single collision, the known quantum algorithms match the query…
The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…
We propose a linear algebraic method, rooted in the spectral properties of graphs, that can be used to prove lower bounds in communication complexity. Our proof technique effectively marries spectral bounds with information-theoretic…
We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…
Coin-flipping is a cryptographic task in which two physically separated, mistrustful parties wish to generate a fair coin-flip by communicating with each other. Chailloux and Kerenidis (2009) designed quantum protocols that guarantee…
Key-agreement protocols whose security is proven in the random oracle model are an important alternative to protocols based on public-key cryptography. In the random oracle model, the parties and the eavesdropper have access to a shared…
In this paper, we present a very important primitive called Information Checking Protocol (ICP) which plays an important role in constructing statistical Verifiable Secret Sharing (VSS) and Weak Secret Sharing (WSS) protocols. Informally,…
This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities,…
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…
In secure multiparty computation (MPC), mutually distrusting users collaborate to compute a function of their private data without revealing any additional information about their data to other users. While it is known that information…
We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs…
We study the fundamental communication limits of information-theoretic secure aggregation in a hierarchical network consisting of a server, multiple relays, and multiple users per relay. Communication proceeds over two rounds and two hops,…
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…
Broadcast protocols enable a set of $n$ parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, randomization and cryptography were harnessed to achieve…
We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(\log n) qubits for…
We consider information theoretic secret key agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the…
Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…