Asymmetric Multi-Party Computation

Current protocols for Multi-Party Computation (MPC) consider the setting where all parties have access to similar resources. For example, all parties have access to channels bounded by the same worst-case delay upper bound ?, and all channels have the same cost of communication. As a consequence, the overall protocol performance (resp. the communication cost) may be heavily affected by the slowest (resp. the most expensive) channel, even when most channels are fast (resp. cheap). Given the state of affairs, we initiate a systematic study of asymmetric MPC. In asymmetric MPC, the parties are divided into two categories: fast and slow parties, depending on whether they have access to high-end or low-end resources. We investigate two different models. In the first, we consider asymmetric communication delays: Fast parties are connected via channels with small delay ? among themselves, while channels connected to (at least) one slow party have a large delay ? ? ?. In the second model, we consider asymmetric communication costs: Fast parties benefit from channels with cheap communication, while channels connected to a slow party have an expensive communication. We provide a wide range of positive and negative results exploring the trade-offs between the achievable number of tolerated corruptions t and slow parties s, versus the round complexity and communication cost in each of the models. Among others, we achieve the following results. In the model with asymmetric communication delays, focusing on the information-theoretic (i-t) setting: - An i-t asymmetric MPC protocol with security with abort as long as t+s < n and t < n/2, in a constant number of slow rounds. - We show that achieving an i-t asymmetric MPC protocol for t+s = n and with number of slow rounds independent of the circuit size implies an i-t synchronous MPC protocol with round complexity independent of the circuit size, which is a major problem in the field of round-complexity of MPC. - We identify a new primitive, asymmetric broadcast, that allows to consistently distribute a value among the fast parties, and at a later time the same value to slow parties. We completely characterize the feasibility of asymmetric broadcast by showing that it is possible if and only if 2t + s < n. - An i-t asymmetric MPC protocol with guaranteed output delivery as long as t+s < n and t < n/2, in a number of slow rounds independent of the circuit size. In the model with asymmetric communication cost, we achieve an asymmetric MPC protocol for security with abort for t+s < n and t < n/2, based on one-way functions (OWF). The protocol communicates a number of bits over expensive channels that is independent of the circuit size. We conjecture that assuming OWF is needed and further provide a partial result in this direction

Asymmetric Multi-Party Computation

Current protocols for Multi-Party Computation (MPC) consider the setting where all parties have access to similar resources. For example, all parties have access to channels bounded by the same worst-case delay upper bound $\Delta$, and all channels have the same cost of communication. As a consequence, the overall protocol performance (resp. the communication cost) may be heavily affected by the slowest (resp. the most expensive) channel, even when most channels are fast (resp. cheap). Given the state of affairs, we initiate a systematic study of \u27asymmetric\u27 MPC. In asymmetric MPC, the parties are divided into two categories: fast and slow parties, depending on whether they have access to high-end or low-end resources. We investigate two different models. In the first, we consider asymmetric communication delays: Fast parties are connected via channels with small delay $\delta$ among themselves, while channels connected to (at least) one slow party have a large delay $\Delta \gg \delta$. In the second model, we consider asymmetric communication costs: Fast parties benefit from channels with cheap communication, while channels connected to a slow party have an expensive communication. We provide a wide range of positive and negative results exploring the trade-offs between the achievable number of tolerated corruptions $t$ and slow parties $s$, versus the round complexity and communication cost in each of the models. Among others, we achieve the following results. In the model with asymmetric communication delays, focusing on the information-theoretic (i-t) setting: - An i-t asymmetric MPC protocol with security with abort as long as $t+s < n$ and $t<n/2$, in a constant number of slow rounds. - We show that achieving an i-t asymmetric MPC protocol for $t+s = n$ and with number of slow rounds independent of the circuit size implies an i-t synchronous MPC protocol with round complexity independent of the circuit size, which is a major problem in the field of round-complexity of MPC. - We identify a new primitive, \emph{asymmetric broadcast}, that allows to consistently distribute a value among the fast parties, and at a later time the same value to slow parties. We completely characterize the feasibility of asymmetric broadcast by showing that it is possible if and only if $2t + s < n$. - An i-t asymmetric MPC protocol with guaranteed output delivery as long as $t+s < n$ and $t<n/2$, in a number of slow rounds independent of the circuit size. In the model with asymmetric communication cost, we achieve an asymmetric MPC protocol for security with abort for $t+s<n$ and $t<n/2$, based on one-way functions (OWF). The protocol communicates a number of bits over expensive channels that is independent of the circuit size. We conjecture that assuming OWF is needed and further provide a partial result in this direction

Secure multi-party protocols under a modern lens

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 263-272).A secure multi-party computation (MPC) protocol for computing a function f allows a group of parties to jointly evaluate f over their private inputs, such that a computationally bounded adversary who corrupts a subset of the parties can not learn anything beyond the inputs of the corrupted parties and the output of the function f. General MPC completeness theorems in the 1980s showed that every efficiently computable function can be evaluated securely in this fashion [Yao86, GMW87, CCD87, BGW88] using the existence of cryptography. In the following decades, progress has been made toward making MPC protocols efficient enough to be deployed in real-world applications. However, recent technological developments have brought with them a slew of new challenges, from new security threats to a question of whether protocols can scale up with the demand of distributed computations on massive data. Before one can make effective use of MPC, these challenges must be addressed. In this thesis, we focus on two lines of research toward this goal: " Protocols resilient to side-channel attacks. We consider a strengthened adversarial model where, in addition to corrupting a subset of parties, the adversary may leak partial information on the secret states of honest parties during the protocol. In presence of such adversary, we first focus on preserving the correctness guarantees of MPC computations. We then proceed to address security guarantees, using cryptography. We provide two results: an MPC protocol whose security provably "degrades gracefully" with the amount of leakage information obtained by the adversary, and a second protocol which provides complete security assuming a (necessary) one-time preprocessing phase during which leakage cannot occur. * Protocols with scalable communication requirements. We devise MPC protocols with communication locality: namely, each party only needs to communicate with a small (polylog) number of dynamically chosen parties. Our techniques use digital signatures and extend particularly well to the case when the function f is a sublinear algorithm whose execution depends on o(n) of the n parties' inputs.by Elette Chantae Boyle.Ph.D

Experimental Investigations of Millimeter Wave Beamforming

The millimeter wave (mmW) band, commonly referred to as the frequency band between 30 GHz and 300 GHz, is seen as a possible candidate to increase achievable rates for mobile applications due to the existence of free spectrum. However, the high path loss necessitates the use of highly directional antennas. Furthermore, impairments and power constraints make it difficult to provide full digital beamforming systems. In this thesis, we approach this problem by proposing effective beam alignment and beam tracking algorithms for low-complex analog beamforming (ABF) systems, showing their applicability by experimental demonstration. After taking a closer look at particular features of the mmW channel properties and introducing the beamforming as a spatial filter, we begin our investigations with the application of detection theory for the non-convex beam alignment problem. Based on an M-ary hypothesis test, we derive algorithms for defining the length of the training signal efficiently. Using the concept of black-box optimization algorithms, which allow optimization of non-convex algorithms, we propose a beam alignment algorithm for codebook-based ABF based systems, which is shown to reduce the training overhead significantly. As a low-complex alternative, we propose a two-staged gradient-based beam alignment algorithm that uses convex optimization strategies after finding a subregion of the beam alignment function in which the function can be regarded convex. This algorithm is implemented in a real-time prototype system and shows its superiority over the exhaustive search approach in simulations and experiments. Finally, we propose a beam tracking algorithm for supporting mobility. Experiments and comparisons with a ray-tracing channel model show that it can be used efficiently in line of sight (LoS) and non line of sight (NLoS) scenarios for walking-speed movements

Resource-Efficient and Robust Distributed Computing

There has been a tremendous growth in the size of distributed systems in the past three decades. Today, distributed systems, such as the Internet, have become so large that they require highly scalable algorithms; algorithms that have asymptotically-small communication, computation, and latency costs with respect to the network size. Moreover, systems with thousands or even millions of parties distributed throughout the world is likely in danger of faults from untrusted parties. In this dissertation, we study scalable and secure distributed algorithms that can tolerate faults from untrusted parties. Throughout this work, we balance two important and often conflicting characteristics of distributed protocols: security and efficiency. Our first result is a protocol that solves the MPC problem in polylogarithmic communication and computation cost and is secure against an adversary than can corrupt a third of the parties. We adapted our synchronous MPC protocol to the asynchronous setting when the fraction of the corrupted parties are less than 1/8. Next, we presented a scalable protocol that solves the secret sharing problem between rational parties in polylogarithmic communication and computation cost. Furthermore, we presented a protocol that can solve the interactive communication problem over a noisy channel when the noise rate in unknown. In this problem, we have focused on the cost of the protocol in the resource-competitive analysis model. Unlike classic models, resource-competitive models consider the cost that the adversary must pay to succeed in corrupting the protocol

CAD Tools for DNA Micro-Array Design, Manufacture and Application

Motivation: As the human genome project progresses and some microbial and eukaryotic genomes are recognized, numerous biotechnological processes have attracted increasing number of biologists, bioengineers and computer scientists recently. Biotechnological processes profoundly involve production and analysis of highthroughput experimental data. Numerous sequence libraries of DNA and protein structures of a large number of micro-organisms and a variety of other databases related to biology and chemistry are available. For example, microarray technology, a novel biotechnology, promises to monitor the whole genome at once, so that researchers can study the whole genome on the global level and have a better picture of the expressions among millions of genes simultaneously. Today, it is widely used in many fields- disease diagnosis, gene classification, gene regulatory network, and drug discovery. For example, designing organism specific microarray and analysis of experimental data require combining heterogeneous computational tools that usually differ in the data format; such as, GeneMark for ORF extraction, Promide for DNA probe selection, Chip for probe placement on microarray chip, BLAST to compare sequences, MEGA for phylogenetic analysis, and ClustalX for multiple alignments. Solution: Surprisingly enough, despite huge research efforts invested in DNA array applications, very few works are devoted to computer-aided optimization of DNA array design and manufacturing. Current design practices are dominated by ad-hoc heuristics incorporated in proprietary tools with unknown suboptimality. This will soon become a bottleneck for the new generation of high-density arrays, such as the ones currently being designed at Perlegen [109]. The goal of the already accomplished research was to develop highly scalable tools, with predictable runtime and quality, for cost-effective, computer-aided design and manufacturing of DNA probe arrays. We illustrate the utility of our approach by taking a concrete example of combining the design tools of microarray technology for Harpes B virus DNA data

Powers of Tau in Asynchrony

The $q$-Strong Diffie-Hellman ($q$-SDH) parameters are foundational to efficient constructions of many cryptographic primitives such as zero-knowledge succinct non-interactive argument of knowledge, polynomial/vector commitments, verifiable secret sharing, and randomness beacon. The only existing method to generate these parameters securely is highly sequential, requires strong network synchrony assumptions, and has very high communication and computation cost. For example, to generate parameters for any given $q$, each party incurs a communication cost of $\Omega(nq)$ and requires $\Omega(n)$ rounds. Here $n$ is the number of parties in the secure multiparty computation protocol. Since $q$ is typically large, i.e., on the order of billions, the cost is highly prohibitive. In this paper, we present Tauron, a distributed protocol to generate $q$-SDH parameters in an asynchronous network. In a network of $n$ parties, Tauron tolerates up to one-third of malicious parties. Each party incurs a communication cost of $O(q + n^2\log q)$ and the protocol finishes in $O(\log q + \log n)$ expected rounds. We provide a rigorous security analysis of our protocol. We implement Tauron and evaluate it with up to 128 geographically distributed parties. Our evaluation illustrates that Tauron is highly scalable and results in a 2-6$\times$ better runtime and 4-13$\times$ better per-party bandwidth usage

The Round Complexity of Perfect MPC with Active Security and Optimal Resiliency

In STOC 1988, Ben-Or, Goldwasser, and Wigderson (BGW) established an important milestone in the fields of cryptography and distributed computing by showing that every functionality can be computed with perfect (information-theoretic and error-free) security at the presence of an active (aka Byzantine) rushing adversary that controls up to $n/3$ of the parties. We study the round complexity of general secure multiparty computation in the BGW model. Our main result shows that every functionality can be realized in only four rounds of interaction, and that some functionalities cannot be computed in three rounds. This completely settles the round-complexity of perfect actively-secure optimally-resilient MPC, resolving a long line of research. Our lower-bound is based on a novel round-reduction technique that allows us to lift existing three-round lower-bounds for verifiable secret sharing to four-round lower-bounds for general MPC. To prove the upper-bound, we develop new round-efficient protocols for computing degree-2 functionalities over large fields, and establish the completeness of such functionalities. The latter result extends the recent completeness theorem of Applebaum, Brakerski and Tsabary (TCC 2018, Eurocrypt 2019) that was limited to the binary field