Adaptively Secure Coin-Flipping, Revisited

The full-information model was introduced by Ben-Or and Linial in 1985 to study collective coin-flipping: the problem of generating a common bounded-bias bit in a network of $n$ players with $t=t(n)$ faults. They showed that the majority protocol can tolerate $t=O(\sqrt n)$ adaptive corruptions, and conjectured that this is optimal in the adaptive setting. Lichtenstein, Linial, and Saks proved that the conjecture holds for protocols in which each player sends a single bit. Their result has been the main progress on the conjecture in the last 30 years. In this work we revisit this question and ask: what about protocols involving longer messages? Can increased communication allow for a larger fraction of faulty players? We introduce a model of strong adaptive corruptions, where in each round, the adversary sees all messages sent by honest parties and, based on the message content, decides whether to corrupt a party (and intercept his message) or not. We prove that any one-round coin-flipping protocol, regardless of message length, is secure against at most $\tilde{O}(\sqrt n)$ strong adaptive corruptions. Thus, increased message length does not help in this setting. We then shed light on the connection between adaptive and strongly adaptive adversaries, by proving that for any symmetric one-round coin-flipping protocol secure against $t$ adaptive corruptions, there is a symmetric one-round coin-flipping protocol secure against $t$ strongly adaptive corruptions. Returning to the standard adaptive model, we can now prove that any symmetric one-round protocol with arbitrarily long messages can tolerate at most $\tilde{O}(\sqrt n)$ adaptive corruptions. At the heart of our results lies a novel use of the Minimax Theorem and a new technique for converting any one-round secure protocol into a protocol with messages of $polylog(n)$ bits. This technique may be of independent interest

Automatic Code Placement Alternatives for Ad-Hoc And Sensor Networks

Developing applications for ad-hoc and sensor networks poses significant challenges. Many interesting applications in these domains entail collaboration between components distributed throughout an ad-hoc network. Defining these components, optimally placing them on nodes in the ad-hoc network and relocating them in response to changes is a fundamental problem faced by such applications. Manual approaches to code and data migration are not only platform-dependent and error-prone, but also needlessly complicate application development. Further, locally optimal decisions made by applications that share the same network can lead to globally unstable and energy inefficient behavior. In this paper we describe the design and implementation of a distributed operating system for ad-hoc and sensor networks whose goal is to enable power-aware, adaptive, and easy-to-develop ad-hoc networking applications. Our system achieves this goal by providing a single system image of a unified Java virtual machine to applications over an ad-hoc collection of heterogeneous nodes. It automatically and transparently partitions applications into components and dynamically finds a placement of these components on nodes within the ad-hoc network to reduce energy consumption and increase system longevity. This paper outlines the design of our system and evaluates two practical, power-aware, online algorithms for object placement that form the core of our system. We demonstrate that our algorithms can increase system longevity by a factor of four to five by effectively distributing energy consumption, and are suitable for use in an energy efficient operating system in which applications are distributed automatically and transparently

Lower Bounds for Leader Election and Collective Coin-Flipping in the Perfect Information Model

Collective coin-flipping is the problem of producing common random bits in a distributed computing environment with adversarial faults. We consider the perfect information model: all communication is by broadcast and corrupt players are computationally unbounded. Protocols in this model may involve many asynchronous rounds; we focus on protocols which permit each player to broadcast a single bit per round. We demonstrate that any n-player coin-flipping protocol resilient against corrupt coalitions of linear size must use \Theta 1=2 \Gamma o(1) log n rounds of communication. Such a bound also applies to the leader election problem. This extends work of Kahn, Kalai, and Linial, who proved a similar result for single-round protocols. The primary component of the above result is a new bound on the influence of random sets of variables on Boolean functions. Finally, in the one-round case, we prove a new bound on the influence of sets of variables of size fin, for fi ? 1=3