Zoë Diamadi

Computation in networks of passively mobile finite-state sensors

We explore the computational power of networks of small resource-limited mobile agents. We define two new models of computation based on pairwise interactions of finite-state agents in populations of finite but unbounded size. With a fairness condition on interactions, we define the concept of stable computation of a function or predicate, and give protocols that stably compute functions in a class including Boolean combinations of threshold-k, parity, majority, and simple arithmetic. We prove that all stably computable predicates are in NL. With uniform random sampling of pairs to interact, we define the model of conjugating automata and show that any counter machine with O(1) counters of capacity O(n) can be simulated with high probability by a protocol in a population of size n. We prove that all predicates computable with high probability in this model are in P ∩ RL. Several open problems and promising future directions are discussed.

Fault-tolerant routing in peer-to-peer systems

We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer system. We argue that many existing approaches to this problem can be modeled as the construction of a random graph embedded in a metric space whose points represent resource identifiers, where the probability of a connection between two nodes depends only on the distance between them in the metric space. We study the performance of a peer-to-peer system where nodes are embedded at grid points in a simple metric space: a one-dimensional real line. We prove upper and lower bounds on the message complexity of locating particular resources in such a system, under a variety of assumptions about failures of either nodes or the connections between them. Our lower bounds in particular show that the use of inverse power-law distributions in routing, as suggested by Kleinberg [5], is close to optimal. We also give heuristics to efficiently maintain a network supporting efficient routing as nodes enter and leave the system. Finally, we give some experimental results that suggest promising directions for future work.

A simple game for the study of trust in distributed systems

Trust is an important aspect of the design and analysis of secure distributed systems. It is often used informally to designate those portions of a system that must function correctly in order to achieve the desired outcome. But it is a notoriously diffcult notion to formalize. What are the properties of trust? How is it learned, propagated, and utilized successfully? How can it be modeled? How can a trust model be used to derive protocols that are effcient and reliable when employed in today’s expansive networks? Past work has been concerned with only a few of these issues, without concentrating on the need for a comprehensive approach to trust modeling.In this paper, we take a first step in that direction by studying an artificial community of agents that uses a notion of trust to succeed in a game against nature. The model is simple enough to analyze and simulate, but also rich enough to exhibit phenomena of real-life interactive communities. The model requires agents to make decisions. To do well, the agents are informed by knowledge gained from their own past experience as well as from the experience of other agents. Communication among agents allows knowledge to propagate faster through the network, which in turn can allow for a more successful community. We analyze the model from both a theoretical and an experimental point of view.

Spreading Alerts Quietly and the Subgroup Escape Problem

We introduce a new cryptographic primitive called a blind coupon mechanism (BCM). In effect, a BCM is an authenticated bit commitment scheme, which is AND-homomorphic. We show that a BCM has natural and important applications. In particular, we use it to construct a mechanism for transmitting alerts undetectably in a message-passing system of

Greedy Routing in Peer-to-Peer Systems ∗

n

Spreading Alerts Quietly and the Subgroup Escape Problem.

n nodes. Our algorithms allow an alert to quickly propagate to all nodes without its source or existence being detected by an adversary, who controls all message traffic. Our proofs of security are based on a new subgroup escape problem, which seems hard on certain groups with bilinear pairings and on elliptic curves over the ring