Unstructured, decentralized systems --- including ad-hoc/sensor networks and peer-to-peer networks --- are emerging as a central focus of computer science research. Methods for securing these systems are critical; however, these systems differ markedly from classical distributed systems (which are, in comparison, more ``structured'' and well-organized) and thus current cryptographic models and mechanisms are simply not sufficient for addressing the full range of security requirements. This work aims to provide solid theoretical foundations as well as novel cryptographic protocols and primitives for this new area. In particular, research focuses on (1) new models for formally reasoning about, and rigorously proving the security of, various applications within unstructured, decentralized systems; (2) issues of ``trust'' and ``reputation'' within such systems; and (3) new cryptographic protocols emphasizing both efficiency (for potential use by resource-limited devices within, e.g., ad-hoc networks) as well as new security concerns (such as anonymity) arising in multi-user distributed environments. The models and techniques developed as part of this work are expected to be broadly applicable to security problems arising in many distributed systems, and it is hoped that this work will serve as an impetus for future research in this area, while providing suitable tools and frameworks within which such research can be performed. Results will be incorporated into graduate-level courses and presented at a ``crypto reading group'' being organized at the University of Maryland; they will be further disseminated to a wide audience at conferences and via publicly-available lecture notes.