In this project we design efficient secure algorithms for various multi-party protocol tasks. The protocols must be provably secure based on well-understood cryptographic assumptions, they need to satisfy requirements imposed by the real-world applications of these protocols, and they need to be efficient enough to be usable in practice. Among the protocol tasks we address are private authentication schemes, aggregate signature schemes, dynamic group key agreement schemes, and proactive cryptosystems. The challenge in designing such protocols is to achieve efficiency without making assumptions that would impede the adoption of these protocols in practice. For example, protocols that rely on a public key infrastructure cannot assume universally trusted authorities, and they should remain efficient if protocol participants hold certificates from multiple sources. Moreover, to be truly useful a multi-party protocol must remain efficient in realistic communication conditions, e.g. if the participating nodes do not have synchronized clocks, or if the communication mechanism between any two protocol participants can be disrupted. Development of efficient secure multi-party protocols which meet these efficiency goals and operational requirements relies on construction of public key primitives with novel security properties, and on finding new approaches to fundamental questions related to multi-party protocols, e.g. fairness, limitations imposed by trust assumptions, and security under protocol composition. This project can also have an immediate impact on a variety of computer systems, improving their reliability, security, and privacy properties. Examples of prospective applications of our protocols are provision of fault-tolerant security services, and enabling of group-wide security mechanisms in ad-hoc and mobile networks.