Approaches to efficient and robust cryptographic protocols

The growing influence of the Internet and other communication networks on our daily lives and on the global economy shows clearly that the security issues in such networks are of the uttermost importance. Motivated both by the theoretical questions and by the potential real-world applications, in this dissertation we study problems of secure cooperation in communication networks. In particular we focus on constructing efficient and robust protocols for various cryptographic tasks. In the first part of this thesis we study the problem of secure multiparty computation (MPC), which allows a set of n players to evaluate an agreed function of their inputs in a secure way, i.e., so that an adversary corrupting some of the players cannot achieve more than controlling the inputs and outputs of these players. The concept of MPC is very general and powerful, since it allows to realize essentially any distributed computational task in a secure way. For that reason the MPC problem has been studied extensively since its introduction by Yao in 1982. A major goal of these studies is to design protocols with low communication complexity, and two main research directions emerged over the time, with focus on reducing round-, resp. bit-complexity. In this thesis we focus on the bitcomplexity, i.e., the number of bits communicated between the parties during the computation, and we consider this problem in asynchronous networks, which model pretty closely real-world networks. We propose an MPC protocol, which is secure with respect to an active adversary corrupting up to t < n/3 players (this is optimal in an asynchronous network), and which is the most efficient protocol currently known. For our constructions we develop several novel techniques, which were used also in subsequent works on efficient MPC protocols. In the second part of this thesis we turn to a problem which is common to all cryptographic research based on computational assumptions.