New notions of security

Secure multi-party computation (MPC, for short) is a powerful cryptographic concept which lets mutually distrusting parties collaborate without compromising their private information (beyond what is required by the functionality for which they collaborate). The functionality allowed in such a collaboration is so general that MPC subsumes virtually all other cryptographic tasks. Much of the two and a half decades of cryptographic research can be seen as striving towards the Holy Grail of realizing secure MPC in the most challenging scenario in which the parties carry out multiple tasks concurrently, the entire communication is adversarially controlled and there are no universally trusted entities.; In this thesis, for the first time we show how to realize secure MPC in such a general setting. Our contribution can be considered three-fold: (1) Definition of security. We present a new framework---called Los Angeles Network aware security---for defining security of MPC protocols. This builds on Canetti's Universally Composable security framework, under which it was known that very few distributed tasks can be carried out securely (unless globally trusted entities were used by the protocol). (2) Protocols and proofs. We build a new protocol for Multi-Party Computation which uses no globally trusted entities, and prove that it is secure in the Los Angeles Network aware security framework, under certain complexity theoretic assumptions. The high-level structure of the protocol and proof of security resembles that in previous works on Multi-Party Computation, but we employ novel approaches in designing the lower level elements of our protocol. (3) Complexity theoretic assumptions. We introduce new complexity theoretic assumptions, and show their use in proving the security of our protocols. The assumptions we make are somewhat different from those used in previous works. We informally argue why our assumptions are reasonable.; Also, we introduce an extension to the Los Angeles Network aware security framework---called monitored security---to obtain a greater security-efficiency trade off. We show how Network aware security guarantees, albeit weak, can be given under this framework for much more efficient and simpler protocols.