Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is the most realistic model of physically feasible computation, then we must ask: What classical protocols remain secure against quantum attackers? Our main contribution is showing the existence of classical two-party protocols for the secure evaluation of any polynomial-time function under reasonable computational assumptions (for example, it suffices that the learning with errors problem be hard for quantum polynomial time). Our result shows that the basic two-party feasibility picture from classical cryptography remains unchanged in a quantum world.
We show that, in the ideal-cipher model, triple encryption (the cascade of three independently-keyed blockciphers) is more secure than single or double encryption, thereby resolving a long-standing open problem. Our result demonstrates that for DES parameters (56-bit keys and 64-bit plaintexts) an adversary's maximal advantage against triple encryption is small until it asks about 278 queries. Our proof uses code-based game-playing in an integral way, and is facilitated by a framework for such proofs that we provide. We investigate the question of whether the security of protocols in the information-theoretic setting (where the adversary is computationally unbounded) implies the security of these protocols under concurrent composition. This question is motivated by the folklore that all known protocols that are secure in the information-theoretic setting are indeed secure under concurrent composition. We provide answers to this question for a number of different settings (i.e., considering perfect versus statistical security, and concurrent composition with adaptive versus fixed inputs). Our results enhance the understanding of what is necessary for obtaining security under composition, as well as providing tools (i.e., composition theorems) that can be used for proving the security of protocols under composition while considering only the standard stand-alone definitions of security.