Relationships between functionality, security, and privacy for multiparty computation, hashing, and encryption

Abstract

One of the fundamental goals of cryptography is to be able to offer security and privacy without sacrificing functionality. Cryptographers have been able to achieve the best of all three by exploiting the assumed hardness of some problems (e.g. discrete log), and have been able to build protocols for secure multiparty computation, collision-resistant hash functions, public key cryptography, and much more. This thesis explores three facets of this balance. First, we delve into Topology-Hiding Computation, which is multiparty computation where we also hide the communication network, strengthening the notion of privacy. Second, we study Property Preserving Hashing, which can be thought of as an extension of collision-resistant hashing where we add functionality. Finally, we explore Fine-Grained Cryptography, and develop a public key cryptosystem. In this model of cryptography, security takes on a much less restrictive role (e.g. adversaries must run in O(n¹⁰) time), but the protocols and security reductions must run in "fine-grained" time (e.g. less than O(n⁵)).