# Biblio

Threshold cryptography provides a mechanism for protecting secret keys by sharing them among multiple parties, who then jointly perform cryptographic operations. An attacker who corrupts up to a threshold number of parties cannot recover the secrets or violate security. Prior works in this space have mostly focused on definitions and constructions for public-key cryptography and digital signatures, and thus do not capture the security concerns and efficiency challenges of symmetric-key based applications which commonly use long-term (unprotected) master keys to protect data at rest, authenticate clients on enterprise networks, and secure data and payments on IoT devices. We put forth the first formal treatment for distributed symmetric-key encryption, proposing new notions of correctness, privacy and authenticity in presence of malicious attackers. We provide strong and intuitive game-based definitions that are easy to understand and yield efficient constructions. We propose a generic construction of threshold authenticated encryption based on any distributed pseudorandom function (DPRF). When instantiated with the two different DPRF constructions proposed by Naor, Pinkas and Reingold (Eurocrypt 1999) and our enhanced versions, we obtain several efficient constructions meeting different security definitions. We implement these variants and provide extensive performance comparisons. Our most efficient instantiation uses only symmetric-key primitives and achieves a throughput of upto 1 million encryptions/decryptions per seconds, or alternatively a sub-millisecond latency with upto 18 participating parties.

Private Set Intersection (PSI) is a cryptographic technique that allows two parties to compute the intersection of their sets without revealing anything except the intersection. We use fully homomorphic encryption to construct a fast PSI protocol with a small communication overhead that works particularly well when one of the two sets is much smaller than the other, and is secure against semi-honest adversaries. The most computationally efficient PSI protocols have been constructed using tools such as hash functions and oblivious transfer, but a potential limitation with these approaches is the communication complexity, which scales linearly with the size of the larger set. This is of particular concern when performing PSI between a constrained device (cellphone) holding a small set, and a large service provider (e.g. WhatsApp), such as in the Private Contact Discovery application. Our protocol has communication complexity linear in the size of the smaller set, and logarithmic in the larger set. More precisely, if the set sizes are Ny textless Nx, we achieve a communication overhead of O(Ny log Nx). Our running-time-optimized benchmarks show that it takes 36 seconds of online-computation, 71 seconds of non-interactive (receiver-independent) pre-processing, and only 12.5MB of round trip communication to intersect five thousand 32-bit strings with 16 million 32-bit strings. Compared to prior works, this is roughly a 38–115x reduction in communication with minimal difference in computational overhead.