Oblivious Transfer (OT) is at the heart of secure computation and is a foundation for many applications in cryptography. Over two decades of work have led to extremely efficient protocols for evaluating OT instances in the preprocessing model, through a paradigm called OT extension. A few OT instances generated in an offline phase can be used to perform many OTs in an online phase efficiently, i.e., with very low communication and computational overheads. Specifically, traditional OT...

EdDSA, standardized by both IRTF and NIST, is a variant of the well-known Schnorr signature scheme based on Edwards curves, benefitting from stateless and deterministic derivation of nonces (i.e., it does not require a reliable source of randomness or state continuity). Recently, NIST called for multi-party threshold EdDSA signatures in one mode of verifying such nonce derivation via zero-knowledge (ZK) proofs. However, it is challenging to translate the stateless and deterministic benefits...

We instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), $\mathsf{PRF}(k, x) := \mathsf{wPRF}(k, \mathsf{RO}(x))$, which builds a PRF $\mathsf{PRF}$ from a weak PRF $\mathsf{wPRF}$ via a public preprocessing random oracle $\mathsf{RO}$. In applications to secure multiparty computation (MPC), only the low-complexity wPRF performs secret-depending operations. Our construction replaces RO by $f(k_H , \mathsf{elf}(x))$, where $f$ is a non-adaptive PRF and the key $k_H$...

Pseudorandom correlation functions (PCF), introduced in the work of (Boyle et al., FOCS 2020), allow two parties to locally gen- erate, from short correlated keys, a near-unbounded amount of pseu- dorandom samples from a target correlation. PCF is an extremely ap- pealing primitive in secure computation, where they allow to confine all preprocessing phases of all future computations two parties could want to execute to a single short interaction with low communication and computation,...

Structured random strings (SRSs) and correlated randomness are important for many cryptographic protocols. In settings where interaction is expensive, it is desirable to obtain such randomness in as few rounds of communication as possible; ideally, simply by exchanging one reusable round of messages which can be considered public keys. In this paper, we describe how to generate any SRS or correlated randomness in such a single round of communication, using, among other things,...

Recently, number-theoretic assumptions including DDH, DCR and QR have been used to build powerful tools for secure computation, in the form of homomorphic secret-sharing (HSS), which leads to secure two-party computation protocols with succinct communication, and pseudorandom correlation functions (PCFs), which allow non-interactive generation of a large quantity of correlated randomness. In this work, we present a group-theoretic framework for these classes of constructions, which unifies...

We describe a simple method for solving the distributed discrete logarithm problem in Paillier groups, allowing two parties to locally convert multiplicative shares of a secret (in the exponent) into additive shares. Our algorithm is perfectly correct, unlike previous methods with an inverse polynomial error probability. We obtain the following applications and further results. - Homomorphic secret sharing. We construct homomorphic secret sharing for branching programs with *negligible*...

Correlated secret randomness is a useful resource for many cryptographic applications. We initiate the study of pseudorandom correlation functions (PCFs) that offer the ability to securely generate virtually unbounded sources of correlated randomness using only local computation. Concretely, a PCF is a keyed function $F_k$ such that for a suitable joint key distribution $(k_0,k_1)$, the outputs $(f_{k_0}(x),f_{k_1}(x))$ are indistinguishable from instances of a given target correlation. An...