International Association
for Cryptologic Research

We introduce reductions of knowledge, a generalization of arguments of knowledge, which reduce checking knowledge of a witness in one relation to checking knowledge of a witness in another (simpler) relation. Reductions of knowledge unify a growing class of modern techniques as well as provide a compositional framework to modularly reason about individual steps in complex arguments of knowledge. As a demonstration, we simplify and unify recursive arguments over linear algebraic statements by decomposing them as a sequence of reductions of knowledge. To do so, we develop the tensor reduction of knowledge, which generalizes the central reductive step common to many recursive arguments. Underlying the tensor reduction of knowledge is a new information-theoretic reduction, which, for any modules $U$, $U_1$, and $U_2$ such that $U \cong U_1 \otimes U_2$, reduces the task of evaluating a homomorphism in $U$ to evaluating a homomorphism in $U_1$ and evaluating a homomorphism in $U_2$.

A secret sharing scheme enables one party to distribute shares of a secret to n parties and ensures that an adversary in control of t out of n parties will learn no information about the secret. However, traditional secret sharing schemes are often insufficient, especially for applications in which the set of parties who hold the secret shares might change over time. To achieve security in this setting, dynamic proactive secret sharing (DPSS) is used. DPSS schemes proactively update the secret shares held by the parties and allow changes to the set of parties holding the secrets. We propose FaB-DPSS (FAst Batched DPSS) -- a new and highly optimized batched DPSS scheme. While previous work on batched DPSS focuses on a single client submitting a batch of secrets and does not allow storing and releasing secrets independently, we allow multiple different clients to dynamically share and release secrets. FaB-DPSS is the most efficient robust DPSS scheme that supports the highest possible adversarial threshold of 1/2. We prove FaB-DPSS secure and implement it. All operations complete in seconds, and we outperform a prior state-of-the-art DPSS scheme by over 6 times. Additionally, we propose new applications of DPSS in the context of blockchains. Specifically, we propose a protocol that uses blockchains and FaB-DPSS to provide conditional secret storage. The protocol allows parties to store secrets along with a release condition, and once a (possibly different) party satisfies this release condition, the secret is privately released to that party. This functionality is similar to extractable witness encryption. While there are numerous compelling applications (e.g., time-lock encryption, one-time programs, and fair multi-party computation) which rely on extractable witness encryption, there are no known efficient constructions (or even constructions based on any well-studied assumptions) of extractable witness encryption. However, by utilizing blockchains and FaB-DPSS, we can easily build all those applications. We provide an implementation of our conditional secret storage protocol as well as several applications building on top of it.

We propose to use blockchains to achieve MPC which does not require the participating parties to be online simultaneously or interact with each other. Parties who contribute inputs but do not wish to receive outputs can go offline after submitting a single message. In addition to our main result, we study combined communication- and state-complexity in MPC, as it has implications for the communication complexity of our main construction. Finally, we provide a variation of our main protocol which additionally provides guaranteed output delivery.

Project Everest is constructing a high-performance, standards-compliant, formally verified implementation of the HTTPS ecosystem, including TLS, X.509, and the core cryptographic algorithms. This talk will present an overview of how we verify our implementations are correct, cryptographically secure, and resilient to basic side channels. We will focus on our EverCrypt cryptographic provider, a comprehensive collection of verified, high-performance cryptographic functionalities available via a carefully designed API. The API provably supports agility (choosing between multiple algorithms for the same functionality) and multiplexing (choosing between multiple implementations of the same algorithm). Through a combination of abstraction and zero-cost generic programming, we show how agility can simplify verification without sacrificing performance, and we demonstrate how C and assembly can be composed and verified against shared specifications. The result is several functionalities whose performance matches or exceeds the best unverified implementations. Altogether, EverCrypt consists of over 100K verified lines of specs, code, and proofs, and it produces over 45K lines of C and assembly code.