International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Alex J. Malozemoff

Publications

Year
Venue
Title
2021
CRYPTO
Mac'n'Cheese: Zero-Knowledge Proofs for Boolean and Arithmetic Circuits with Nested Disjunctions 📺
Zero knowledge proofs are an important building block in many cryptographic applications. Unfortunately, when the proof statements become very large, existing zero-knowledge proof systems easily reach their limits: either the computational overhead, the memory footprint, or the required bandwidth exceed levels that would be tolerable in practice. We present an interactive zero-knowledge proof system for boolean and arithmetic circuits, called Mac'n'Cheese, with a focus on supporting large circuits. Our work follows the commit-and-prove paradigm instantiated using information-theoretic MACs based on vector oblivious linear evaluation to achieve high efficiency. We additionally show how to optimize disjunctions, with a general OR transformation for proving the disjunction of $m$ statements that has communication complexity proportional to the longest statement (plus an additive term logarithmic in $m$). These disjunctions can further be \emph{nested}, allowing efficient proofs about complex statements with many levels of disjunctions. We also show how to make Mac'n'Cheese non-interactive (after a preprocessing phase) using the Fiat-Shamir transform, and with only a small degradation in soundness. We have implemented the online phase of Mac'n'Cheese and achieve a runtime of 144~ns per AND gate and 1.5~$\mu$s per multiplication gate in $\mathbb{F}_{2^{61}-1}$ when run over a network with a 95~ms latency and a bandwidth of 31.5~Mbps. In addition, we show that the disjunction optimization improves communication as expected: when proving a boolean circuit with eight branches and each branch containing roughly 1 billion multiplications, Mac'n'Cheese requires only 75 more bytes to communicate than in the single branch case.
2019
ASIACRYPT
Public-Key Function-Private Hidden Vector Encryption (and More)
We construct public-key function-private predicate encryption for the “small superset functionality,” recently introduced by Beullens and Wee (PKC 2019). This functionality captures several important classes of predicates:Point functions. For point function predicates, our construction is equivalent to public-key function-private anonymous identity-based encryption.Conjunctions. If the predicate computes a conjunction, our construction is a public-key function-private hidden vector encryption scheme. This addresses an open problem posed by Boneh, Raghunathan, and Segev (ASIACRYPT 2013).d-CNFs and read-once conjunctions of d-disjunctions for constant-size d. Our construction extends the group-based obfuscation schemes of Bishop et al. (CRYPTO 2018), Beullens and Wee (PKC 2019), and Bartusek et al. (EUROCRYPT 2019) to the setting of public-key function-private predicate encryption. We achieve an average-case notion of function privacy, which guarantees that a decryption key $$\mathsf {sk} _f$$ reveals nothing about f as long as f is drawn from a distribution with sufficient entropy. We formalize this security notion as a generalization of the (enhanced) real-or-random function privacy definition of Boneh, Raghunathan, and Segev (CRYPTO 2013). Our construction relies on bilinear groups, and we prove security in the generic bilinear group model.
2017
EUROCRYPT
2015
EPRINT
2015
EPRINT
2015
EPRINT
2015
ASIACRYPT
2014
CRYPTO
2014
CRYPTO
2014
EPRINT

Program Committees

Crypto 2018