Correlated pseudorandomness from expand-accumulate codes
A pseudorandom correlation generator (PCG) is a recent tool for securely generating useful sources of correlated randomness, such as random oblivious transfers (OT) and vector oblivious linear evaluations (VOLE), with low communication cost. We introduce a simple new design for PCGs based on so-called expand-accumulate codes, which first apply a sparse random expander graph to replicate each message entry, and then accumulate the entries by computing the sum of each prefix. Our design offers the following advantages compared to state-of-the-art PCG constructions: Competitive concrete efficiency backed by provable security against relevant classes of attacks; An offline-online mode that combines near-optimal cache-friendliness with simple parallelization; Concretely efficient extensions to pseudorandom correlation functions, which enable incremental generation of new correlation instances on demand, and to new kinds of correlated randomness that include circuit-dependent correlations. To further improve the concrete computational cost, we propose a method for speeding up a full-domain evaluation of a puncturable pseudorandom function (PPRF). This is independently motivated by other cryptographic applications of PPRFs.
|NTT Research, Sunnyvale, CA, USA|
|Lecture Notes in Computer Science|
Boyle, E, Couteau, G, Gilboa, N, Ishai, Y, Kohl, L.M, Resch, N.A, & Scholl, P. (2022). Correlated pseudorandomness from expand-accumulate codes. In Advances in Cryptology - CRYPTO 2022 (pp. 603–633). doi:10.1007/978-3-031-15979-4_21