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 simple parallelization with a cache-friendly offline phase;

• 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 fulldomain evaluation of a puncturable pseudorandom function (PPRF). This is independently motivated by other cryptographic applications of PPRFs.