Pseudorandom Correlation Functions from Variable-Density LPN, Revisited Abstract
Pseudorandom correlation functions (PCF), introduced in the work of (Boyle et al., FOCS 2020), allow two parties to locally generate, from short correlated keys, a near-unbounded amount of pseudorandom samples from a target correlation. PCF is an extremely appealing 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, followed solely by offline computations. Beyond introducing the notion, Boyle et al. gave a candidate construction, using a new variable-density} variant of the learning parity with noise (LPN) assumption. Then, to provide support for this new assumption, the authors showed that it provably resists a large class of linear attacks, which captures in particular all known attacks on LPN. In this work, we revisit the analysis of the VDLPN assumption. We make two key contributions: - First, we observe that the analysis of Boyle et al is purely asymptotic: they do not lead to any concrete and efficient PCF instantiation within the bounds that offer security guarantees. To improve this state of affairs, we combine a new variant of a VDLPN assumption with an entirely new, much tighter security analysis, which we further tighten using extensive computer simulations to optimize parameters. This way, we manage to obtain for the first time a set of provable usable parameters (under a simple combinatorial conjecture which is easy to verify experimentally), leading to a concretely efficient PCF resisting all linear tests. - Second, we identify a flaw in the security analysis of Boyle et al., which invalidates their proof that VDLPN resists linear attacks. Using several new non-trivial arguments, we repair the proof and fully demonstrate that VDLPN resists linear attack; our new analysis is more involved than the original (flawed) analysis. Our parameters set leads to PCFs with keys around 3MB allowing ~ 500 evaluations per second on one core of a standard laptop for 110 bits of security; these numbers can be improved to 360kB keys and ~ 3800 evaluations/s using a more aggressive all-prefix variant. All numbers are quite tight: only within a factor 3 of the best bounds one could heuristically hope for.
- Geoffroy Couteau (1)