Pseudorandom Correlation Functions from Variable-Density LPN, Revisited

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 pseudorandom samples target correlation. PCF is an extremely appealing primitive secure computation, where they confine all preprocessing phases future computations could want execute single interaction with low communication and followed solely by offline computations. Beyond introducing notion, Boyle al. gave candidate construction, using new variable-density variant learning parity noise (LPN) assumption. Then, provide support for this assumption, authors showed that it provably resists large class linear attacks, which captures particular known attacks on LPN. In work, we revisit analysis VDLPN We make key contributions: Our parameters set leads PCFs keys around 3 MB allowing $$\sim 500$$ evaluations per second one core standard laptop 110 bits security; these numbers can be improved 350 kB 3950$$ evaluations/s more aggressive all-prefix variant. All are quite tight: only within factor best bounds heuristically hope for.