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:

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