Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding

A recent paradigm put forth by Boyle et al. (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators (PCG) can be used to generate large amounts of useful forms correlated (pseudo)randomness, using minimal interactions followed solely local computations, yielding silent secure two-party computation protocols. This extended $$N $$ -party programmable PCG’s. Previous works constructed very efficient (non-programmable) PCG’s for correlations such as random oblivious transfers. However, the situation is less satisfying linear evaluations ( $${\textsf{OLE}}$$ ’s), their generalisation over fields. The state-of-the-art work (Crypto 2020) , but suffers from two important downsides: (1) it only generates ’s fields, and (2) relies on a relatively new “splittable” ring- $$\textsf{LPN}$$ assumption, which lacks strong security foundations. In this work, we introduce quasi-abelian syndrome decoding problem $$\textsf{QA}\text {-}\textsf{SD}$$ ), family assumptions generalises well-established quasi-cyclic assumption allows construct any field $$\mathbb {F}_{q}$$ with $$q>2$$ . Our analysis also sheds light in al., 2020). Using our PCG’s, obtain first protocols computing general arithmetic circuit {F}_q$$ $$q > 2$$