  Secure computation often benefits from the use of correlated randomness to
achieve fast, non-cryptographic online protocols. A recent paradigm put forth
by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom
correlation generators (PCG) can be used to generate large amounts of useful
forms of correlated (pseudo)randomness, using minimal interactions followed
solely by local computations, yielding silent secure two-party computation
protocols (protocols where the preprocessing phase requires almost no
communication). An additional property called programmability allows to extend
this to build N-party protocols. However, known constructions for programmable
PCG's can only produce OLE's over large fields, and use rather new splittable
Ring-LPN assumption.
  In this work, we overcome both limitations. To this end, we introduce the
quasi-abelian syndrome decoding problem (QA-SD), a family of assumptions which
generalises the well-established quasi-cyclic syndrome decoding assumption.
Building upon QA-SD, we construct new programmable PCG's for OLE's over any
field $\mathbb{F}_q$ with $q>2$. Our analysis also sheds light on the security
of the ring-LPN assumption used in Boyle $\textit{et al.}$ (Crypto 2020). Using
our new PCG's, we obtain the first efficient N-party silent secure computation
protocols for computing general arithmetic circuit over $\mathbb{F}_q$ for any
$q>2$.
