Summary: There has been a lot of recent progress in constructing efficient zero-knowledge proofs for showing knowledge of an \(\vec{\mathfrak{s}}\) with small coefficients satisfying \(\mathfrak{A}\vec{\mathfrak{s}}=\vec{\mathfrak{t}} \). For typical parameters, the proof sizes have gone down from several megabytes to a bit under 50KB [M. F. Esgin et al., “Practical exact proofs from lattices: new techniques to exploit fully-splitting rings”, Lect. Notes Comput. Sci. 12492, 259–288 (2020; doi:10.1007/978-3-030-64834-3_9)]. These are now within an order of magnitude of the sizes of lattice-based signatures, which themselves constitute proof systems which demonstrate knowledge of something weaker than the aforementioned equation. One can therefore see that this line of research is approaching optimality. In this paper, we modify a key component of these proofs, as well as apply several other tweaks, to achieve a further reduction of around \(30\%\) in the proof output size. We also show that this savings propagates itself when these proofs are used in a general framework to construct more complex protocols.
For the entire collection see [Zbl 1476.94003].