Zero-knowledge succinct arguments of knowledge (zkSNARKs) enable efficient privacy-preserving proofs of membership for general
NP languages. Our focus in this work is on post-quantum zkSNARKs,
with a focus on minimizing proof size. Currently, there is a 1000×
gap in the proof size between the best pre-quantum constructions
and the best post-quantum ones. Here, we develop and implement
new lattice-based zkSNARKs in the designated-verifier preprocessing model. With our construction, after an initial preprocessing
step, a proof for an NP relation of size 2
20 is just over 16 KB. Our
proofs are 10.3× shorter than previous post-quantum zkSNARKs
for general NP languages. Compared to previous lattice-based zkSNARKs (also in the designated-verifier preprocessing model), we
obtain a 42× reduction in proof size and a 60× reduction in the
prover’s running time, all while achieving a much higher level of
soundness. Compared to the shortest pre-quantum zkSNARKs by
Groth (Eurocrypt 2016), the proof size in our lattice-based construction is 131× longer, but both the prover and the verifier are faster
(by 1.2× and 2.8×, respectively).
Our construction follows the general blueprint of Bitansky et al.
(TCC 2013) and Boneh et al. (Eurocrypt 2017) of combining a linear
probabilistically checkable proof (linear PCP) together with a linearonly vector encryption scheme. We develop a concretely-efficient
lattice-based instantiation of this compiler by considering quadratic
extension fields of moderate characteristic and using linear-only
vector encryption over rank-2 module lattices.
