We propose a new characterization of NP using square span programs
(SSPs). We first characterize NP as affine map constraints on small
vectors. We then relate this characterization to SSPs, which are
similar but simpler than Quadratic Span Programs (QSPs) and
Quadratic Arithmetic Programs (QAPs) since they use a single series
of polynomials rather than 2 or 3.
We use SSPs to construct succinct non-interactive zero-knowledge
arguments of knowledge. For performance, our proof system is
defined over Type III bilinear groups; proofs consist of just 4
group elements, verified in just 6 pairings. Concretely, using the
Pinocchio libraries, we estimate that proofs will consist of 160
bytes verified in less than 6 ms.
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