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Published in:
2014 | OriginalPaper | Chapter
Square Span Programs with Applications to Succinct NIZK Arguments
Authors : George Danezis, Cédric Fournet, Jens Groth, Markulf Kohlweiss
Published in: Advances in Cryptology – ASIACRYPT 2014
Publisher: Springer Berlin Heidelberg
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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.