Paper 2014/718

Square Span Programs with Applications to Succinct NIZK Arguments

George Danezis, Cedric Fournet, Jens Groth, and Markulf Kohlweiss


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.

Available format(s)
Public-key cryptography
Publication info
Published by the IACR in ASIACRYPT 2014
square span programquadratic span programSNARKs
Contact author(s)
markulf @ microsoft com
2014-09-16: received
Short URL
Creative Commons Attribution


      author = {George Danezis and Cedric Fournet and Jens Groth and Markulf Kohlweiss},
      title = {Square Span Programs with Applications to Succinct {NIZK} Arguments},
      howpublished = {Cryptology ePrint Archive, Paper 2014/718},
      year = {2014},
      note = {\url{}},
      url = {}
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