Quadratic Span Programs and Succinct NIZKs without PCPs

The authors introduce a new characterization of the NP complexity class, called Quadratic Span Programs (QSPs), which is a natural extension of span programs defined by Karchmer and Wigderson. Their main motivation is the construction of succinct arguments of NP-statements that are quick to construct and verify. QSPs seem well-suited for this task, perhaps even better than Probabilistically Checkable Proofs (PCPs). In 2010, Groth constructed a NIZK argument in the Common Reference String (CRS) model for Circuit-SAT consisting of only 42 elements in a bilinear group. Interestingly, this argument does not (explicitly) use PCPs. But this scheme has some disadvantages, namely, the CRS size and prover computation are both quadratic in the circuit size.

Provided by: IBM Topic: Software Date Added: Jun 2012 Format: PDF

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