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> Theory Seminar - April 20
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Theory Seminar - April 20
Event date: Friday, April 20, 2012, at 11:00 AM
Location: GB221
Speaker:
Mariana Raykova
Columbia University
Title: Quadratic Span Programs for Succinct NIZKs without PCPs
Abstract:
We 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. Our 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, his argument does not (explicitly) use PCPs. But his scheme has some disadvantages -- namely, the CRS size and prover computation are both quadratic in the circuit size. In 2011, Lipmaa reduced the CRS size to quasi-linear, but with prover computation still quadratic.
Using QSPs we construct a NIZK argument in the CRS model for Circuit-SAT consisting of just 7 group elements. The CRS size is {\em linear} in the circuit size, and prover computation is {\em quasi-linear}, making our scheme seemingly quite practical. (The prover only needs to do a linear number of group operations; the quasi-linear computation is a multipoint evaluation.)
Our results are complementary to those of Valiant (TCC 2008) and Bitansky et al. (2012), who use ``bootstrapping"(recursive composition) of arguments to reduce CRS size and prover and verifier computation. QSPs also provide a crisp mathematical abstraction of some of the techniques underlying Groth's and Lipmaa's constructions.
Joint work with Rosario Gennaro, Craig Gentry and Bryan Parno