Succinct non-interactive zero knowledge arguments from span programs and linear error-correcting codes

Abstract

Gennaro, Gentry, Parno and Raykova proposed an efficient NIZK argument for Circuit-SAT, based on non-standard tools like conscientious and quadratic span programs. We propose a new linear PCP for the Circuit-SAT, based on a combination of standard span programs (that verify the correctness of every individual gate) and high-distance linear error-correcting codes (that check the consistency of wire assignments). This allows us to simplify all steps of the argument, which results in significantly improved efficiency. We then construct an NIZK Circuit-SAT argument based on existing techniques. © 2013 Springer-Verlag.