Correlation Intractability and SNARGs from Sub-exponential DDH.

We provide the first constructions of SNARGs for Batch- NP and P based solely on the sub-exponential Decisional Diffie Hellman (DDH) assumption. Our schemes achieve poly-logarithmic proof sizes. We obtain our results by following the correlation-intractability framework for secure instantiation of the Fiat-Shamir paradigm. The centerpiece of our results and of independent interest is a new construction of correlation-intractable hash functions for “small input” product relations verifiable in TC 0 , based on sub-exponential DDH.