Towards better SNARGs for P from Fiat-Shamir

We study the problem of constructing succinct non-interactive arguments (SNARGs), an important tool in cryptography for delegating computations. In recent years, several results related to SNARGs have appeared due to the progress in provably instantiating the Fiat-Shamir transformation. In this note, we show that some techniques used in constructing SNARGs can be improved to work in more general settings, which may be useful in constructing better SNARGs (e.g., a DDH-based SNARG) or in some other applications in cryptography.

See the report here.

UPD: the problem of SNARGs based solely on DDH mentioned in the report has been solved by a recent work (see 2022/1486). The main technique is rougly a DDH-based correlation-intractable hash for product relations, which was only known from LWE before.