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Non-interactive batch arguments for provide a way to amortize the cost of verification across multiple instances. In particular, they allow a prover to convince a verifier of multiple statements with communication that scales sublinearly in the number of instances.

   In this work, we study fully succinct batch arguments for in the common reference string (CRS) model where the length of the proof scales not only sublinearly in the number of instances T, but also sublinearly with the size of the relation. Batch arguments with these properties are special cases of succinct non-interactive arguments (SNARGs); however, existing constructions of SNARGs either rely on idealized models or strong non-falsifiable assumptions. The one exception is the Sahai-Waters SNARG based on indistinguishability obfuscation. However, when applied to the setting of batch arguments, we must impose an a priori bound on the number of instances. Moreover, the size …