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We present a methodology to construct preprocessing zkSNARKs where the structured reference string (SRS) is universal and updatable. This exploits a novel use of holography [Babai et al., STOC 1991], where fast verification is achieved provided the statement being checked is given in encoded form.

We use our methodology to obtain a preprocessing zkSNARK where the SRS has linear size and arguments have constant size. Our construction improves on Sonic [Maller et al., CCS 2019], the prior state of the art in this setting, in all efficiency parameters: proving is an order of magnitude faster and verification is thrice as fast, even with smaller SRS size and argument size. Our construction is most efficient when instantiated in the algebraic group model (also used by Sonic), but we also demonstrate how to realize it under concrete knowledge assumptions. We implement and evaluate our construction.

The core of our preprocessing zkSNARK is an efficient algebraic holographic proof (AHP) for rank-1 constraint satisfiability (R1CS) that achieves linear proof length and constant query complexity.

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