Cryptology ePrint Archive: Report 2019/148

On the efficiency of pairing-based proofs under the d-PKE

Ariel Gabizon

Abstract: We investigate the minimal number of group elements and prover running time in a zk-SNARK when using only a symmetric ``linear'' knowledge assumption, like the $d$-Power Knowledge of Exponent assumption, rather than a ``quadratic'' one as implicitly happens in the most efficient known construction by Groth [Groth16]. The proofs of [Groth16] contain only 3 group elements. We present 4 element proofs for quadratic arithmetic programs/rank 1 constraint systems under the $d$-PKE with very similar prover running time to [Groth16]. Central to our construction is a simple lemma for ``batching'' knowledge checks, which allows us to save one proof element.

Category / Keywords: cryptographic protocols / zk-SNARKs, Knowledge Assumptions

Date: received 12 Feb 2019, last revised 18 Mar 2019

Contact author: ariel gabizon at gmail com

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Version: 20190318:144432 (All versions of this report)

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