Zero-Knowledge Extension of PARI

PARI is a recent SNARK based on equifficient polynomial commitments, giving an exceptionally compact proof of just 1280 bits over the BLS12-381 curve, which is the smallest among all the known SNARKs in the literature. However, PARI does not achieve the zero-knowledge property; despite being very efficient, it is therefore less suitable for applications requiring witness privacy. In this work, we propose a zero-knowledge extension of PARI making it ideal for privacy-centric applications yet keeping the proof size compact. We prove perfect completeness, perfect zero-knowledge in the random-oracle model with challenge space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>𝔽</mml:mi> <mml:mi>⧵</mml:mi> <mml:mi>K</mml:mi> </mml:mrow> </mml:math> , and knowledge soundness in the algebraic group model with random oracles under the SDH assumption.