Introduction

This week, Anna and Ariel Gabizon cover the SNARK trilogy; a history of pairing-based SNARKs in 3 acts. Starting from Jens Groth’s early works on SNARKs, Ariel takes us on a journey through key moments and breakthroughs in SNARKs over the last decade. They also dive into the emerging accumulation research on folding schemes and Ariel’s latest work surrounding lookup tables! This is an episode you won’t want to miss.

Here are some additional links for this episode:

Relevant Jens Groth Papers

• Short Non-interactive Zero-Knowledge Proofs by Jens Groth
• Short Pairing-based Non-interactive Zero-Knowledge Arguments by Jens Groth
• On the Size of Pairing-based Non-interactive Arguments by Jens Groth
• Zero-knowledge Argument for Polynomial Evaluation with Application to Blacklists by Stephanie Bayer and Jens Groth

PLONK-Relative Papers

• PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge by Gabizon, Williamson, Ciobotaru
• HyperPlonk: Plonk with Linear-Time Prover and High-Degree Custom Gates by Chen, Bünz, Boneh and Zhang
• Proposal: The Turbo-PLONK program syntax for specifying SNARK programs by Gabizon and Williamson

Lookup-Relative Papers

• plookup: A simplified polynomial protocol for lookup tables by Gabizon and Williamson
• Caulk: Lookup Arguments in Sublinear Time by Zapico, Buterin, Khovratovich, Maller, Nitulescu and Simkin
• A Close Look at a Lookup Argument - Mary Maller at The 13th BIU Winter School on cryptography
• cq: Cached quotients for fast lookups by Eagen, Fiore, and Gabizon

Additional Resources

• Pinocchio: Nearly Practical Verifiable Computation by Parno, Howell, Gentry and Raykova
• Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updateable Structured Reference Strings by Maller, Bowe, Kohlweiss, and Meiklejohn
• Perpetual Powers of Tau GitHub
• Delegating Computation: Interactive Proofs for Muggles by Goldwasser, Kalai and Rothblum
• Efficient Zero-Knowledge Arguments for Arithmetic Circuits in Discrete Log Setting by Bootle, Cerulli, Chaidos, Groth and Petit
• Nova: Recursive Zero-Knowledge Arguments from Folding Schemes by Kothapalli, Setty and Tzialla
• Episode 232: Cutting Edge ZK Research with Mary Maller
• ZK Whiteboard Sessions - Module Six: Lookup Tables for Performance Optimisation

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