Ariel Gabizon and Zac Williamson from Aztec discuss Plonk, a highly efficient SNARK construction. They explore Plonk's focus on Lagrange-bases, compare it to other constructions, and mention the influence of the Bayer groth permutation argument. They also discuss polynomial commitment schemes and optimizations, metrics and naming software libraries, the Plonk protocol, and enabling private value transfers and privacy preserving smart contracts.
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Quick takeaways
Plonk is a universal zero-knowledge proof system that allows for custom gate structures and enables hyper-efficient proofs for common circuit types.
Lagrange bases and multiplicative subgroups play a critical role in the efficiency of the Plonk protocol, resulting in more concise circuits and enhanced performance.
Deep dives
Developing the Plonk Protocol with Zach Williamson and Ariel Gabizon
In this podcast episode, Zach Williamson and Ariel Gabizon discuss the Plonk protocol. Developed over a period of three months, Plonk is a universal zero-knowledge proof system that utilizes a multiplicative subgroup and Lagrange bases to encode polynomials. Unlike previous systems like Sonic, Plonk allows for custom gate structures, enabling hyper-efficient proofs for common circuit types. The protocol has impressive performance metrics, with proof sizes ranging from 512 to 768 bytes and verification times of approximately 1.3 milliseconds. Plonk is a crucial step towards achieving privacy-preserving smart contracts, referred to as dark contracts, where the identities of the sender, the executed code, and the transaction's purpose are all hidden.
The Power of Lagrange Bases and Multiplicative Subgroups in Plonk
Lagrange bases and multiplicative subgroups play a critical role in the structure and efficiency of the Plonk protocol. Lagrange bases are used to encode vectors as polynomials, enabling efficient representation and evaluation. Multiplicative subgroups, consisting of powers of a specific element, allow for easy access to neighboring points and facilitate memory within Plonk's custom gate structures. The combination of these techniques results in more concise circuits, fewer constraints, and enhanced performance. Plonk's innovative use of Lagrange bases and multiplicative subgroups differentiates it from other proof systems and opens up possibilities for privacy-preserving smart contracts.
Expanding the Horizons with Turbo-Plonk and Dark Contracts
As Plonk continues to evolve, the team at Aztec is working on Turbo-Plonk, which formalizes custom gate structures and optimizes the protocol for specific circuit types. This advancement enables hyper-efficient proofs and enhances the capabilities of Plonk. Looking ahead, Aztec aims to build privacy-preserving smart contracts called dark contracts on Ethereum, introducing function privacy in addition to data privacy. Dark contracts hide the identities of the sender, the executed code, and the transaction's purpose, while still utilizing public blockchain consensus mechanisms for correct execution. Aztec's vision is to combine privacy and function privacy to bring a new level of privacy to public blockchain applications.
Exciting Developments in Zero-Knowledge Proofs
The field of zero-knowledge proofs is continually evolving, and there are several exciting developments on the horizon. New advancements in polynomial commitment schemes, such as DARC, are revolutionizing the way polynomials are represented and committed. Additionally, the concept of dark contracts, which bring function privacy to public blockchains, holds great promise for enhancing privacy and confidentiality. The Plonk protocol, with its efficient performance and innovative use of Lagrange bases and multiplicative subgroups, is just one example of how zero-knowledge proofs are pushing the boundaries of privacy and security in decentralized systems.
In this week’s episode, we learn more about Plonk with Ariel Gabizon and Zac Williamson from Aztec. PLONK is a recent highly efficient, universal SNARK construction. We explore what distinguishes Plonk from some other other new constructions including their focus on Lagrange-bases to deconstruct complex problem statements into simple polynomial identities.
This episode goes very deep and so we do recommend you check out a few of previous episodes to help you follow along! All mentioned can be found here along with the other deep zk-topic episodes: https://www.zeroknowledge.fm/zkseries
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