Orest Tarasiuk (𝚝𝟷’s co-founder and CTO) will explore the rollup fragmentation problem. While rollups scaled Ethereum, they also isolated users, fragmented liquidity and broke composability between ecosystems. Users are locked into an individual rollup ecosystem unless they use risky and limited third-party bridges. Application developers must choose between low transaction costs and access to Ethereum users, applications and liquidity. This fragmentation weakens the network effects crucial for the growth of the Ethereum ecosystem.

During the 18th Meetup Dr Emanuele Ragnoli (Co-Founder of Provably.ai) will explore the maths of mature inner product protocols designed to address the challenge of verifying aggregate queries, particularly targeting analytics for Big Data. Unlike traditional methods that rely on general-purpose Zero-Knowledge (ZK) proof systems, this protocol leverages specialised cryptographic tools to achieve secure and efficient query verification.

In this talk, Adam Gągol (CO-Founder @ Aleph Zero) will explore three modern edge designs of private decentralised exchanges grounded in cryptographic techniques. He will provide a comparison of their economic properties, highlighting the unique benefits each design offers. Additionally, Adam will address the known limitations and tradeoffs inherent in these systems.

​Brandon Kase - CEO of o1Labs - the incubators of Mina Protocol will lead a focused discussion on the application of zero-knowledge proofs in the Mina Protocol. Mina Protocol is known for its lightweight blockchain, aiming to be the world's lightest blockchain by maintaining a consistent size regardless of network growth. This unique approach provides a more accessible and efficient network that ensures decentralization.

ZK enables new applications, but comes at a prohibitive cost or latency for many other ones. This talk by Orest Tarasiuk explores the tradeoffs that can be made by increasing the security assumptions towards temporarily accepting TEEs (Trusted Execution Environments) in order to get to cheaper or lower-latency execution. It will focus on DeFi and highlight some new use cases that become feasible this way.

During our next meeting Bartosz Nowak will explore the fundamentals of STARK protocol, uncover how polynomial constraints ensure computational integrity. Latest optimisations in zkSTARKS provers and verifiers.

Leonid Logvinov will explore the internals of how ZK programs get compiled & proved starting with some theory. Then we will move on to example programs. The Noir & Barretenberg will be used as a tool to broader exploration of the concepts.

Ariel Gabizon, one of the authors of the PLONK paper, will walk us through the recent advances in the field of (Zero-Knowledge) Succinct Non-interactive ARguments of Knowledge. He will focus on GKR which received significant interest recently and attempt to explain it to us.

Marek Kirejczyk will present the so-called "Vitalik trick" for optimised Schnorr signature validation. By using it, you can reduce the gas cost from 100k+ to just 3k.