Courses and Lectures

• ZKDL Lecture Notes

  Book on Zero-Knowledge Proofs by Distributed Lab

  This is a series of lectures on zero-knowledge (ZK) proofs, conducted at Distributed Lab, exploring "from scratch" how modern zk-SNARKs such as Groth16, PlonK, GKR work, including all the mathematical components they rely on. The course covers not only ZK theory itself and its applications, but also the basic mathematics needed to understand ZK and cryptography in general.

  [Course Website]

• Cryptography: A Modern Approach

  University Course by Distributed Lab (in Ukrainian)

  Introductory course in Cryptography for Ukrainian students and professors by Distributed Lab. The course covered all core topic in Cryptography: from basic Mathematics and Symmetric Cryptography to Digital Signatures and Multiparty computing. Composed course's contents and conducted lectures in Mathematics, Security Analysis, and Zero-Knowledge. Composed tests and final project topics.

  [GitHub]

Talks & Presentations

• 🕸️ Introduction to Lattice-based Cryptography

  Foundations of modern LWE-based cryptographic protocols.

  In recent years, the interest in lattice-based cryptography has been steadily increasing. One primary reason is, of course, that problems related to lattices and their derivatives are widely believed to be hard even for quantum computers. Furthermore, there are settings where the algebraic structure of lattices is natural: e.g., for fully-homomorphic encryption.
  This brief paper is a technical introduction to lattice-based cryptography. We give formal definitions of lattices and introduce key related hardness assumptions such as SVP, CVP, and several variants of LWE. We show how to build public-key encryption (PKE) and digital signature schemes based on LWE assumptions and partially prove the security of key constructions. Finally, we provide a high-level specification of Kyber PKE and Dilithium signature schemes.
  We aim to make these notes accessible while preserving rigorousness where appropriate. Basic knowledge of cryptography and algebra is required.
  [PDF Notes]

• 🔐 Zero-Knowledge Proofs: A Practical Introduction

  Student Mathematical Seminar at Kyiv School of Economics

  Zero-Knowledge (ZK) is a novel active subfield of cryptography that has introduced numerous solutions to privacy and scalability. Use cases of ZK include anonymous national passport verification, fighting disinformation by verifying photo authenticity, ensuring the integrity of generative AI, and scaling public blockchain infrastructure, among others. While useful, the technology is challenging to use and even more difficult to understand, as it requires a deep understanding of mathematics. In this lecture, we give a technical yet practical overview of zero-knowledge protocols. Namely, we:

  • Introduce the basic notions of ZK and define the security characteristics of ZK systems.
  • Demonstrate them using the basic example of an interactive proof of knowledge of the modular square root.
  • Provide a brief overview of modern ZK and ZK-SNARK (succinct non-interactive argument of knowledge) systems.
  • Show domain-specific languages used for encoding ZK relations and the performance of real-world ZK systems.
  [Slides] [Youtube]

• 🌾 Finite Field Extensions: Existence and Uniqueness

  Mathematical Seminar at Kyiv School of Economics

  This small lecture is devoted to a quick glance at the structure of finite fields. One obvious well-known example of the finite field is $\mathbb{Z}/p\mathbb{Z}$, but is this the only possible finite field? We show that (i) finite fields are always of order $p^n$, (ii) such finite fields always exist, (iii) two finite fields of the same order are always isomorphic. In particular, (ii) and (iii) make notation $\mathbb{F}_{p^n}$ valid.
  [PDF Notes]

• 🍁 UltraGroth: Interactive Groth16

  Overview of the UltraGroth protocol: Groth16 modification that enables lookup checks and sampling randomness.

  [Slides]

• 🌿 Bionetta: Ultimate ZKML Framework

  Presentation of the client-side ZKML framework based on UltraGroth and R1CS arithmetization.

  [Slides]

• 🐦 Nero: BitVM2-Based Optimistic Verifiable Computation on Bitcoin

  Research on implementing Bitcoin on-chain public verifiable computation scheme (based on BitVM2 research).

  [Slides]

• 📈 Elliptic Curve Optimizations. EC Pairing.

  Lecture about implementing Elliptic Curve (EC) operations efficiently. Basics of EC pairing.

  [Slides]

• 🧠 Introduction to Deep Learning

  What are neural networks. Their applications, basic dense neural network, demonstration of MNIST dataset training.

  [Slides]

• 😐 Deep Learning Applications to Biometric Analysis (in Ukrainian)

  Applications of Deep Learning to Biometric Analysis problem. Triplet Loss function, contrastive learning, face recognition models.

  [Slides]

Blogs

• UltraGroth Protocol Explained

  By Dmytro Zakharov, Lasha Antadze, Oleksandr Kurbatov

  [HackMD]

• Bionetta: Ultimate Client-Side ZKML. Technical Overview

  By Dmytro Zakharov, Lasha Antadze, Oleksandr Kurbatov

  [HackMD]