Scientific program

A. Introductory courses

A1

Title: Decentralized Algorithms

MSC: 68W15#68Q25

Keywords: distributed computing#decentralization#algorithms

Description: We provide an introduction course to decentralized systems that work when no single party is in charge or fully trusted. This course starts with design of basic algorithms such as broadcast (1-to-all messaging), gossip (all-to-all messaging) leader election, random number generation all in the context of decentralized algorithms. Next, we will design and analyze various consensus protocols when there is no faulty or malicious processes. Then we will study some protocols when there are crash and Byzantine failures. Namely, this part of the course will show solvability (and impossibility) results for some agreement problems.

Bibliography: – Distributed Computing. Fundamentals, Simulations and Advanced Topics. Second Edition. Hagit Attiya. Jennifer Welch

Lecturer: Vlady RAVELOMANANA -- University of Paris Cité and University of Antananarivo (6 sessions)

A2

Title: Scalability and Interoperability: from 2-layer payments to inter-blockchain protocols

MSC: Theoretical Computer Science

Keywords: distributed protocols#blockchain#interoperability

This activity will start by introducing basic blockchain concepts before raising awareness of scalability and interoperability problems in the blockchain realm, which are especially important to envisage the next Web3 revolution. After presenting the performance bottlenecks of blockchains, we will review recent developments to overcome these bottlenecks, such as 2-layer protocols for payments, rollups, and sharding techniques.

We will also explore distributed protocols used to guarantee the consistency of transactions spanning different blockchains, such as atomic cross-chain swaps and atomic-commit for distributed cross-shard transactions.

Lecturer: Antonella DEL POZZO -- University Paris Saclay, Commissariat à l'Energie Atomique -- CEA LIST (6 sessions)

A3

Title: The cryptographic tools behind the Blockchain

Domains: Number Theory

MSC: 11T71#94A60

Keywords: Elementary arithmetic#elliptic curves#cryptography

Description: This activity will develop the basic knowledge of cryptography and security needed to run a blockchain. This includes notions of complexity and bits of security. Then, we will define the concept of public key cryptography (PKC) including encryption and digital signatures. In the Blockchain, elliptic curve cryptography is utilized since relatively small keys can be used to provide high levels of security. Finally, we will provide some insights about the quantum paradigm and its implications in cryptographic algorithms.

Bibliography: – Network Security Essentials: Applications and Standards 6th Edition by William Stallings. – The handbook of applied cryptography by Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone.

Lecturer: Jorge URROZ -- Universidad Politécnica de Madrid (6 sessions)

B. Advanced courses

B1

Title:  Mastering Pinocchio: A Backend for Proving R1CS. 

Domains: Information Theory

Keywords: ZKP#zk-SNARKS#privacy#scalability

Description: Pinocchio is a zk-SNARK, a cryptographic that allows a prover to generate a succinct proof that can convince a verifier of the correctness of a computation without revealing any underlying data. Pinocchio achieves this through a series of innovations, including the use of quadratic arithmetic programs (QAPs) for efficient encoding of computations and a pairing-based cryptographic setup that significantly reduces the size and verification time of the proofs. Pinocchio's efficiency and non-interactive nature make it well-suited for applications in blockchain technology, secure cloud computing, and privacy-preserving protocols, where it provides robust guarantees of integrity and confidentiality with minimal computational overhead. This course aims to provide in-depth insights into how verifiable computation operates behind the scenes. We will explore a classical cryptographic protocol (Pinocchio), focusing on the significant computational benefits for a verifier who only needs to verify ratherthan execute. 

Lecturer: Marc GUZMAN -- Polytechnical University of Catalonia (6 sessions)

B2

Title: Understanding Automated Market Makers (AMMs) in Decentralized Finance 

Domains: Decentralized Finance

Keywords: Automated Market Makers, Decentralized exchanges

Description: We will dive into the fascinating world of Automated Market Makers (AMMs), the backbone of decentralized cryptocurrency exchanges. This course is designed to provide students with a solid understanding of how AMMs function, the mathematics behind them, and their practical implementation in decentralized finance. No prior knowledge of advanced mathematics or programming is required, but a basic understanding of blockchain technology and cryptocurrency concepts would be beneficial. 

We will

a) learn how AMMs differ from traditional order book exchanges,

b) explore major AMM protocols: Uniswap, Balancer, and Curve,

c) dive into the mathematical formulae behind AMM operations, and learn how to derive and interpret these formulae,

d) understand how trading and liquidity provision work in practice,

e) see how mathematical concepts translate into actual smart contract logic,

f) the implementation in Solidity language. 

Lecturer: Jules MBA -- University of Johannesburg (6 sessions)

C. Exercise sessions

For each course, there will be exercise sessions of at least 4 hours.