Post-Quantum Cryptography

Courses

Course 1

Title: Lattice-based post-quantum cryptography

Level: Master/PhD

Lecturer: Alice Pellet-Mary

Abstract Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions are currently important candidates for post-quantum cryptography. In this course we will mainly study the basics of some public-key encryption schemes based on NTRU (shortest vector problem) and on LWE (Learning with Errors problem).

Course 2

Title: Code-based post-quantum cryptography

Level: Master/PhD

Lecturer: Jean-Christophe Deneuville

Abstract Code-based cryptography (CBC) is one of the well-known post-quantum cryptography primitives and secured its position in the outcome of 3rd round NIST competition as one of the finalist encryption schemes. One of its most promising applications is the design of cryptographic schemes with exceptionally strong security guarantees and other desirable properties. In this course we will mainly study the basics of some public-key encryption schemes based on McEliece and the Niederreiter encryption schemes.

Course 3

Title: Isogeny-based post-quantum cryptography

Level: Master/PhD

Lecturer: Annamaria Iezzi

Abstract Isogeny-based cryptography is a young and very active subfield of post-quantum cryptography based on the mathematical problem of constructing an isogeny, i.e. a well-behaved map, between two given elliptic curves over finite fields. Since 1997 and especially in the past 10-15 years, several schemes based on isogenies have been proposed, mostly in the context of post-quantum key exchange and post-quantum digital signatures. In this course, after reviewing the mathematical and cryptographic setting, we will describe some of the most promising isogeny-based protocols and we will discuss some open problems related to the field.

Course 4

Title: Hash functions based post-quantum cryptography

Level: Master/PhD

Lecturers: Peter Schwabe and Vishal Saraswat

Abstract Hash functions are most widely deployed tools to construct cryptographic algorithms in practice and lead an alternate direction to achieve post-quantum security. Starting with Lamport’s one-time signature, designing few-time signatures and further devising stateful and stateless signatures is the current state of development. In this course the speaker will mainly cover the basics of these signature schemes and some recently shortlisted constructions by NIST.

Course 5

Title: Multivariate post-quantum cryptography

Level: Master/PhD

Lecturer: Dhananjoy Dey

Abstract Multivariate-based cryptography is based on the hardness of finding a solution to a system of multivariate quadratic equations over finite fields. Multivariate-based primitives make it possible to obtain signature schemes which provide short signatures. Additionally, this primitive also makes it possible to design signature schemes in which the verification of the signature is very fast. By this approach, high performances can also often be reached for the signature phase. Thus, digital signature schemes can be implemented cheaply on ASICs. Another advantage of multivariate-based primitives is their flexibility in the design of various schemes, with ad-hoc properties. In this course we will mainly study the basics of multivariate-based signatures schemes such as Rainbow scheme, and the GeMMS scheme.

Course 6

Title: Programming for cryptography with a focus on Python for blockchain

Level: Master/PhD

Lecturer: Denis Verstraeten

Abstract This practice course intends to introduce Python as the main scripting language. The objective is to teach how this programming can be used to perform cryptographic operations and to deal with blockchain related Application Programming Interfaces (API).This course also introduces the Ethereum Smart Contract paradigm, as well as its most popular language, Solidity. Ideally, the teaching should be based on a small project which should be doable in the allocated time frame.

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