The Fall School consists of three lecture series and associated exercise sessions.

The roadmap from polynomials to quantum-safe cryptosystems

• Speaker: Chunlei Li (University of Bergen, Norway)

• Abstract: NIST in 2017 announced their post-quantum cryptography standardisation process to combat potential threats from powerful quantum computers to today’s number-theoretic techniques, like RSA, DLP, that have been used as one of pillars for the Internet security till date. In April 2025, NIST completed their evaluation on all submissions in the last round and chosen the scheme Hamming Quasi-Cyclic (HQC) as the code-based solution to protect key exchange in secure communication in the post-quantum age.

  The HQC was designed based a difficult problem related to quasi-cyclic codes, and its efficient decryption relies on Reed-Muller codes and Reed-Solomon codes. All these codes are classic algebraic codes heavily origin from basic algebraic structures, including finite fields, rings, polynomial evaluation and interpolation, etc.

  In this series of lectures, I will provide a gentle introduction to all closely relevant subjects involved in HQC , and explain how those basic ingredients in algebra were crafted together into the final design of HQC Key-Encapsulation Mechanism. The series is divided into four lectures:

  1. Quasi-cyclic codes over finite fields
  2. Reed-Solomon codes and their decoding
  3. Reed-Muller codes and their decoding
  4. A Gentle Introduction to the HQC KEM

Lamination hulls and secure computation

• Speaker: Hemanta Maji (Purdue, USA)

• Abstract: TBA. The series is divided into four lectures:

  1. Lamination Hull: Introduction
  2. Solving Systems of Linear Inequalities over Convex Sets
  3. Computing Lamination Hulls
  4. Secure Computation using Lamination Hulls

Different perspectives on the notion of information: their interactions and applications

• Speaker: Andrei Romashchenko (LIRMM, France)

• Abstract: In mathematics and theoretical computer science, there are several ways to formalize our intuitive notion of the “amount of information.” We will briefly discuss two classical approaches to this problem — Shannon entropy and Kolmogorov complexity — and explore some fundamental information inequalities. We then examine how information measures relate to communication complexity: how much information must be exchanged between remote parties to jointly solve a task (such as computing a function or sampling from a distribution). Finally, we look at applications of information-theoretic techniques in cryptography with unconditional security, such as secret sharing and key agreement.

Fall school on Geometry in Cryptography and Communication | UiT The Arctic University of Norway | 2025 | Contact: tobias.a.boege@uit.no