Kryptographie, 2025

Professor: Prof. Dr. Joachim Rosenthal,
Teaching Assistants:

• Giacomo Borin
• Silvia Sconza
• Abhinaba Mazumder

Here some material for the course. A few useful links:

• 2025 : Reference link of the course.
• Sagemath is a computer algebra software based on python that can be installed here and the docs are here.
• Jupyter Notebook is a popular, open-source web application used for creating and sharing documents that combine live code, text, visualizations, and rich media. You can download it here. If you really don’t want to run it locally there are services like Binder to run it online.

Exercise Session 04

Arguments: factorization and LFSR. Script used:

• notebook, online view

Exercise Session 07

Arguments: AES key scheduling and Elliptic Curve introduction. Scripts used:

• Sagemath notebook with descriptive AES key scheduling and EC formulas,
• Python notebook with a more serious AES key scheduling.

Tips:

• see hyperelliptic.org for a database of explicit EC formulas.

Lesson 2025.04.17

Here some gifs showing the use of the LLL algorithm to solve the knapsack problem. There are generated with this script and inspired by Tanja Lange lesson on LLL.

Example 0:

• weights: $430, 138, 495, 49, 463, 196, 165$;
• target: $942$;
• solution: $430 + 49 + 463 = 942$

Example 1:

• weights: $2381, 1094, 2188, 2442, 2280, 1129, 1803, 2259, 1665$;
• target: $7598$;
• solutions: $1094 + 2442 + 1803 + 2259 = 7598$