The MinRank and Rank Syndrome Decoding problem are the basis of the security of many cryptographic schemes. Therefore it is important to understand the complexity of solving these problems.

In this project, the goal is to:
1. Understand the the existing solvers for these problems, in particular, [1] and [2].
2. Apply some ideas to slightly improve their complexity.
3. Understand if it affects the security of the existing cryptographic schemes.

[1] Gaborit, Philippe, Olivier Ruatta, and Julien Schrek. 2016. “On the Complexity of the Rank Syndrome Decoding Problem.” IEEE Transactions on Information Theory 62 (2): 1006–19. https://doi.org/10.1109/TIT.2015.2511786.
[2] L. Goubin and N. T. Courtois, “Cryptanalysis of the TTM Cryptosystem,” in Advances in Cryptology — ASIACRYPT 2000, T. Okamoto, Ed., Berlin, Heidelberg: Springer, 2000, pp. 44–57. https://doi.org/10.1007/3-540-44448-3_4.

Voraussetzungen

(External Master Thesis) With the emergence of quantum computing, cryptographic protocols like IPsec/IKEv2 must transition to post-quantum cryptographic (PQC) algorithms. This thesis focuses on integrating PQC into IPsec/IKEv2 for embedded systems, leveraging FPGA-based acceleration to optimize performance and resource usage.
Thesis includes evaluation of suitable PQC algorithms to create a hardware/software codesign concept, implementing critical cryptographic operations in FPGA hardware, and integrating them into an embedded software stack. The goal is to achieve a balanced co-design where FPGA handles computationally expensive tasks while maintaining flexibility in software.