The McEliece cryptosystem is a well-known public-key encryption scheme using Goppa codes in the Hamming metric. The GPT cryptosystem is the rank-metric counterpart of this scheme using Gabidulin codes. While this promises much better message security than McEliece, it has been subject to several successful key attacks, most prominent of which is known as Overbeck's attack [1, 2].

The task of the student is to understand the different proposed versions of the GPT cryptosytem and how they were attacked. Further, the student will look at a more recent version of this scheme [3] which has so far resisted Overbeck's attack.

[1] R. Overbeck, “Public Key Cryptography based on Coding Theory,” phd, Technische Universität Darmstadt, Darmstadt, 2007. Accessed: Oct. 01, 2024. [Online]. Available: https://tuprints.ulb.tu-darmstadt.de/823/
[2] R. Overbeck, “Structural Attacks for Public Key Cryptosystems based on Gabidulin Codes,” J Cryptol, vol. 21, no. 2, pp. 280–301, Apr. 2008, doi: 10.1007/s00145-007-9003-9.
[3] P. Loidreau, “A New Rank Metric Codes Based Encryption Scheme,” in Post-Quantum Cryptography, T. Lange and T. Takagi, Eds., Cham: Springer International Publishing, 2017, pp. 3–17. doi: 10.1007/978-3-319-59879-6_1.

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.