Homomorphic Encryption for Machine Learning
Partial/Somewhat Homomorphic Encryption, Federated Learning
Beschreibung
Homomorphic encryption (HE) schemes are increasingly attracting attention in the era of large scale computing. While lattice-based approaches have been well-studied, recently first progress has been made towards establishing code-based alternatives. Preliminary results show that such alterative approaches might enable undiscovered functionalities not present in current lattice-based schemes. In this project, we particularily study novel code-based Partial/Somewhat HE schemes tailored to applications in artificial intelligence and federated learning.
After familiarizing with SotA methods in relevant fields (such as [1]), the student should analyze the requirements for use-cases at hand and explore suitable modifications to current schemes and novel approaches.
Please take note that this Master Thesis is further designed to open up the possibility for a subsequent PhD position in homomorphic encrpytion with Prof. Dr.-Ing. Antonia Wachter-Zeh.
[1] Aguilar-Melchor, Carlos, Victor Dyseryn, and Philippe Gaborit, "Somewhat Homomorphic Encryption based on Random Codes," Cryptology ePrint Archive (2023).
Voraussetzungen
- Strong foundation in linear algebra
- Channel Coding
- Security in Communications and Storage
- Basic understanding of Machine Learning concepts
Betreuer:
Post-Quantum Cyptography based on Codes: Generalized (U|U+V) codes
post-quantum cryptography, code-based, concatenated codes, generalized concatenation
Beschreibung
Due to the recent advances in quantum computers, searching for cryptosystems that survive quantum attacks is of great interest. Code-based cryptography is a promising candidate since it is built on the NP-hard problem of decoding a random code [5].
Random-looking codes replace random codes for most cryptosystems to enable a trapdoor. McEliece originally proposed to use binary Goppa codes. Later, MDPC codes were successfully introduced.
More recently, it was suggested that generalized (U|U+V) codes be used, which belong to the class of generalized concatenated codes.
Concatenated codes play an important role in classical channel coding, but further research is required to evaluate which variants also form a promising basis for code-based cryptography.
The goal of this topic is to analyze constructions of generalized concatenated codes proposed for cryptographic applications, e.g., [1-4]:
- how do proposed constructions work?
- which properties do they have?
- is the secret structure well hidden?
The exact scope can be set depending on your interest.
Main Papers:
[1] Márquez-Corbella, Irene, and Jean-Pierre Tillich. "Using Reed-Solomon codes in the (U| U+ V) construction and an application to cryptography." 2016 IEEE International Symposium on Information Theory (ISIT). IEEE, 2016.
[2] Puchinger, S., Müelich, S., Ishak, K., & Bossert, M. (2017). Code-based cryptosystems using generalized concatenated codes. In Applications of Computer Algebra: Kalamata, Greece, July 20–23 2015 (pp. 397-423). Springer International Publishing.
[3] Debris-Alazard, T., Sendrier, N., & Tillich, J. P. (2018). Wave: A new code-based signature scheme.
[4] Cho, J., No, J. S., Lee, Y., Koo, Z., & Kim, Y. S. (2022). Enhanced pqsigRM: code-based digital signature scheme with short signature and fast verification for post-quantum cryptography. Cryptology ePrint Archive.
Further References:
[5] Weger, V., Gassner, N., & Rosenthal, J. (2022). A Survey on Code-Based Cryptography. arXiv preprint arXiv:2201.07119.
Voraussetzungen
Security in Communications and Storage
Channel Coding