In federated learning, a machine learning model shall be trained on private user data with the help of a central server, the so-called federator. This setting differs from other machine learning settings in that the user data shall not be shared with the federator for privacy reasons and/or to decrease the communication load of the system.

Even though only intermediate results are shared, extra care is necessary to guarantee data privacy. An additional challenge arises if the system includes malicious users that breach protocol and send corrupt computation results.

The goal of this work is to design, implement and analyze coding- and information-theoretic solutions for privacy and security in federated learning.

• Information Theory
• Coding Theory (e.g., Channel Coding)
• Machine Learning (Theory and Practice)

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).

- Strong foundation in linear algebra
- Channel Coding
- Security in Communications and Storage
- Basic understanding of Machine Learning concepts

Fully decentralized schemes do not require a central entity and have been studied in [1, 2]. These works aim to reach consensus on a desirable machine learning model among all clients. We can mainly distinguish between i) gossip algorithms [3] where clients share their result with all neighbors, naturally leading to high communication complexities, and ii) random walk approaches like [4, 5] where the model is communicated only to a specific neighbor until matching certain convergence criteria. Such random walk approaches are used in federated learning to reduce the communication load in the network and at the clients’ side.

The main task of the student is to study the work in [5], which additionally accounts for the heterogeneity of the clients’ data. Further, drawbacks and limitations of the proposed approach should be determined.

[1] J. B. Predd, S. B. Kulkarni, and H. V. Poor, “Distributed learning in wireless sensor networks,” IEEE Signal Process. Mag., vol. 23, no. 4, pp. 56–69, 2006.

[2] S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al., “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1–122, 2011.

[3] S. S. Ram, A. Nedi ?c, and V. V. Veeravalli, “Asynchronous gossip algorithms for stochastic optimization,” in IEEE Conf. Decis. Control. IEEE, 2009, pp. 3581–3586.

[4] D. Needell, R. Ward, and N. Srebro, “Stochastic gradient descent, weighted sampling, and the randomized kaczmarz algorithm,” Adv. Neural Inf. Process. Syst., vol. 27, 2014.

[5] G. Ayache, V. Dassari, and S. E. Rouayheb, “Walk for learning: A random walk approach for federated learning from heterogeneous data,” arXiv preprint arXiv:2206.00737, 2022.

- Machine Learning and Statistics
- Information Theory