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Motivated by the cell-free and massive MIMO (multiple input multiple outputs) communication scenarios, the number of power amplifiers (PA), digital to analog converters (DAC), etc., is increased. Thus, using coarse quantized transmission reduces the channel's hardware cost and nonlinear effects. More details can be found in the attached file.

In this project, we investigate algorithms for mapping modulated data to coarsely quantized signals and compare their information rates. 

The student needs an understanding of information theory and communication systems.

This thesis is concerned with developing code constructions for a new weight function (and associated metric) on (Z/qZ)^n called the unit-burst weight, suitable for measuring same-symbol burst errors. A unit burst is defined as a vector that has some consecutive positions of ones and is zero otherwise.

Any vector v in (Z/qZ)^n can be written as a (not necessarily unique) linear combination of these bursts. The burst weight is then the minimum number of bursts that need to be added or subtracted to produce v.

This metric has a connection to the A_n root lattice, a special lattice in Z^n+1 of vectors whose entries sum to zero. More precisely, the unit bursts relate to the shortest vectors of A_n called roots, and the burst weight corresponds to the smallest decomposition of a lattice point into roots.

We have already derived some basic properties and algorithms for this new metric and now would like to find some bounds and code constructions achieving those bounds. 

Private Information Retrieval (PIR) is the problem of retrieving a desired data from a server while preventing the server from finding out the retrieved data.

Private Set Intersection (PSI) is the problem of multiple parties comparing their databases and computing the common elements, without revealing any information about the data they do not commonly possess.

The goal of this project is to understand both problems and to compare them. The main target is to design a protocol that can convert any PIR scheme to a PSI scheme and/or a protocol that can convert any PSI scheme to a PIR scheme.

References:

[1] Z. Wang, K. Banawan, and S. Ulukus, ‘Multi-Party Private Set Intersection: An Information-Theoretic Approach’, IEEE Journal on Selected Areas in Information Theory, vol. 2, no. 1, pp. 366–379, Mar. 2021, doi: 10.1109/JSAIT.2021.3057597.

[2] Z. Wang, K. Banawan, and S. Ulukus, ‘Private Set Intersection Using Multi-Message Symmetric Private Information Retrieval’, in 2020 IEEE International Symposium on Information Theory (ISIT), Jun. 2020, pp. 1035–1040. doi: 10.1109/ISIT44484.2020.9174221.

Voraussetzungen

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.

Voraussetzungen

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.

[1] Aguilar-Melchor, Carlos, Victor Dyseryn, and Philippe Gaborit, "Somewhat Homomorphic Encryption based on Random Codes," Cryptology ePrint Archive (2023).

Voraussetzungen

This thesis is concerned with developing code constructions for a new weight function (and associated metric) on (Z/qZ)^n called the unit-burst weight, suitable for measuring same-symbol burst errors. A unit burst is defined as a vector that has some consecutive positions of ones and is zero otherwise.

Any vector v in (Z/qZ)^n can be written as a (not necessarily unique) linear combination of these bursts. The burst weight is then the minimum number of bursts that need to be added or subtracted to produce v.

This metric has a connection to the A_n root lattice, a special lattice in Z^n+1 of vectors whose entries sum to zero. More precisely, the unit bursts relate to the shortest vectors of A_n called roots, and the burst weight corresponds to the smallest decomposition of a lattice point into roots.

We have already derived some basic properties and algorithms for this new metric and now would like to find some bounds and code constructions achieving those bounds. 

Private Information Retrieval (PIR) is the problem of retrieving a desired data from a server while preventing the server from finding out the retrieved data.

Private Set Intersection (PSI) is the problem of multiple parties comparing their databases and computing the common elements, without revealing any information about the data they do not commonly possess.

The goal of this project is to understand both problems and to compare them. The main target is to design a protocol that can convert any PIR scheme to a PSI scheme and/or a protocol that can convert any PSI scheme to a PIR scheme.

References:

[1] Z. Wang, K. Banawan, and S. Ulukus, ‘Multi-Party Private Set Intersection: An Information-Theoretic Approach’, IEEE Journal on Selected Areas in Information Theory, vol. 2, no. 1, pp. 366–379, Mar. 2021, doi: 10.1109/JSAIT.2021.3057597.

[2] Z. Wang, K. Banawan, and S. Ulukus, ‘Private Set Intersection Using Multi-Message Symmetric Private Information Retrieval’, in 2020 IEEE International Symposium on Information Theory (ISIT), Jun. 2020, pp. 1035–1040. doi: 10.1109/ISIT44484.2020.9174221.

Voraussetzungen

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.

Voraussetzungen

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.

[1] Aguilar-Melchor, Carlos, Victor Dyseryn, and Philippe Gaborit, "Somewhat Homomorphic Encryption based on Random Codes," Cryptology ePrint Archive (2023).

Voraussetzungen