During his PhD studies, Lennart Braun researched cryptographic protocols that allow mutually distrusting parties to jointly solve problems such that the parties learn only what is absolutely necessary: With a zero-knowledge proof a prover can convince a verifier that a given statement is true without revealing anything else, and secure multiparty computation (MPC) allows for arbitrary computation on private data held by multiple parties.

Zero-knowledge proofs are typically designed for the statements encoded over finite fields Fp = {0, 1, ..., p-1} for some prime number p. Actual computer programs, however, usually work on 32- or 64-bit integers instead which can be better modeled as rings Z2k = {0, 1, ..., 2^k-1} for k = 32 or k = 64. Lennart designed efficient zero-knowledge proofs for this setting, which is challenging because rings have less structure than fields. Moreover, he worked on threshold encryption and multiparty computation protocols in a setting using groups where the size is unknown instead of a known prime number.

The PhD study was completed at the Department of Computer Science, Faculty of Natural Sciences, Aarhus University.

This summary was prepared by the PhD student.

Time:  Thursday, 5 September 2024 at 10:00
Place: Building 5335, room 295, Nygaard Building, Aarhus University, Helsingforsgade 14, 8200 Aarhus N
Title of PhD thesis: Cryptography After Prime Time -- Protocols for Z2k and Groups of Unknown Order
Contact information: Lennart Braun, e-mail: braun@cs.au.dk
Members of the assessment committee:
Professor Dario Catalano, Department of Mathematics and Computer Science, University of Catania, Italy
CNRS Research Scientist Geoffroy Couteau, IRIF, Université Paris Cité, France
Professor Ira Assent (chair), Department of Computer Science, Aarhus University, Denmark
Main supervisor:
Professor Ivan Bjerre Damgård, Department of Computer Science, Aarhus University, Denmark
Co-supervisor:
Professor Claudio Orlandi, Department of Computer Science, Aarhus University, Denmark
Language: The PhD dissertation will be defended in English

The defence is public.
The PhD thesis is available for reading at the Graduate School of Natural Sciences/GSNS,
Jens Baggesens Vej 53, building 5221, 8200 Aarhus N.