For cryptography, the art of cipher widely used in today's digital environment, security is key. To be more certain that this is done properly, cryptographic constructions are mathematically proven to be secure. This means that they can only be unsafe if the accepted conjectures turn out to be erroneous. This sounds very convincing, but how sure can we be of the correctness of these results?
This PhD thesis investigates various constructions in symmetric cryptography, where a key is shared beforehand, using techniques from provable security. The results shows that many previous works were flawed and the claimed results incorrect. These results can be improved, but this sometimes leads to much weaker theorems, and in some cases, the original theorem cannot possibly be correct, despite the fact that these theorems were supposedly proven.
This PhD thesis also produces positive results. For example, it introduces new constructions that are more efficient than older versions, it reduces the number of assumptions required to prove existing constructions safely, and it proves old constructions safely in new quantum models.
Aldo Gunsing (1996) obtained his Bachelor's degree in Mathematics summa cum laude from Radboud University in 2017. He continued to study at Radboud University and in 2019 obtained his Master's degree in Mathematics cum laude, specialising in Mathematical Foundations of Computer Science, with the supervisors of his Master's thesis later also supervising his PhD research.