A cryptographic accumulator is a constant-size representation of a (large) set S. For every element in S, there is a short witness such that anyone given the accumulator and the witness can verify that indeed, the element is included in the original set S. For every element not in S, finding such witnesses is computationally intractable (under the usual cryptographic assumptions).
A typical application for accumulators is revocation (e.g., of access rights). When someone gets certain access rights, their ID is included in some public accumulator. To get access, one simply computes a witness for his ID in the accumulator and supplies that to the verifier. If at some point, access needs to be revoked, the responsible party can simply remove the ID from the accumulator, preventing the party from gaining access in the future.
Usually, whenever the accumulator changes to a new set S', every owner of an accumulated ID in S' needs to update his witness so that it fits the accumulator for S' instead of S. A desirable trait of accumulators is being able to update witnesses incrementally instead of having to recompute witnesses for new sets from scratch. Baldimtsi et al. recently published an accumulator with the unique property that if S' is a superset of S (i.e. only additions occured), no witness updates are necessary at all. They base their construction on the strong RSA assumption.
However, in many contexts RSA-based accumulators are inconvenient. Many constructions that would want to use accumulators for revocation are based on prime-order groups with bilinear maps, which makes them incompatible with the published accumulator.
The rough idea behind this thesis topic is to first understand the construction of Baldimtsi et al. and to provide detailed proofs for their claims (they only sketch proof ideas in their paper). Then, you should transfer their ideas to the prime-order group setting, making them applicable for a large range of modern cryptographic constructions. For this, the accumulator by Nguyen serves as a base construction for an accumulator that is extendable with methods similar to Baldimtsi's.