Group Signatures

EDIC candidacy exam
Exam president: Prof. Arjen Lenstra
Thesis advisor: Prof. Serge Vaudenay
Co-examiner: Prof. Viktor Kuncak

Abstract
A signature scheme is a minimal set of tools that enables one to convince others that a particular string value is special, in a way that it could have been generated only through the possession of a secret.
The secret does not have to be unique nor owned by a single entity. In other words, the proven statement might rather imply that a particular signature is output by, not an entity, but a member of a group. A subtle difference lies in that verifiers are assured that the signature comes from an unknown (to the verifier) member of the group, without any revelation on whom it might be --- thus called group signatures.
In this research proposal, we visit the origins of the idea, go over the formal definitions and recall what is the minimal assumption for this primitive. Then, we cover the efficient constructions satisfying those rigid security definitions along with their assumptions.
Finally, albeit knowing the foundations have already been well established, we briefly discuss how recent applications seek for even more flexible schemes, which in return require new definitions.

Background papers
Group Signatures, by Chaum, van Heyst
Foundations of Group Signatures: Formal Definitions, Simplified Requirements, and a Construction Based on General Assumptions, by Bellare, Micciancio, Warinschi
Short Group Signatures, by Boneh, Boyen, Shacham