Quantization using jet space geometry and identity management using credential schemes

The first part takes place at the boundary between mathematics and physics, and is about how specialization and generalization of theories can lead to new ideas. In particular we consider the question how the mathematics of a theory changes when we move from a point particle to, for example, strings or an electromagnetic field, or from classical to quantum mechanical systems. In both cases we use a mathematical tool called jet bundles and their associated geometrical structures to study the partial differential equations in terms of which such systems are expressed.

The second part is about computer science and deals with identity management: how do you prove properties about yourself in a safe and privacy-friendly manner? It is important that people know what information about themselves they disclose, and that they can control this. In this part we therefore study attribute-based credentials: a list of some of your properties (attributes), equipped with a digital signature from the party that gave the credential to you. For example, the government could issue a credential to you containing as attributes your address, and whether or not you are over 18. When you have such a credential you can choose which of the attributes you show, and which of them you keep hidden. We study a number of credential schemes offering such properties, and finally we create our own scheme that is provably secure and more efficient than comparable schemes from the literature.