Fundamentals of Asymmetric Cryptography

Cryptology provides two different flavors of algorithms, namely symmetric and asymmetric (public-key) algorithms. This contribution deals with asymmetric algorithms.

Asymmetric cryptography provides the ability and is used in practical applications to: (a) exchange keys securely over a unprotected channel and (b) sign electronic document (Digital signature). Especially the first scenario is important in any kind of communication between systems. Hence, these cryptographic primitives are a necessity for securely exchanging messages in the car (e.g. between components) and between the car and a third party (e.g. tool station, other car, service provider).

This chapter gives first an introduction to asymmetric cryptography, helping the reader to understand the advantages as well as the problems. In the main part of the chapter we focus on two asymmetric cryptosystems, namely RSA and Elliptic Curve Cryptosystems (ECC). ECC is especially interesting for the usage in the automotive environment, because it is much better suited for the implementation on embedded processors. For each of the two cryptographic primitives we cover briefly the mathematical background and focus then on the engineering aspects (including fast implementation techniques) of these systems. In order to give the reader an idea about the performance of these algorithms we summarize available publications.