Today, electronic data exchange is part of our everyday life. Hence, it is essential to protect valuable information against unauthorized access. To be able to do so, cryptographic* algorithms need to be researched continuously.

The most commonly known asymmetric* crypto system today is RSA*. Due to the development of the number field sieve algorithm*, RSA can only assure a sufficient level of security if very large keys are used. Elliptic curves* are an alternative to RSA, since they guarantee a high level of security even for small keys. Hence, they are mostly used on smart cards* and in similar environments where storage space is limited.

Hyperelliptic curves* are a generalization of elliptic curves. In contrast to the latter, they allow a larger range of parameters to choose from-resulting in a higher level of security.

In this research project, scientists of Fraunhofer ITWM developed algorithms to compute subfields* and automorphisms* as well as to perform explicit calculations in endomorphism rings* of hyperelliptic function fields*. These methods yield a test on potential weaknesses of a specific curve and give hints on the Jacobian's* structure.

Contact:

	Dipl.-Math. Norbert Göb Phone: +49 (0)631/31600-

Scientific Advisors:

	Dr. PD Andreas Guthmann
	Prof. Dr. Wolfram Decker
	Prof. Dr.-Ing. Damian Weber

Partner:

	BGS Systemplanung AG