Abstract:
Hyperelliptic Cryptosystems on Embedded Microprocessors
Security aspects for embedded systems play an important role in almost all modern
communication networks. Embedded microprocessors in mobile phones or Personal Digital
Assistants (PDAs) are becoming more and more part of our private and professional 
life. The supply of security for data exchange on basis of embedded systems is a 
very important objection to accomplish. Therefore we are faced with an increased 
demand for fast asymmetric algorithms especially for small devices.

Hyperelliptic curve cryptosystems (HECC) allow for shorter operands the same level 
of security than other public-key cryptosystems, such as RSA or Diffie-Hellman. 
These shorter operands make HECC well suited for the use in embedded systems which 
have shorter word lengths and less memory than common desktop systems. Hyperelliptic 
curves are a generalization of elliptic curves and can be used for building discrete 
logarithm public-key schemes.

A major part of this work is the development and the implementation of explicit, 
fast formulas for group operations on hyperelliptic curves. We present a complete 
implementation of the group operations in the Jacobian of a hyperelliptic curve 
on an embedded processor and show that HECC of genus three can perform much better 
than genus two HECC.

Finally a comparison of HECC and ECC based on a theoretical and practical point of 
view is given.

BibTeX:
@MastersThesis{MT-Pel02,
author = {Jan Pelzl},
title = {Hyperelliptic Curve Cryptosystems on Embedded Microprocessors},
school = {Ruhr University of Bochum},
year = {2002},
address = {\url{http://www.crypto.rub.de}},
month = {September}
}