Elliptic curve cryptosystem development and design
Christina Miller · The University of Queensland · 1999
With the development of the Internet and the current increasing demands for electronic business transactions, the need for secure communication via insecure channels is becoming of paramount importance. Public-key cryptosystems such as RSA and DSS have traditionally been used for this purpose. However, Elliptic curve Cryptosystems (ECCs) have become a viable alternative since they provide greater security. ECCpert is an implementation of an ECC which is based over a finite field from a special class called Optimal Extension Fields (OEFs). OEFs utilise the fast integer arithmetic available on modern processors to produce very efficient results without resorting to multiprecision operations or arithmetic using polynomials of large degree. This thesis discusses the theoretical and implementation issues associated with the development of this system. Comparisons of current ECCs over prime and binary extension fields with ECCpert has shown that it has the potential to outperform these existing systems. n