Platform Independent Elliptic Curve Cryptography over

Elliptic curve cryptography has long since moved into several wellknown standards like IEEE’s 1363, SEC and X9.62. With its small key sizes it is just right for many crypto applications, in particular for mobile computing and communication devices. To make ECC easily available for all these different applications, a highly efficient and platformindependent implementation of ECC is necessary. The efficiency of such an implementation depends on the choice of methods for point multiplication and the choice of point representation. Many different combinations are possible but only one for each ec-application leads to the best result. In this paper we present an highly efficient, platform-independent implementation for ec-signature generation, ec-signature verification and ec-key exchange. It only requires an additional storage of 2 MB and therefore is applicable also for small mobile devices. On the basis of extensive experiments we show, that in our implementation, algorithms and parameters are chosen such that the efficiency of each of above ec-applications is optimal.