Abstract

Elliptic curve cryptosystems (ECCs) are becoming more popular because of the reduced number of key bits required in comparison to other cryptosystems (eg. a 160 bit ECC has roughly the same security as 1024 bit RSA). ECCs are especially suited to smart cards because of their limited memory and computational power. This paper discusses an implementation of the elliptic curve Digital Signature Algorithm implemented over the field GF (p) on a smartcard and gives timings and algorithms for the most efficient methods of point addition, point doubling and scalar multiplication analysed. It also discusses the effects of different memory usage, code size and speed tradeoffs which were considered during the implementation.

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