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Elliptic curve cryptography

Nigel Smart, Elliptic curve cryptography. Chapter in Handbook of Information Security. ISBN 0-471-64833-7. January 2006. No electronic version available.

Abstract

In this paper we introduce elliptic curves and their arithmetic. We show how such mathematical objects are realised in a computer and then go on to describe some of the cryptographic protocols one can implement with elliptic curves. Since elliptic curves are particularly interesting in constrained environments such as smart cards we also describe some of the side-channel defences which have been proposed for elliptic curve systems.

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