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Elliptic Curve Protocols

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Security in Embedded Devices

Part of the book series: Embedded Systems ((EMSY))

Abstract

An entire chapter is dedicated to elliptic curves since there is great hope that advances in this area will bring higher levels of security to many embedded devices. Compared to previous public key systems, elliptic curve cryptography (ECC) promises equivalent security strength with smaller key sizes. Since key size impacts storage and in general has been shown to impact performance and thus energy dissipation, these elliptic curves are of great interest to embedded systems. The notion of using elliptic curves in cryptography is generally agreed to have emerged from two famous papers: those of Miller (1986) and Koblitz (1987).

This chapter will provide only a brief introduction to elliptic curves to enable engineers and scientists without significant knowledge of cryptography to gain an appreciation for elliptic curves as well as general understanding of the involved computations. Thus, we start out by addressing high-level algorithms first. The detailed lower level mathematics as well as the general elliptic curve protocols follows. This allows the reader to be introduced to the fundamental mathematical computations of elliptic curves and finally how they are used in standardized protocols. A brief overview of the mathematical background required to understand basic elliptic curve protocols is also presented wherever necessary; however, more in-depth discussion can be found in Hankerson et al. (2000, 2004) as well as in Cohen and Frey (2006) and Stinson (2005).

It is possible to write endlessly on Elliptic Curves…

from [1] in Miller (1986)

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Authors and Affiliations

  1. Department of Electrical & Computer Engineering, University of Waterloo, 200 University Avenue W., Waterloo, ON, N2L 3G1, Canada

    Catherine H. Gebotys

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  1. Catherine H. Gebotys
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Correspondence to Catherine H. Gebotys .

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Gebotys, C.H. (2010). Elliptic Curve Protocols. In: Security in Embedded Devices. Embedded Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1530-6_5

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  • DOI: https://doi.org/10.1007/978-1-4419-1530-6_5

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  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-1529-0

  • Online ISBN: 978-1-4419-1530-6

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