Elliptic Curve Cryptography and Its Applications to Mobile Devices.

Elliptic Curve Cryptography and Its Applications to Mobile Devices.
Wendy Chou, University of Maryland, College Park. Advisor: Dr. Lawrence Washington, Department of Mathematics Abstract: The explosive growth in the use of mobile and wireless devices demands a new generation of PKC schemes that has to accommodate limitations on power and bandwidth, at the same time, to provide an adequate level of security for such devices. This paper examines the use of ECC in such constrained environments and discusses the basis of its security, explores its performance and lastly, surveys the use of ECC applications on the market today.

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Introduction

In 1976, Whitfield Diffie and Martin Hellman introduced the concept of public key cryptography (PKC). Since then, many implementations of it have been proposed, and many of these cryptographic applications base their security on the intractability of hard mathematical problems, namely the integer factorization problem (IFP) and the finite field discrete logarithm problem (DLP). Over the years, sub-exponential time algorithms were developed to solve these problems. As a result, key sizes grew to more than 1000 bits, so as to attain a reasonable level of security. In constrained environments where computing power, storage and bandwidth are limited, carrying out thousand-bit operations becomes an impractical approach to providing adequate security. This is most evident in hand-held devices such as the mobile phones, pagers and PDAs that have very limited processing power and battery life. Proposed independently by Neal Koblitz and Victor Miller in 1985, elliptic curve cryptography (ECC) has the special characteristic that to date, the best known algorithm that solves it runs in full exponential time. Its security comes from the elliptic curve logarithm, which is the DLP in a group defined by points on an elliptic curve over a finite field. This results in a dramatic decrease in key size needed to achieve the same level of

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