Elliptic Curve Cryptography
Abstract— This paper gives an introduction to elliptic curve cryptography (ECC) and how it is used in the implementation of digital signature (ECDSA) and key agreement (ECDH) Algorithms. The paper discusses the implementation of ECC on two finite fields, prime field and binary field. It also gives an overview of ECC implementation on different coordinate systems called the projective coordinate systems. The paper also discusses the basics of prime and binary field arithmetic. This paper also discusses why ECC is a better option than RSA in modern day systems. This paper also discusses why ECC's unique properties make it especially well suited to smart card applications.
Index Terms—Elliptic Curve Cryptography, Smart Cards, Discrete Logarithm problem
I. INTRODUCTION
Over the past 30 years, public key cryptography has become a mainstay for secure communications over the Internet and throughout many other forms of communications. It provides the foundation for both key......
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Approximate Word Count: 6237
Approximate Pages: 25 (250 words per double-spaced page)
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