Computer Security and Cryptography

CHAPTER 15

ELLIPTIC CURVE CRYPTOGRAPHY

JUST TWENTY years ago, Koblitz and Miller suggested the use of elliptic curves to construct cryptographic systems. Using a result from the nineteenth century of Carl Gustav Jacob Jacobi, a group structure can be defined. There is a tremendous cryptographic advantage to encipherment based on elliptic groups. In the ensuing 20 years, a considerable body of results has been published so that there are now elliptic curve encryption, key exchange, and signature algorithms. These are the subjects of this chapter.