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Purdue University
Center for Education and Research in Information Assurance and Security

Finite Fields Of Low Characteristic in Elliptic Curve Cryptography

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Author

Shuo Shen

Tech report number

CERIAS TR 2007-33

Entry type

phdthesis

Abstract

The use of finite fields of low characteristic can make the implementation of elliptic curve cryptography more efficient. There are two approaches to lower the characteristic of the finite field in ECC while maintaining the same security level: Elliptic curves over a finite field extension and hyperelliptic curves over a finite field. This thesis solves some problems in both approaches. The group orders of elliptic curves over finite field extensions are described as polynomials. The irreducibility of these polynomials is proved, and hence the primality of the group orders can be studied. Asymptotic formulas for the number of traces of elliptic curves over field extensions with almost prime orders are given and a proof based on Bateman-Horn

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Date

2007 – 05

Key alpha

FINITE FIELDS, ELLIPTIC CURVE, CRYPTOGRAPHY

School

Purdue University

Publication Date

2007-05-01

Contents

1 INTRODUCTION 2 ELLIPTIC CURVES OVER FINITE FIELD EXTENTIONS 3 ARITHMETIC OF REAL HYPERELLIPTIC CURVES

Subject

Elliptic Curve Crytography

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