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The arithmetic of signed binary fields

Title
The arithmetic of signed binary fields
Authors
김희선
Issue Date
2003
Department/Major
대학원 수학과
Keywords
Binary fieldsArithmeticMathematicsSigned binary fields
Publisher
이화여자대학교 대학원
Degree
Master
Abstract
이 논문에서는 Elliptic Curve Cryptosystem (ECC)을 위한 유한체연산의 알고리즘에 대하여 공부한다. Characteristic이 2와 3인 유한체의 알고리즘을 정리 및 발전시키고, 특히 signed binary field를 새롭게 정의하여 characteristic이 3인 유한체 연산의 효율성을 증진하고자 한다. 그리고 논문이 완성되기까지 지도를 도와주신 이향숙 교수님과 이혜숙, 이준엽 교수님 그리고 영란선배, 연진, 정민, 호정, 경래선배에게 고마움을 표한다.;In this thesis, we show the arithmetic algorithms of finite fields for the elliptic curve cryptosystem. Since elliptic curve cryptosystems over finite fields have proposed, many algorithms have been developed in characteristic two. However, most of these results do not consider the arithmetics of finite fields in characteristic three because these are not applied to bit operation for computing the finite field in characteristic two such as exclusive-or and bitwise-and. In this thesis, we provide the arithmetics of the finite fields in characteristic three using signed binary.
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