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Constructing elliptic curves with bilinear groups of composite order

Title
Constructing elliptic curves with bilinear groups of composite order
Authors
안소영
Issue Date
2011
Department/Major
대학원 수학과
Publisher
이화여자대학교 대학원
Degree
Master
Advisors
이향숙
Abstract
Bilinear group 이란 암호적인 pairing이 잘 정의된 cyclic group 이다. 특히 bilinear group의 order가 composite 일 때, 암호학적으로 유용한 protocol들을 만들 수 있다. 이러한 protocol들의 보안성은 bilinear group의 주어진 원소가 특정한 subgroup 안에 있는지의 여부에 따라 결정되는 subgroup decision problem에 의존한다. 이 논문에서는 composite order인 bilinear gorup을 갖는 elliptic curve를 만들기 위해 Boneh, Rubin and Silverberg에 의해 소개된 algorithm을 소개하고, 이를 기본으로 좀 더 많은 elliptic curve를 찾을 수 있도록 algorithm을 제안한다. 마지막으로 새롭게 제안한 algorithm을 이용하여 elliptic curve 를 생성한 예를 제시한다.;A bilinear group is a cyclic group on which a cryptographic pairing is defined. When the order of a bilinear group is composite, one can construct useful cryptographic protocols. The security of the protocols relies on the subgroup decision problem which decides whether a given element of the bilinear group is contained in a specific subgroup or not. In this paper, we provide an algorithm to construct an elliptic curve which has composite bilinear groups. For this purpose, we extend the algorithm proposed by Boneh, Rubin and Silverberg and search for good parameters in the sense of easy construction of bilinear groups. We show elliptic curves and their bilinear groups which have reasonable size so that a subgroup decision problem is hard and a pairing is well-defined.
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일반대학원 > 수학과 > Theses_Master
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