Pairing-Friendly Elliptic Curves with Various Discriminants
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概要
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This paper extends the Brezing-Weng method by parameterizing the discriminant D by a polynomial D(x). To date, the maximum of CM discriminant can be adequately addressed is about 14-digits. Thus the degree of the square free part of D(x) has to be sufficiently small. By making the square free part of D(x) a linear monomial, the degree of the square free part is small and by substituting x to some quadratic monomial, pairing-friendly curves with various discriminants can be constructed. In order that a square free part of D(x) is of the form ax, ax has to be a square element as a polynomial representation in a number field. Two methods are introduced to apply this construction. For k = 5, 8, 9, 15, 16, 20, 24 and 28, the proposed method gives smaller ρ value than those in previous studies.
著者
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Kim Ki
Department of Oral Biology, Research Center for Orofacial Hard Tissue Regeneration, Oral Science Res
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Kang Woo
Department of Obstetrics and Gynecology, Chonnam National University Medical School
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