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CONSTRUCTING PAIRING-FRIENDLY CURVES WITH VARIABLE CM DISCRIMINANT

박철민|이향숙
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회보 (Bulletin of the KMS)|제49권 제1호|pp. 75-88

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참고문헌

키워드

elliptic curvespairing-friendly curvesCM discriminant
주제분류수학

초록

A new algorithm is proposed for the construction of Brezing-Weng-like elliptic curves such that polynomials de ning the CM discrim-inant are linear. Using this construction, new families of curves with variable discriminants and embedding degrees of k∈2｛8, 16, 20, 24g｝, which were not covered by Freeman, Scott, and Teske [9], are presented. Our re-sult is useful for constructing elliptic curves with larger and more exible discriminants.

Abstract

A new algorithm is proposed for the construction of Brezing-Weng-like elliptic curves such that polynomials de ning the CM discrim-inant are linear. Using this construction, new families of curves with variable discriminants and embedding degrees of k∈2｛8, 16, 20, 24g｝, which were not covered by Freeman, Scott, and Teske [9], are presented. Our re-sult is useful for constructing elliptic curves with larger and more exible discriminants.

참고문헌 (17)

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  8. D. Freeman, "Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10, Algorithmic Number Theory Symposium ANTS-VII", Lecture Notes in Computer Sci- ence, 4076, pp.452~465 (2006), Springer-Verlag
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  11. T. W. Hungerford, "Algebra", Graduate Texts in Mathematics, 73 (1996), Springer
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  14. 이향숙, "Generating Pairing-friendly curves with the cm equation of degree 1", Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5671 LNCS(0), pp.66~77, Springer Verlag
  15. R. Sakai, "Cryptosystems based on pairing", The 2000 Symposium on Cryptography and Information Security(SCIS 2000) (2000)
  16. J. H. Silverman, "The Arithmetic of Elliptic Curves" (1986), Springer-Verlag
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