A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves
In this paper we present a new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves with small rho-values, and we improve on previously known best rho-values of families [J. Cryptology 23 (2010), 224–280], [Lecture Notes in Comput. Sci. 5209, Springer (...
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| Format: | Article |
| Language: | English |
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De Gruyter
2015-03-01
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| Series: | Journal of Mathematical Cryptology |
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| Online Access: | https://doi.org/10.1515/jmc-2013-0017 |
| Summary: | In this paper we present a new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves with small rho-values, and we improve on previously known best rho-values of families [J. Cryptology 23 (2010), 224–280], [Lecture Notes in Comput. Sci. 5209, Springer (2008), 126–135]
for the embedding degrees k=16$k=16$, 22, 28, 40 and 46. We consider elements of the form (a+b-D)ζk$(a+b\sqrt{-D})\zeta _k$ for rational numbers a, b and a square-free positive integer D, where ζk$\zeta _k$ is a primitive k-th root of unity. We also investigate the conditions for an element of the proposed form to be suitable for our construction. Our construction uses fixed discriminants. |
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| ISSN: | 1862-2976 1862-2984 |