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 |
| _version_ | 1798026339576446976 |
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| author | Yoon Kisoon |
| author_facet | Yoon Kisoon |
| author_sort | Yoon Kisoon |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T18:34:54Z |
| format | Article |
| id | doaj.art-f7c994e3de024f2bac208851e1a0eca4 |
| institution | Directory Open Access Journal |
| issn | 1862-2976 1862-2984 |
| language | English |
| last_indexed | 2024-04-11T18:34:54Z |
| publishDate | 2015-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Mathematical Cryptology |
| spelling | doaj.art-f7c994e3de024f2bac208851e1a0eca42022-12-22T04:09:20ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842015-03-01911910.1515/jmc-2013-0017A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curvesYoon Kisoon0NSHC Inc. 55, Gwangjinmal-gil, Uiwang-si, Gyeonggi-do, 437-060, Republic of KoreaIn 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.https://doi.org/10.1515/jmc-2013-0017elliptic curvesfinite fieldspairing-based cryptographycomplete families14h5211t7111g2094a60 |
| spellingShingle | Yoon Kisoon A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves Journal of Mathematical Cryptology elliptic curves finite fields pairing-based cryptography complete families 14h52 11t71 11g20 94a60 |
| title | A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves |
| title_full | A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves |
| title_fullStr | A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves |
| title_full_unstemmed | A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves |
| title_short | A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves |
| title_sort | new method of choosing primitive elements for brezing weng families of pairing friendly elliptic curves |
| topic | elliptic curves finite fields pairing-based cryptography complete families 14h52 11t71 11g20 94a60 |
| url | https://doi.org/10.1515/jmc-2013-0017 |
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