On the ρ-values of complete families of pairing-friendly elliptic curves
The parameter ρ of a complete family of pairing-friendly elliptic curves represents how suitable some given elliptic curves are in pairing-based cryptographic schemes. The superiority of the curves depends on how close ρ is to 1. Especially, the situation is ideal. We study whether a complete famil...
| Main Author: | |
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| Format: | Article |
| Language: | English |
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De Gruyter
2012-12-01
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| Series: | Journal of Mathematical Cryptology |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jmc-2012-0011 |
| _version_ | 1797999530303553536 |
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| author | Okano Keiji |
| author_facet | Okano Keiji |
| author_sort | Okano Keiji |
| collection | DOAJ |
| description | The parameter ρ of a complete family of pairing-friendly elliptic curves
represents how suitable some given elliptic curves are in pairing-based cryptographic schemes.
The superiority of the curves depends on how close ρ is to 1.
Especially, the situation is ideal.
We study whether a complete family of pairing-friendly elliptic curves has a ρ-value 1 or not.
In this paper, we consider the original idea of Brezing and Weng that we put a parameter for constructing families of elliptic curves as cyclotomic polynomials.
We show that the ρ-values cannot be 1 in many cases. |
| first_indexed | 2024-04-11T11:06:08Z |
| format | Article |
| id | doaj.art-387854a6215749c2ae045d446fcdec91 |
| institution | Directory Open Access Journal |
| issn | 1862-2976 1862-2984 |
| language | English |
| last_indexed | 2024-04-11T11:06:08Z |
| publishDate | 2012-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Mathematical Cryptology |
| spelling | doaj.art-387854a6215749c2ae045d446fcdec912022-12-22T04:28:21ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842012-12-0163-424926810.1515/jmc-2012-0011On the ρ-values of complete families of pairing-friendly elliptic curvesOkano Keiji0Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, 278-8510, JapanThe parameter ρ of a complete family of pairing-friendly elliptic curves represents how suitable some given elliptic curves are in pairing-based cryptographic schemes. The superiority of the curves depends on how close ρ is to 1. Especially, the situation is ideal. We study whether a complete family of pairing-friendly elliptic curves has a ρ-value 1 or not. In this paper, we consider the original idea of Brezing and Weng that we put a parameter for constructing families of elliptic curves as cyclotomic polynomials. We show that the ρ-values cannot be 1 in many cases.https://doi.org/10.1515/jmc-2012-0011elliptic curvespairing-based cryptographyembedding degree |
| spellingShingle | Okano Keiji On the ρ-values of complete families of pairing-friendly elliptic curves Journal of Mathematical Cryptology elliptic curves pairing-based cryptography embedding degree |
| title | On the ρ-values of complete families of pairing-friendly elliptic curves |
| title_full | On the ρ-values of complete families of pairing-friendly elliptic curves |
| title_fullStr | On the ρ-values of complete families of pairing-friendly elliptic curves |
| title_full_unstemmed | On the ρ-values of complete families of pairing-friendly elliptic curves |
| title_short | On the ρ-values of complete families of pairing-friendly elliptic curves |
| title_sort | on the ρ values of complete families of pairing friendly elliptic curves |
| topic | elliptic curves pairing-based cryptography embedding degree |
| url | https://doi.org/10.1515/jmc-2012-0011 |
| work_keys_str_mv | AT okanokeiji onthervaluesofcompletefamiliesofpairingfriendlyellipticcurves |