Generating pairing-friendly elliptic curve parameters using sparse families
The majority of methods for constructing pairing-friendly elliptic curves are based on representing the curve parameters as polynomial families. There are three such types, namely complete, complete with variable discriminant and sparse families. In this paper, we present a method for constructing s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-06-01
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| Series: | Journal of Mathematical Cryptology |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jmc-2017-0024 |
| _version_ | 1798026344575008768 |
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| author | Fotiadis Georgios Konstantinou Elisavet |
| author_facet | Fotiadis Georgios Konstantinou Elisavet |
| author_sort | Fotiadis Georgios |
| collection | DOAJ |
| description | The majority of methods for constructing pairing-friendly elliptic curves are based on representing the curve parameters as polynomial families. There are three such types, namely complete, complete with variable discriminant and sparse families. In this paper, we present a method for constructing sparse families and produce examples of this type that have not previously appeared in the literature, for various embedding degrees. We provide numerical examples obtained by these sparse families, considering for the first time the effect of the recent progress on the tower number field sieve (TNFS) method for solving the discrete logarithm problem (DLP) in finite field extensions of composite degree. |
| first_indexed | 2024-04-11T18:33:53Z |
| format | Article |
| id | doaj.art-06568c079e774eb79aaa3905ed2afb50 |
| institution | Directory Open Access Journal |
| issn | 1862-2976 1862-2984 |
| language | English |
| last_indexed | 2024-04-11T18:33:53Z |
| publishDate | 2018-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Mathematical Cryptology |
| spelling | doaj.art-06568c079e774eb79aaa3905ed2afb502022-12-22T04:09:20ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842018-06-01122839910.1515/jmc-2017-0024Generating pairing-friendly elliptic curve parameters using sparse familiesFotiadis Georgios0Konstantinou Elisavet1Department of Information & Communication Systems Engineering, University of the Aegean, Karlovassi, Samos, 83200, GreeceDepartment of Information & Communication Systems Engineering, University of the Aegean, Karlovassi, Samos, 83200, GreeceThe majority of methods for constructing pairing-friendly elliptic curves are based on representing the curve parameters as polynomial families. There are three such types, namely complete, complete with variable discriminant and sparse families. In this paper, we present a method for constructing sparse families and produce examples of this type that have not previously appeared in the literature, for various embedding degrees. We provide numerical examples obtained by these sparse families, considering for the first time the effect of the recent progress on the tower number field sieve (TNFS) method for solving the discrete logarithm problem (DLP) in finite field extensions of composite degree.https://doi.org/10.1515/jmc-2017-0024pairing-based cryptographypairing-friendly elliptic curvessparse familiespell equation14h52 11g20 94a60 |
| spellingShingle | Fotiadis Georgios Konstantinou Elisavet Generating pairing-friendly elliptic curve parameters using sparse families Journal of Mathematical Cryptology pairing-based cryptography pairing-friendly elliptic curves sparse families pell equation 14h52 11g20 94a60 |
| title | Generating pairing-friendly elliptic curve parameters using sparse families |
| title_full | Generating pairing-friendly elliptic curve parameters using sparse families |
| title_fullStr | Generating pairing-friendly elliptic curve parameters using sparse families |
| title_full_unstemmed | Generating pairing-friendly elliptic curve parameters using sparse families |
| title_short | Generating pairing-friendly elliptic curve parameters using sparse families |
| title_sort | generating pairing friendly elliptic curve parameters using sparse families |
| topic | pairing-based cryptography pairing-friendly elliptic curves sparse families pell equation 14h52 11g20 94a60 |
| url | https://doi.org/10.1515/jmc-2017-0024 |
| work_keys_str_mv | AT fotiadisgeorgios generatingpairingfriendlyellipticcurveparametersusingsparsefamilies AT konstantinouelisavet generatingpairingfriendlyellipticcurveparametersusingsparsefamilies |