On the non-idealness of cyclotomic families of pairing-friendly elliptic curves
Let k=2mpn$k=2^mp^n$ for an odd prime p and integers m ≥ 0 and n ≥ 0. We obtain lower bounds for the ρ-values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r(x)=Φk(x)$r(x)=\Phi _k(x)$. Our bounds imply that none of the families are ideal.
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| Language: | English |
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De Gruyter
2014-12-01
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| Series: | Journal of Mathematical Cryptology |
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| Online Access: | https://doi.org/10.1515/jmc-2013-0042 |
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doaj-0313912538d74b2c9e7810af660178a92021-09-06T19:40:44ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842014-12-018441744010.1515/jmc-2013-0042On the non-idealness of cyclotomic families of pairing-friendly elliptic curvesSha Min0Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 33405 Talence Cedex, FranceLet k=2mpn$k=2^mp^n$ for an odd prime p and integers m ≥ 0 and n ≥ 0. We obtain lower bounds for the ρ-values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r(x)=Φk(x)$r(x)=\Phi _k(x)$. Our bounds imply that none of the families are ideal.https://doi.org/10.1515/jmc-2013-0042pairing-friendly elliptic curvecyclotomic familyideal familycyclotomic polynomial 11t7114h52 11t22 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sha Min |
| spellingShingle |
Sha Min On the non-idealness of cyclotomic families of pairing-friendly elliptic curves Journal of Mathematical Cryptology pairing-friendly elliptic curve cyclotomic family ideal family cyclotomic polynomial 11t71 14h52 11t22 |
| author_facet |
Sha Min |
| author_sort |
Sha Min |
| title |
On the non-idealness of cyclotomic families of pairing-friendly elliptic curves |
| title_short |
On the non-idealness of cyclotomic families of pairing-friendly elliptic curves |
| title_full |
On the non-idealness of cyclotomic families of pairing-friendly elliptic curves |
| title_fullStr |
On the non-idealness of cyclotomic families of pairing-friendly elliptic curves |
| title_full_unstemmed |
On the non-idealness of cyclotomic families of pairing-friendly elliptic curves |
| title_sort |
on the non-idealness of cyclotomic families of pairing-friendly elliptic curves |
| publisher |
De Gruyter |
| series |
Journal of Mathematical Cryptology |
| issn |
1862-2976 1862-2984 |
| publishDate |
2014-12-01 |
| description |
Let k=2mpn$k=2^mp^n$ for an odd prime p and integers m ≥ 0 and n ≥ 0. We obtain lower bounds for the ρ-values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r(x)=Φk(x)$r(x)=\Phi _k(x)$. Our bounds imply that none of the families are ideal. |
| topic |
pairing-friendly elliptic curve cyclotomic family ideal family cyclotomic polynomial 11t71 14h52 11t22 |
| url |
https://doi.org/10.1515/jmc-2013-0042 |
| work_keys_str_mv |
AT shamin onthenonidealnessofcyclotomicfamiliesofpairingfriendlyellipticcurves |
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1717767860096335872 |