Timeline for Pairing-friendly curves in small characteristic fields
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S Apr 8, 2022 at 12:23 | history | suggested | Glorfindel | CC BY-SA 4.0 |
broken link fixed
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| Apr 8, 2022 at 9:01 | review | Suggested edits | |||
| S Apr 8, 2022 at 12:23 | |||||
| Jan 18, 2012 at 1:51 | comment | added | Samuel Neves | Understood. Should not have just skimmed the paper... | |
| Jan 18, 2012 at 1:23 | comment | added | Mehdi Tibouchi | I should perhaps note, however (and sorry for commenting twice), that in principle, it might be possible to construct pairing-friendly curves over extension fields of a form like $\mathbb{F}_{p^2}$ with the CM method (see e.g. the discussion in 4.1 of Barreto and Naehrig's paper). But $p$ still has to be large and you cannot fix it in advance, so it doesn't solve the problem in small characteristic. | |
| Jan 18, 2012 at 1:11 | comment | added | Mehdi Tibouchi | If you check the output of Algorithms 4.2 and 5.1 in Freeman's paper, you'll find that all of his curves (and hence their Jacobians) are defined over prime fields. The $J(\mathbb{F}_{q^k})$ in the abstract is about finding where the full r-torsion of the Jacobian in contained. | |
| Jan 17, 2012 at 19:46 | vote | accept | Samuel Neves | ||
| Jan 17, 2012 at 19:46 | vote | accept | Samuel Neves | ||
| Jan 17, 2012 at 19:46 | |||||
| Jan 17, 2012 at 19:45 | comment | added | Samuel Neves | I marked the above reply correct because I failed to specify genus in my question --- Freeman does seem to provide pairing-friendly curves in $J(F_{q^k})$ for genus 2. In genus 1, what you say makes sense. | |
| Jan 17, 2012 at 9:55 | history | answered | Mehdi Tibouchi | CC BY-SA 3.0 |