<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">And <a href="https://github.com/herumi/ate-pairing" class="">https://github.com/herumi/ate-pairing</a>, which also claims to be the fastest. But the real question may be which has the nicest API.</div><div class=""><br class=""></div><div class="">Unfortunately, BN curves only really shine at the ~WF128 level, where a 256-bit curve matches a 256*12-bit extension field discrete log problem (EFDLP). At higher WFs (or if you’re worried about improvements in EFDLP), you need a higher embedding degree so that the EFDLP will be harder, or else a very large base field. I don’t think there’s any any known curve at those higher levels which is as simple as the BN curves. In particular, last I heard all known families with higher embedding degrees have huge cofactors, on the order of p^(1/5) or higher.</div><div class=""><br class=""></div><div class="">— Mike</div><br class=""><div><blockquote type="cite" class=""><div class="">On Jan 26, 2015, at 1:21 AM, Filipe <<a href="mailto:filipe.beato@esat.kuleuven.be" class="">filipe.beato@esat.kuleuven.be</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html charset=us-ascii" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">There is the MIRACL library from Mike Scott that has already an implementation from Boneh-Franklin IBE scheme.<div class="">I have used it and from what I have seen, its the most efficient pairing library.<div class=""><br class=""><div apple-content-edited="true" class=""> <span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; border-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-stroke-width: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; border-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-stroke-width: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><span class="Apple-style-span" style="border-collapse: separate; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; border-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-stroke-width: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><span class="Apple-style-span" style="border-collapse: separate; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; border-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-stroke-width: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><span class="Apple-style-span" style="border-collapse: separate; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; border-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-stroke-width: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><span class="Apple-style-span" style="border-collapse: separate; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; border-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-stroke-width: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><span class="Apple-style-span" style="border-collapse: separate; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; border-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-stroke-width: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class=""><font class="Apple-style-span" face="'Gill Sans'">Filipe</font></div><br class=""><br class=""></div></span></div></span></div></span></div></span></div></span></div></span></div></span></div></span> </div> <br class=""><div class=""><div class="">On 26 Jan 2015, at 04:05, Watson Ladd <<a href="mailto:watsonbladd@gmail.com" class="">watsonbladd@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite" class="">BN curves offer very high speeds. I haven't looked at the code myself,<br class="">but DCLXVI by Michael Naehrig, Ruben Niederhagen, and Peter Schwabe<br class="">promises lots of speed. There is also a Go implementation by AGL: I<br class="">don't know if they are compatible.<br class=""><br class="">On Sun, Jan 25, 2015 at 6:52 PM, Trevor Perrin <<a href="mailto:trevp@trevp.net" class="">trevp@trevp.net</a>> wrote:<br class=""><blockquote type="cite" class="">Supposing I wanted to implement an IBE scheme (like Boneh-Franklin).<br class="">Does anyone know what the "best" curves and implementations are<br class="">(hopefully with conservative security, but high speed)?<br class=""><br class=""><br class="">Trevor<br class="">_______________________________________________<br class="">Curves mailing list<br class=""><a href="mailto:Curves@moderncrypto.org" class="">Curves@moderncrypto.org</a><br class=""><a href="https://moderncrypto.org/mailman/listinfo/curves" class="">https://moderncrypto.org/mailman/listinfo/curves</a><br class=""></blockquote><br class=""><br class=""><br class="">-- <br class="">"Those who would give up Essential Liberty to purchase a little<br class="">Temporary Safety deserve neither Liberty nor Safety."<br class="">-- Benjamin Franklin<br class="">_______________________________________________<br class="">Curves mailing list<br class=""><a href="mailto:Curves@moderncrypto.org" class="">Curves@moderncrypto.org</a><br class=""><a href="https://moderncrypto.org/mailman/listinfo/curves" class="">https://moderncrypto.org/mailman/listinfo/curves</a><br class=""></blockquote></div><br class=""></div></div></div>_______________________________________________<br class="">Curves mailing list<br class=""><a href="mailto:Curves@moderncrypto.org" class="">Curves@moderncrypto.org</a><br class="">https://moderncrypto.org/mailman/listinfo/curves<br class=""></div></blockquote></div><br class=""></body></html>