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Date: Tue, 11 Nov 2014 04:02:23 +0000 (UTC)
From: Oleg Gryb <oleg_gryb@yahoo.com>
To: "djb@cr.yp.to" <djb@cr.yp.to>, "tls@ietf.org" <tls@ietf.org>
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Subject: [TLS] Twist security for brainpoolp256r1
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Hi Daniel and TLS community,
I was going through SafeCurves pages recently and wanted to ask a question =
about brainpoolP256r1's twist security. According to this research http://s=
afecurves.cr.yp.to/twist.html,,=C2=A0 a combined cost of attacks on brainpo=
olP256t1, which is a P256r1's "twist" is rather low. At the same time it's =
obvious that small-group-attack is not applicable, because "h=3D1" is a req=
uirement for all brainpool curves including the one under consideration.
The other two "invalid-curve" attacks should be mitigated by openssl contro=
ls, since latter does have a point-on-the-curve validation (e,g. see EC_POI=
NT_is_on_curve function and its usage in the latest openssl stable versions=
).
Given all that, can I consider the curve as secure? Are there any other att=
acks that I should consider before adopting the curve as a standard?
Thank you also for the wonderful research related to Curve25519 and Curve41=
417. They both seem to be perfect. I hope openssl community will adopt them=
 soon.
Oleg
=C2=A0
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<html><body><div style=3D"color:#000; background-color:#fff; font-family:He=
lveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;fo=
nt-size:12px"><div style=3D"" class=3D"" id=3D"yiv0843426377"><div style=3D=
"" class=3D""><div class=3D"" style=3D"color:#000;background-color:#fff;fon=
t-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sa=
ns-serif;font-size:12px;"><div style=3D"" class=3D"" dir=3D"ltr" id=3D"yiv0=
843426377yui_3_16_0_1_1415677219604_2596">Hi Daniel and TLS community,</div=
><div style=3D"" class=3D"" id=3D"yiv0843426377yui_3_16_0_1_1415677219604_2=
602" dir=3D"ltr"><br style=3D""></div><div style=3D"" class=3D"" id=3D"yiv0=
843426377yui_3_16_0_1_1415677219604_2620" dir=3D"ltr">I was going through S=
afeCurves pages recently and wanted to ask a question about brainpoolP256r1=
's twist security. According to this research <a style=3D"" class=3D"" rel=
=3D"nofollow" id=3D"yiv0843426377yui_3_16_0_1_1415677219604_2623" target=3D=
"_blank" href=3D"http://safecurves.cr.yp.to/twist.html">http://safecurves.c=
r.yp.to/twist.html,,</a>&nbsp; a combined cost of attacks on brainpoolP256t=
1, which is a P256r1's "twist" is rather low. At the same time it's obvious=
 that small-group-attack is not applicable, because "h=3D1" is a requiremen=
t for all brainpool curves including the one under consideration.</div><div=
 style=3D"" class=3D"" id=3D"yiv0843426377yui_3_16_0_1_1415677219604_2676" =
dir=3D"ltr"><br style=3D"" class=3D""></div><div style=3D"" class=3D"" id=
=3D"yiv0843426377yui_3_16_0_1_1415677219604_2671" dir=3D"ltr">The other two=
 "invalid-curve" attacks should be mitigated by openssl controls, since lat=
ter does have a point-on-the-curve validation (e,g. see EC_POINT_is_on_curv=
e function and its usage in the latest openssl stable versions).</div><div =
style=3D"" class=3D"" id=3D"yiv0843426377yui_3_16_0_1_1415677219604_2702" d=
ir=3D"ltr"><br style=3D"" class=3D""></div><div style=3D"" class=3D"" id=3D=
"yiv0843426377yui_3_16_0_1_1415677219604_2701" dir=3D"ltr">Given all that, =
can I consider the curve as secure? Are there any other attacks that I shou=
ld consider before adopting the curve as a standard?</div><div style=3D"" c=
lass=3D"" id=3D"yiv0843426377yui_3_16_0_1_1415677219604_2700" dir=3D"ltr"><=
br style=3D"" class=3D""></div><div style=3D"" class=3D"" id=3D"yiv08434263=
77yui_3_16_0_1_1415677219604_2699" dir=3D"ltr">Thank you also for the wonde=
rful research related to Curve25519 and Curve41417. They both seem to be pe=
rfect. I hope openssl community will adopt them soon.</div><div style=3D"" =
class=3D"" id=3D"yiv0843426377yui_3_16_0_1_1415677219604_2703" dir=3D"ltr">=
<br style=3D"" class=3D""></div><div style=3D"" class=3D"" dir=3D"ltr">Oleg=
<br style=3D"" class=3D""></div><div style=3D"" class=3D"" id=3D"yiv0843426=
377yui_3_16_0_1_1415677219604_2620" dir=3D"ltr">&nbsp;</div></div></div></d=
iv></div></body></html>
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