Thanks for the explanation! I was reading the paper but not being an expert I could hardly pass beyond the abstract.<p>So if I understand correctly, the idea would be to have only one curve that has been thoroughly examined for weaknesses and then use that curve and only that curve (ideally) in encryption applications, for example for future versions of TLS or whatever other encryption scheme supports elliptic curves.<p>That would avoid introducing potentially exploitable curves to consumer applications, and maybe even make the NSA&#x27;s work harder, right?<p>Now my other question is, I&#x27;m guessing there&#x27;s no easy way to determine the rigidity of a curve without the proper knowledge and tools, but if there was a way (let&#x27;s say some smart guy managed to make an algorithm to determine the curve&#x27;s weakness) the interested parties could determine the other party&#x27;s curve weakness and negotiate a minimum level? So if you are using a very nonrigid curve then the other party could say &quot;hey, I won&#x27;t send encrypted messages to you unless you use a curve&#x27;s rigidity index &gt; X&quot;. Does this make sense? is this were future consumer encryption is&#x2F;should be moving?<p>EDIT: I&#x27;m assuming a nonrigid curve can be considered &quot;weak&quot; by your explanation. A rigid one would be much stronger since it would leave less space for exploitable curves, right?