I don&#x27;t think that&#x27;s the thesis. I think the thesis is that there could be a &quot;BADA55 construction&quot; even in Curve25519. Even though all of the individual pieces are justifiable, for instance the 2^255-19 is justifiable because it&#x27;s the smallest number. They knew the entire curve before trying to make it popular. Also, they could have used 2^255+95 because it&#x27;s the smallest <i>larger</i> than 2^255 with some justification that it needed to be larger than 2^255. With enough arbitrary decisions a &quot;one-in-a-million&quot; vulnerability is possible. The premise of this curve is that there are no arbitrary decisions, since you commit to supporting the curve before even knowing what it is.<p>I think the analogy is someone shuffling a deck of cards, and taking a peek at the first card. Then betting someone $20 that it&#x27;s the ace of spades. The process is justifiable, because you don&#x27;t have any control of what the top card happens to be. It&#x27;s just that you know what card it is and wouldn&#x27;t make the bet if you didn&#x27;t know it was already an ace of spades. Similarly, Curve25519 might have been constructed and happened to have the &quot;one-in-a-million&quot; vulnerability. How many other &quot;Curve25519s&quot; are there that we didn&#x27;t hear about. Imagine that instead, the procedure was shuffle the cards <i>after</i> you commit to the bet.<p>I really doubt there&#x27;s anything wrong with 25519. I feel like if anything, if djb et al knew about some vulnerability in curves that 25519 happened to have before releasing it, they would have put the weakness as one of the failing criteria to pick a new set of parameters.