From a mathematical perspective, all of the mainstream curves, from the NIST p- curves to the Brainpool curves, are solid.<p>There are four reasons people use Curve25519: it&#x27;s faster in software than most implementations of the other curves, it was designed to be mostly misuse-resistant, so you don&#x27;t have to be as careful checking parameters (a very common vector for ECC curve attacks), it&#x27;s designed to be simple to make leak-proof implementations (unlike the NIST curves, which are hard to do in constant time), and it has the Dan Bernstein brand.<p>But if we&#x27;re talking about index calculus attacks, the NIST curves do fine there too.