If this interested you, you might want to check out SafeCurves[1]. I didn't see it mentioned in these slides (likely because it approaches the material at a higher/theoretical level), but ECDLP is not the only determining factor in elliptic curve safety; there are also implementation difficulties that can make ECC unsafe even though attackers cannot solve the ECDLP.<p>DJ Bernstein maintains the SafeCurves website and explains the foregoing in greater detail; the site also tracks security assessments on specific curves. Some are actively used and others are either not well-studied or are just toy examples.<p>_________<p>1. <a href="http://safecurves.cr.yp.to" rel="nofollow">http://safecurves.cr.yp.to</a>