13
$\begingroup$

I know that the algorithm used to generate the Brainpool curves and the NIST curves is published. The algorithm should be this one (RFC5639 Appendix A). From what it looks like it's rather slow to find secure parameters.

After some research I've also found "Efficient Algorithms for Generating Elliptic Curves over Finite Fields Suitable for Use in Cryptography" by Harald Baier (in fact it's a PhD thesis I think) on the generation of secure elliptic curves. I've also googled around and found a tool that actually generates such curves (using this algorithm I think). From an efficiency point of view this algorithm looks faster than the NIST's one.

Now my question:
Are the above two algorithms the only ones (published) for generating safe elliptic curves or are there other ones?

$\endgroup$
  • $\begingroup$ You can refer "Standards for Efficient Cryptography 1 : Elliptic Curve Cryptography" from Certicom research for developing new curves. $\endgroup$ – Venkatesh Feb 7 '17 at 5:44
7
$\begingroup$

Of course there are others. Of interest might be the paper 'Efficient ephemeral elliptic curve cryptographic keys' by Mieli and Lenstra, which claims to generate fresh Elliptic Curves sufficiently quickly that they can be created on the fly for a single ECDH exchange, and then discarded.

$\endgroup$
  • $\begingroup$ really nice and recent paper :) May I ask if this was pre-Logjam? $\endgroup$ – SEJPM Jun 16 '15 at 19:01
  • $\begingroup$ @SOJPM: I suspect that the ideas within the paper predated Logjam; however the paper itself is obviously recent (it references a paper published on ePrint in April). $\endgroup$ – poncho Jun 17 '15 at 2:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.