# Why are supersingular elliptic curves useful for cryptography?

I don't know very much about cryptography and would like to learn more. I know the basics of RSA alogrithm and how elliptic curves over finite fields can be used to do something similar. But I would like to know why supersingular elliptic curves are particularly interesting for this purpose. Thank you!

• Why the downvote? I know this question is slightly broader than usual. But I'll be interested to read a good answer. – Simon S Oct 9 '15 at 1:01
• Generally, they are weaker than other elliptic curves, thanks to Menezes, Okamoto, and Vanstone (MOV) algorithm. Having embedding degree $k \leq 6$, solving DLP in them is equivalent to DLP in finite field $F^*_{p^k}$, which is easy using index calculus algorithms at such low values of $k$. – Weaam Oct 9 '15 at 1:47
• Thank you for the answers. You will have to excuse me for my ignorance. But what is DLP? Where can I learn more about it? Thanks. – user119481 Oct 9 '15 at 15:02