# Mike Rosing - Elliptic Curve Cryptography - Security Considerations (Highlights)  ## Highlights - Over a finite field when we have $y= g^x \mod{p}$ with y and g known, finding x is called the Discrete Log Problem. ([View Highlight](https://read.readwise.io/read/01hsthqk4s1za3kh1tn67n2w6b)) ^697671003 - [For elliptic curve algebra](https://www.embeddedrelated.com/showarticle/1590.php) over a finite field the equation $Y=xG$ with known points Y and G, finding x is called the Elliptic Curve Discrete Log Problem (ECDLP). This is really hard to do with the best algorithms solving for x being proportional to the $\sqrt r$, where r is the order of the point G. ([View Highlight](https://read.readwise.io/read/01hstjqdz2nmfyrsrhgwqxshaj)) ^697674670 - The embedding degree is the smallest value of k for an elliptic curve over $F_{q^k}$ that has the same very large prime factor. ([View Highlight](https://read.readwise.io/read/01hstjwz115sn3jh7f3vntjhea)) ^697675168 - However, for algorithms which use the pairing of elliptic curve points we want small values of k such as those listed in the above table. ([View Highlight](https://read.readwise.io/read/01hstjzey9scdy92vsmwjtt2c6)) ^697676692