# Mike Rosing - Elliptic Curve Cryptography - Security Considerations (Highlights)  ## Metadata **Review**:: [readwise.io](https://readwise.io/bookreview/39010427) **Source**:: #from/readwise #from/reader **Zettel**:: #zettel/fleeting **Status**:: #x **Authors**:: [[Mike Rosing]] **Full Title**:: Elliptic Curve Cryptography - Security Considerations **Category**:: #articles #readwise/articles **Category Icon**:: 📰 **URL**:: [www.embeddedrelated.com](https://www.embeddedrelated.com/showarticle/1591.php) **Host**:: [[www.embeddedrelated.com]] **Highlighted**:: [[2024-03-25]] **Created**:: [[2024-03-25]] ## 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