# Mike Rosing - Elliptic Curve Cryptography - Basic Math (Highlights)
## Metadata
**Review**:: [readwise.io](https://readwise.io/bookreview/38981894)
**Source**:: #from/readwise #from/reader
**Zettel**:: #zettel/fleeting
**Status**:: #x
**Authors**:: [[Mike Rosing]]
**Full Title**:: Elliptic Curve Cryptography - Basic Math
**Category**:: #articles #readwise/articles
**Category Icon**:: 📰
**URL**:: [www.embeddedrelated.com](https://www.embeddedrelated.com/showarticle/1590.php)
**Host**:: [[www.embeddedrelated.com]]
**Highlighted**:: [[2024-03-25]]
**Created**:: [[2024-03-25]]
## Highlights
- as long as the field characteristic is greater than 3 ([View Highlight](https://read.readwise.io/read/01hsr3gcgnwkqj6eb5b81eb90c)) ^697223247
(**Reference**:: [[Field Characteristic]])
- As I explain [elsewhere](https://hackernoon.com/defense-against-power-analysis-attacks-avoiding-elliptic-curve-side-channel-attacks), for embedded systems we want a value for $\lambda$ which is the same if P and Q are the same point or different points. ([View Highlight](https://read.readwise.io/read/01hsthd1b16ssm4a6zccbdj5mv)) ^697669715
$\lambda = \frac{x_1^2 + x_1x_2 + x_2^2 + a}{y_1 + y_2}$
- The first important concept is that the finite field is defined by some large prime number. So all the formulas listed above are modulo that prime number. The second important concept is that the number of points on an elliptic curve over a finite field is finite. The algebra of the elliptic curve acts just like a modulo addition. For cryptographic usefulness we want the elliptic curve to have a group of points which is a very large prime number. ([View Highlight](https://read.readwise.io/read/01hsthgy6rpysrzb0xjqyqhkny)) ^697669909
They are two different numbers.
- The two numbers will not be the same in a cryptographic setting. I think this is one of the most confusing aspects of elliptic curves over finite fields - the field prime is essential for computing equations and the order of points is essential for security. ([View Highlight](https://read.readwise.io/read/01hsthm42et1mgq4nberxm3c5h)) ^697670872