Hello! , this will be the sequel of: _Alright! , so we’ve talked about D-H and RSA , and those we’re sort of easy to follow , you didn’t need to know a lot…_hackernoon.com Elliptic Curve Crypto , The Basics Today let’s try to tackle as in addition and multiplication , keep in mind that these are “invented” operations , the fact that it is called addition it’s a mere coincidence , They should’ve been called something different but such is life. operations I will split this into a few concepts and then lately write about some of the exceptions. The Slope The Slope is calculated between two , and it’s got it’s own formulas for it , depending on the location of and (two points on the curve). points P Q So let’s see these formulas: Slope is also called (lambda) , but i think slope makes more sense to me . λ The Slope is calculated differently if = , let’s look at that example: P Q Alright so that’s pretty simple , or are crucial to then do point doubling and point addition. S λ , Point Addition: So this is one of the most basic elliptic curve operations , and remember that when we say addition about addition as , it’s a different kind of operation that follows and algorithm as well. we’re not talking 1+1 So let’s look at the formula or mathematical identity , it goes like: would be the third point in question , the result of “adding” and R P Q: RX = S ** 2 - QX - PXRY = -( QY + S * ( RX - QX)) If you’re paying attention , you noticed in the graph above that the resultant of the addition it’s called and that is cause , the result we want , is the reflection over the axis of in such way: -R , R X -R , Below is a small code sample of how this should work : That’s all for today , there’s still one very important operation called point doubling that we need to look at , probably in the next article. There has been a few about , situations where a line would cross two points but not a third one , defeating the rule we spoke in the first article: questions exceptions You can see that neither of these possibilities will cross a third point , we will cover all these in the next article , but if you can’t wait check “ ” in wikipedia :) the group law Thanks a lot for the tons of reads this is getting and also the comments!
