arno/bitcoinbook
1
0
Fork 0
mirror of https://github.com/bitcoinbook/bitcoinbook synced 2024-11-22 16:18:11 +00:00
Code Issues Releases Wiki Activity

Made changes to ch04.asciidoc

Browse Source
This commit is contained in:
myarbrough@oreilly.com 2014-11-18 07:13:15 -08:00
parent 53e09dea89
commit 266bcb0d44
1 changed files with 1 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
ch04.asciidoc
View File

@ -157,7 +157,7 @@ There is also((("+ operator")))((("elliptic curve cryptography","addition operat
Geometrically, this third point P~3~ is calculated by drawing a line between P~1~ and P~2~. This line will intersect the elliptic curve in exactly one additional place. Call this point P~3~' = (x, y). Then reflect in the x-axis to get P~3~ = (x, –y). Geometrically, this third point P~3~ is calculated by drawing a line between P~1~ and P~2~. This line will intersect the elliptic curve in exactly one additional place. Call this point P~3~' = (x, y). Then reflect in the x-axis to get P~3~ = (x, –y).
There are a couple of special cases which explain the need for the "point at infinity." There are a couple of special cases that explain the need for the "point at infinity."
If P~1~ and P~2~ are the same point, the line "between" P~1~ and P~2~ should extend to be the tangent on the curve at this point P~1~. This tangent will intersect the curve in exactly one new point. You can use techniques from calculus to determine the slope of the tangent line. These techniques curiously work even though we are restricting our interest to points on the curve with two integer coordinates! If P~1~ and P~2~ are the same point, the line "between" P~1~ and P~2~ should extend to be the tangent on the curve at this point P~1~. This tangent will intersect the curve in exactly one new point. You can use techniques from calculus to determine the slope of the tangent line. These techniques curiously work even though we are restricting our interest to points on the curve with two integer coordinates!