# Calculating the point on the curve during ECDSA signature verification

• What is your missing point? Is it point addition on the Elliptic Curves or the double-and-add algorithm work? Jan 13, 2021 at 7:38
• Hi new user and welcome. Please make your title as descriptive as possible and try and tag your question the best way you can. ECDSA is not encryption. Jan 13, 2021 at 15:08

To obtain (62, 4) you just add points $$\textbf{but on elliptic curves}$$.

This is different from a "regular" addition, since the result must be a point of the curve (or a point said to be at infinity, I'm not explaining I try to keep things simple) .

Addition is defined and to do so either you use the heavy addition formulas (If you have seen groups theory), either you do as explain in the coindesk article :

let $$P$$ and $$Q$$ be two points on the curve to do $$(P) + (Q)$$ you trace the line passing by both $$(P)$$ and $$(Q)$$.

This line will intersect the curve on a third point, call it $$(R')$$, then $$(P) + (Q) = (-R')$$ and you have your result,

i.e. if $$(R') = (x, y)$$ then $$(-R') = (x, -y)$$. (In the coindesk article $$(-R') = (R)$$)

This is an $$\textbf{incomplete}$$ explanation but you should catch the thing, I didn't discuss the special points (when the last coordinate's member is $$0$$), inflexion points (when $$P = Q = R$$), or why there is another point on both the line and the curve.

If you want to double a point $$(P)$$ you trace the tangent passing by $$(P)$$, and this tangent will pass by a second point on the curve and you take the opposite point.

Personally I never use the explicite formulas (I didn't write them here) , which are too heavy in my opinion, I just do it with the last method.

For the first part you just break $$76G$$ in additions and doubles of $$G$$. Then you replace $$G$$ by its coordinates $$(2, 22)$$ and you just double or add.

For example: $$2.(2, 22) = (2, 22) + (2, 22) = (52, 7)$$ using your curve.

To check your results, or to get it easily, you can use : http://christelbach.com/ECCalculator.aspx an online calculator for elliptical curves.

You just have to set the parameters of your curve ($$mod p = 67$$, $$A = 0$$, $$B = 7$$) and you will get the correct answer (I checked).