I have an elliptic curve $y^2 = x^3 + 2x + 2$ over $Z_{17}$. It has order $19$.
I've been given the equation $6\cdot(5, 1) + 6\cdot(0,6)$ and the answer as $(7, 11)$ and I'm unsure how to derive that answer.
I have $6\cdot(5, 1) = (16,13)$ and $6\cdot(0,6)=(0, 11)$ however when I use point addition to add them together I get $(16,13)+(0, 11)=(14,11)$ which isn't even a point on the curve…
Could someone help me identify where and why I've gone wrong?
For further information here's each of the points:
And here's the curve plotted out:
Best Answer
Hints:
Maybe if you show how you did that calculation, I can spot the issue.
Once you fix that, I verified the author's result is correct, that is:
$$(16,13)+(3,1) = (7,11)$$
Update
Here are some additional hints to help you with intermediate calculations: