I have this curve in $E(\mathbb{F}_{131})$: $$Y^2 = X^3 + X + 2$$

I want calculate the sum $P + Q$ considering that $$P= (5,1) \quad Q = (60, 49)$$

For calculating the result I use these formulas:

\begin{align} x_r &= \left(\frac{y_2-y_1}{x_2-x_1}\right)^2 - x_1 - x_2\\ y_r &= -y_1 + \frac{y_2-y_1}{x_2-x_1}(x_1 - x_r) \end{align}

I need to obtain as result of $P + Q = (127 , 14)$ but something that I do is wrong. Can someone show me how I can calculate this sum?

• How do you compute the "division"? – DrLecter May 29 '15 at 20:46
• Thanks.There was one error in the "division". Now i've calculate the inverse in the correct way using the extended euclidean algorithm. – NxA May 29 '15 at 21:33
• Thats a good idea ;) – DrLecter May 29 '15 at 21:34