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?

  • 4
    $\begingroup$ How do you compute the "division"? $\endgroup$ – DrLecter May 29 '15 at 20:46
  • $\begingroup$ Thanks.There was one error in the "division". Now i've calculate the inverse in the correct way using the extended euclidean algorithm. $\endgroup$ – NxA May 29 '15 at 21:33
  • $\begingroup$ Thats a good idea ;) $\endgroup$ – DrLecter May 29 '15 at 21:34

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