Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have the elliptic curve equation $E(\mathbb F_{5^2}): y^2=x^3+10x+17$, and I have that the points $(3,7)$ and $(8,3)$ belong to $E$. According to the addition law, the slope $\lambda=(y_2-y_1)/(x_2-x_1)$ exists when the $\gcd(x_2-x_1,p)=1$, in this case is not equal to $1$. What should I do? Should I say, in this case, $(3,7)+(8,3)= \infty$? I appreciate the help.

share|improve this question
4  
Since $8\equiv 3\pmod{5}$, the points have the same $x$-coordinate; you have a "vertical" line and the third point of intersection with the curve is the point at infinity. –  Arturo Magidin May 12 '12 at 2:58
    
Thank you a lot Arturo. –  megjoh May 12 '12 at 3:19
add comment

1 Answer

up vote 3 down vote accepted

As explained by Arturo, in the field $F_{25}$ we have $(3,7)=(3,2)$ and $(8,3)=(3,3)=(3,-2)$. Therefore the two points that you want to add are negatives of each other (on the same vertical line), so their sum is the point at infinity.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.