3
$\begingroup$

I was reading about elliptic curves from this PDF. Page 44 defines Frobenius map. It defines the frobenius map as $f(x,y) = (x^p, y^p) \bmod p$. Isn't it just an identity map? What's the use of this map in elliptic curves?

$\endgroup$
  • $\begingroup$ For future reference: In SO, cross-posting on two different sites is not a good etiquette. Select one, and give the community a chance to answer. $\endgroup$ – kelalaka Dec 2 '18 at 11:11
-1
$\begingroup$

Hint: $f$ is defined on $E(\overline{\mathbb F_p})$, the curve over the entire algebraic closure $\overline{\mathbb F_p}$ of $\mathbb F_p$. Under what circumstances is $x \mapsto x^p$ the identity on a field of characteristic $p$?

$\endgroup$

Your Answer

By clicking "Post Your Answer", you agree to our terms of service, privacy policy and cookie policy

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