0
$\begingroup$

According to the following paper, Miller inversion is easy and this is exponentiation inversion which hard. Those algorithms are written for fapi‒2 inversion, meaning finding $\mathbb G_1$.

But the problem is as the inversion algorithms don’t seem to take a $\mathbb G_2$ parameter, which is the $\mathbb G_2$ point used for the pairing ? I’m failing to understand this…

Improve this question
$\endgroup$
7
  • $\begingroup$ As a side quetion, would this inversion algorithm work in the case of pairings without final exponentiation like the ate or optimal ate pairing ? $\endgroup$ Commented Jul 9 at 11:50
  • $\begingroup$ Is not the point denoted $A$ the parameter in question? $\endgroup$ Commented Jul 9 at 12:29
  • $\begingroup$ @DanielS in such case, $F_r$ is the finite field element and $d$ is the embedding degree ? $\endgroup$ Commented Jul 9 at 12:51
  • $\begingroup$ AIUI he is using $v$ as the target finite field value and $d$ as the multiplicity of the Miller function (i.e. we're finding $h_{d,A}(Q)=v$ where $h_{d,A}$ is a function with divisor $d[A]-[dA]-(d-1)[\mathcal O]$ $\endgroup$ Commented Jul 9 at 13:00
  • $\begingroup$ @DanielS so $d$ is a specific parameter which is dependent of the pairing being used ? $\endgroup$ Commented Jul 9 at 13:06

0

Reset to default

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.