Let $E(p)$ be a Barretto-Naehrig elliptic curve with r-torsion and embedding degree 12 and $E'$ a sextic twist with homomorphism $\psi$. How to show, that

  • $E'$ has a unique r-torsion group
  • $\psi$ maps the r-torsion of $E'$ to the Trace-0 subgroup of $E(p^{12})$
  • 2
    $\begingroup$ @cryptostase Why should we delete the question? I'm no expert in that area, but it looks like a valid question to me. $\endgroup$ Sep 27, 2015 at 10:03
  • 3
    $\begingroup$ Since you found the answer yourself, you could post an answer referencing the paper and preferably giving a short summary of the proof idea. $\endgroup$ Sep 27, 2015 at 10:05
  • $\begingroup$ The proof can be found in the paper: The Eta Pairing Revisited, section 5 F. Hess, N. Smart, and Frederik Vercauteren $\endgroup$
    – user28038
    Sep 30, 2015 at 16:36


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