# Are the values of Tate and Ate pairing the same?

Assume we have a Baretto Naehrig curve over $GF(p)$ and a field extension $GF(p^{12})$ given by a minimum polynomial. Let $G \in GF(p)$ and $Q \in GF(p^{12})$ from the trace 0 subgroup. Do then the Reduced Tate and Ate pairings produce the same values?

• I found the solution: No, the ate pairing is a power of the Tate pairing. Therefore lets state the question in a diiferent way. Is the ate pairing definition uniquely defined? If not, does there exist some kind of canonical ate pairing? – user27849 Sep 21 '15 at 19:06
• Ah, if you have a solution you can provide the answer. If you have additional questions, like " Is the ate pairing definition uniquely defined? If not, does there exist some kind of canonical ate pairing?" please ask a separate question. Disclaimer: I don't know anything about Tate or Ate pairing, afaik. – Maarten Bodewes Sep 22 '15 at 17:04