As described in this paper(section 3) to implement pairing on Barreto-Naehrig curves. The prime in their case is $p=82434016654300679721217353503190038836571781811386228921167322412819029493183$ and to implement the pairing it is important to find an irreducible polynomial of the form $ W^6-\xi$ in $\mathbb{F}_{P^{2}}$ where $\xi \in \mathbb{F}_{P^{2}}$. However, I can not understand how to find such $\xi$. I have written some scripts in Magma to find such $\xi$ but not successful.Also in that paper they have mentioned that there are some properties of the prime $p$ which is useful in finding such $\xi$ but I can't understand how to use them? Can someone please tell me how to find such irreducible polynomials?
2026-03-31 07:07:12.1774940832
How to find irreducible polynomial for Barreto-Naehrig curves?
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