# Security of ECC over finite fields of characteristic $p\approx2^{50\pm10}$?

What's the security of Elliptic Curve Cryptography over finite fields of word-sized characteristic $$p\approx2^{50\pm10}$$? We are talking about $$\Bbb F_q$$ where $$q=p^k$$ for some suitable $$k$$.

Furthermore, I would like to know about the possibility of pairings over fields of such word-sized characteristics.

References appreciated.

• You might want to take a look at this recent paper which proposes a curve with over the field $\mathbf F_q$ with $q=9767^{19}$. Section 2.2 talks a little about the extension degree. – user69015 Feb 21 '20 at 12:26
• Thanks, this is awesome! However, would you happen to have any reference for characteristic closer to the values I mentioned? Furthermore, I would like some references on pairings over fields of word-sized characteristics too. – Rascalniikov Feb 21 '20 at 18:35