Wikipedia:Reference desk/Archives/Mathematics/2024 September 26

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September 26

Given the optimal ate pairing e(A,B)=y is to possible to determine I and J such as e(I,J)=2y or even e(I,J)=3y?

Simple question : let’s say I have a pairing friendly curve having a very large trace, and that I have a pairing with points A∈$G_{1}$ and B∈$G_{2}$ such as the optimal ate pairing e(A,B)=y, then is it possible to fully determine 2 point I and J such as e(I,J) equals a target multiple of the finite’s field element y ?

Or does it requires full pairing or full generalized Miller’s inversion and thus would be impossible in practice on a curve like bn254 ? 2A01:E0A:401:A7C0:9CB:33F3:E8EB:8A5D (talk) 15:51, 26 September 2024 (UTC)