Rating:

Using properties of elliptic curve pairings, and considering PiH = G1, we can compute PiC = [t^4 - 10 t^3 + ... + 24]G1 and PiCa = [a t^4 - 10 a t^3 + 35 a t^2 - 50 a t + 24 a]G1 which can be computed from PKC and PKCa respectively.

More details in the full writeup

Original writeup (https://github.com/pwning/public-writeup/tree/master/rwctf2023/crypto_0KPR00F).