Almost all elliptic curve operations are computed by the precompute method. There are two cases for fixed point and non-fixed point(q4 in groth16). I think both cases are implemented by putting the coefficients of the precomputed line on the witness (hint). It gives the verifier an opportunity to bypass the chunk.

• For fixed point: The precomputed coefficients should be put in the script.
• For non-fixed point: The precomputed coefficients should be committed by bit commitment.