What is the time requirement for pairing computation and modular exponentiation? I want to design a cryptographic protocol for encrypted search without pairing. I have seen some papers for protocols without pairing. How would I compare pairing computation and modular operations?
I had to do this comparison one year ago in an article, to justify whether it was desirable to avoid pairings in some protocols. Roughly, if you take the (arguably) most efficient up-to-date curves with and without pairing, counting as 1 the cost of a modular exponentiation in the curve without pairing, denoting $\mathbb{G}_1$ and $\mathbb{G}_2$ the (asymmetric) curves with the pairing,


the cost of an exponentiation in $\mathbb{G}_1$ is 3
the cost of an exponentiation in $\mathbb{G}_2$ is 6
the cost of a pairing is 8


For the comparison, we used Bernstein's Curve25519 for the curve without pairing, and  Barreto-Naehrig curves for the curve with pairing (using the implementation of "High-speed software implementation of the optimal Ate pairing over Barreto-Naehrig curves"). Not that the cost of a pairing is not the only thing that matters, as in the best curves without pairing, there are more efficients algorithms for exponentiation than in the best curves with pairings.

Source: https://eprint.iacr.org/2015/246.pdf