Bilinear Pairing Property of Commitments

Bilinear pairing combines two elements from different groups and returns a result in a third group. Specifically, let be three cyclic groups of prime order p, and let g be a generator of A bilinear pairing is a map e: that satisfies the following properties:

Pairings are also used in zkSNARKs primarily for their ability to enhance homomorphic commitments to make our homomorphic commitments even more powerful, enabling us to perform a range of operations:

$$Com(f(x)) = Com(t(x)) Com(h(x)) = Com(t(x) h(x))$$