Multi-Polynomial Commitment Scheme

The KZG commitment scheme is as follows:



Verification is done with the following equality:

Note that KZG enjoys the homomorphic property, which means that if ΞΌ1 and ΞΌ2 represent commitments to polynomials 𝑓1 and 𝑓2 respectively, then the sum of ΞΌ1 and ΞΌ2 is a commitment to their sum of polynomials 𝑓1 + 𝑓2. This homomorphic property enables an optimization when verifying multiple commitments ΞΌ1, . . . , ΞΌπ‘˜ that are claimed to evaluate to values 𝑣1, . . . , π‘£π‘˜ at a shared point 𝑧 ∈ ℀𝑝.

Last updated