In this post, we recall the notion of a polynomial and explain the concept of "blind evaluation" of a polynomial, and how it is implemented using Homomorphic Hiding (HH). (See
part 1 for an explanation of HH). In future posts, we will see that blind evaluation is a central tool in SNARK constructions.
Subsequent posts will go into more detail on how blind evaluation is used in SNARKs. The rough intuition is that the verifier has a "correct" polynomial in mind and wishes to check that the prover knows it. Making the prover blindly evaluate their polynomial at a random point not known to them ensures the prover will give the wrong answer with high probability if their polynomial is not the correct one. This, in turn, relies on the Schwartz-Zippel Lemma, which states that "different polynomials are different at most points".