Polynomials 101

You can't understand ZKPs without understanding polynomials

You know how data structures and algorithms are pretty much Computer Science 101? Theyโ€™re fundamental to just about everything in the field. Well, polynomials are just as fundamental to zero knowledge proofs (ZKPs).

In case you need a primer, ZKPs let us prove a fact without revealing the fact. You can read my ZKP 101 post for all the details. But before we get into level 201, thereโ€™s a bit of math and cryptography we should cover.

In this blog post, weโ€™ll focus on the math that makes ZKPs possible: Polynomials. Why? Because theyโ€™re really helpful in three major ways:

  • They can encode an unbounded amount of data
  • They can encode relationships between data
  • They let us efficiently check whether two pieces of data are the same