A session aimed at exploring the intuition behind proof systems, focusing on the role of polynomials in zero-knowledge proofs (ZKPs). After a brief recap of a previous session, we delve into why polynomials, such as those used in fast Fourier transforms and in proof systems like Starks and Snarks, are crucial to succinctly proving computational statements.
We focus on three key properties of polynomials that make them valuable for proof systems: error correction, efficient batch zero testing, and their multiplication property, which collectively enable scalable, secure, and efficient proofs of computational integrity.
The talk includes several examples and participant questions about mathematical proofs, constraints, and the mapping of computational statements to polynomials.
