ZKP Lecture 6: Polynomial Commitments based on Pairing and Discrete Logarithm (Part 1)

In this lecture, Yupeng Zhang introduces polynomial commitments, essential for building efficient SNARK systems, and outlines their use in verifying polynomial evaluations. The lecture is structured into three parts: a background on groups, discrete logarithms, and bilinear pairings; the construction of KZG polynomial commitments using bilinear pairing; and polynomial commitment schemes without trusted setup, like Bulletproofs, and schemes based on discrete logarithms, such as HIREX, DORI, and DARK. The discussion includes formal definitions of groups, generators, the discrete logarithm problem, the Diffie-Hellman assumption, and bilinear pairing, illustrated with examples like integers under addition and BLS signatures.