ZK/SEC Research notes from zkSecurity
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Variants of KZG

2 parts April 2025 – July 2026 24 min in total Varun Thakore
  1. Part 1

    Variants of KZG: Part I, Univariate

    In this blog post, we dive into the world of polynomial commitment schemes (PCS), which are crucial for constructing most practical SNARKs. We cover the basics of how PCS works, focusing on KZG10, known for its efficiency in proof size and verification time. You'll learn about the essential properties of binding and hiding and explore technical concepts like homomorphism, batching, and unconditionally hiding. We break down various methods to achieve these features, offering insight into how PCS maintains the security and privacy of polynomials in cryptographic systems. Get ready to understand these powerful concepts and their applications in modern cryptography!

  2. Part 2

    Variants of KZG: Part II, Multilinear Commitments with PST

    In this blog post, we extend the ideas behind univariate KZG commitments to multilinear polynomials through the PST commitment scheme. We derive the multilinear quotient identity, explain how PST commits to and opens multilinear polynomials using a specialized multilinear setup and walk through its opening protocol. We conclude by examining the proof size, prover and verifier costs, and the limitations that motivate other multilinear polynomial commitment schemes.

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