Polynomial commitments

Understanding Polynomial Commitments

A polynomial commitment scheme allows a prover to commit to a polynomial, reveal specific evaluations of it later, but not reveal the entire polynomial. The commitments are both hiding and binding.

A polynomial commitment scheme allows a prover to commit to a polynomial, reveal specific evaluations of it later, but not reveal the entire polynomial. The commitments are both hiding and binding.

Applications of Polynomial Commitments

Polynomial commitments have a variety of applications in cryptography. For instance, they are used in zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge), a form of zero-knowledge proof where one can prove possession of certain information without revealing that information and without any interaction between the prover and verifier. They are also used in vector commitments, a kind of commitment scheme where one can commit to a vector of values and then open the commitment at chosen positions.

Polynomial commitments are used in various cryptographic protocols, including zk-SNARKs and vector commitments.

Benefits and Considerations

Polynomial commitments offer numerous benefits, including compactness and efficiency. They allow for efficient verification and short proofs, which are valuable properties in many cryptographic systems. However, like any cryptographic tool, they require careful implementation and usage to maintain their security properties.

Polynomial commitments offer benefits such as compactness, efficiency, and short proofs. However, they require careful implementation to maintain their security properties.