Commitments Schemes in Cryptography

Commitment schemes are fundamental cryptographic protocols that allow one party(the committer) to commit to a value while keeping it hidden from another party(the receiver) until the commitment is revealed. These schemes provide a way for the committer to ensure that the value cannot be altered after it has been committed, thus ensuring both secrecy and integrity.

Key properties

  • Hiding: The commitment should not reveal any information about the committed value. This means that the receiver cannot determine the value until the committer decides to reveal it.
  • Binding: Once the committer has made a commitment, they cannot change the committed value. This encures that the committer cannot later claim to have committed to a different value.

These properties make commitment schemes useful in various cryptographic applications, including secure voting, digital signatures, and zero-knowledge proofs.

Applications

  • Secure Voting: Voters can commit to their votes and later reveal them, ensuring privacy and preventing vote manipulation.

  • Digital Signatures: Commitment schemes are often used in the generation of digital signatures, where a message is committed to before being signed.

  • Zero-Knowledge Proofs: They play a critical role in zero-knowledge proofs, where one party can prove knowledge of a value without revealing the value itself.