Bulletproofs

Cryptography

Cryptography is the science of secure communication and data protection using mathematical techniques. In blockchain, it provides the backbone for verifying transactions, controlling asset access, and ensuring the immutability of the ledger. By using public and private key pairs, hashing functions, and digital signatures, cryptography prevents unauthorized access and tampering. It transforms human-readable data into a secure, encrypted format that only authorized parties can manipulate or verify.

Prover

The participant or software that generates a cryptographic proof showing a statement or computation satisfies specified conditions.

Verifier

The participant or algorithm that checks whether a cryptographic proof is valid.

Zero-Knowledge Proof

A zero-knowledge proof (ZKP) is a cryptographic protocol that allows one party, the prover, to prove to another party, the verifier, that a statement is true without revealing any information beyond the validity of the statement itself. ZKPs provide a mechanism for verifying facts, such as identity, account balances, or transaction validity, while maintaining full user privacy. They are increasingly used in blockchain for scaling solutions (ZK-rollups) and confidential transactions.

Arithmetic Circuit

A mathematical circuit representation of computation using arithmetic constraints for zero-knowledge proof systems.

Circuit

A formal representation of the computation or constraints that a zero-knowledge prover must demonstrate were satisfied.