What Is the Difference between an On-Chain and an Off-Chain Cryptographic Proof?

An on-chain cryptographic proof is a signature or mathematical proof that is verified directly by the smart contract on the blockchain. This verification consumes gas but provides the highest level of security.

An off-chain cryptographic proof is verified by a separate system or node off the blockchain. While faster and cheaper, it requires the consumer to trust the off-chain verifier.

Decentralized oracles typically generate the proof off-chain but verify the final aggregated signature on-chain.

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