Explain why a message hash is used for digital signatures rather than just using the private key to encrypt the message?
Try an answer before revealing the guidance below.
Key Concepts
- Public-key operation cost
- Message digest
- Fixed-length hash
- Signing
Answer Approach
- Compare the cost of a public-key operation on a long message with one on a short digest.
- Recall the size and properties of a hash output.
- Explain why signing the digest still binds the signature to the whole message.
Full Answer
Answer status: Verified against study notes. Revision notes, not an official marking scheme.
Public-key (private-key) operations are computationally expensive, so applying them to a long message is slow. A cryptographic hash produces a short fixed-length digest of the whole message; signing only the digest is much cheaper. Because it is infeasible to find another message with the same hash, the signed digest still authenticates the sender and protects the integrity of the entire message.
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