Digital signatures
Signing and verifying: hash, then transform the digest with the private key, verify with the public key; what a signature guarantees and what it does not; RSA signing on small numbers; signing is not encrypting.
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Digital signature: what is it?
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A value computed from a message and the signer's private key, which anyone can check with the matching public key.
It depends on the message: copied onto another message, it no longer verifies. Only the holder of the private key can produce it.
Alice signs a message and sends it with her signature. An attacker changes one letter of the message without touching the signature. What does verification give on Bob's side?
- It fails: the digests differ
- It succeeds: the signature did not change
- It succeeds: Alice's key is still valid
- Bob recovers the original message
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It fails: the digests differ
Bob hashes the received message and gets a digest different from the one the public key extracts from the signature. A signature fixes nothing: it detects.
To sign, the message is first …, then the digest is transformed with the signer's … key.
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To sign, the message is first hashed, then the digest is transformed with the signer's private key.
Hashing first avoids running an expensive calculation on a long message, and the signature keeps the same size whatever the message.
Non-repudiation: what is it?
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A signer's inability to deny having signed, since only the signer holds the private key.
An HMAC does not give it: the key is shared, so either party could have produced the code. An asymmetric signature does.