What are the differences between key, key_hash, address, contract and signature in Michelson?

Question

There is a related question, but the differences are still not clear. These five types are mentioned in the Michelson whitedoc with the following definitions:

• address: An untyped address (implicit account or smart contract).
• contract 'param: A contract, with the type of its code, contract unit for implicit accounts.
• key: A public cryptographic key.
• key_hash: The hash of a public cryptographic key.

• signature: A cryptographic signature.

  1. What is the difference between key_hash and address? It seems like for both I can do PUSH address "tz1..." and PUSH key_hash "tz1..." using the same string literal. I remember seeing something about reveal. What does reveal mean?

  2. Why can I convert between address and contract. But not between address and key_hash?

  3. What is the difference between key and key_hash? When would I have a key, but not a key_hash?

  4. What is a cryptographic signature and what are some of the use cases in Michelson?

  5. Any other important details about these data types.

Answer 1

1. key_hash is blake2b hash of a public key, in the base58 encoded form it can start only with tz, but address is more general, it can also hold KT accounts;
2. There are no instructions for that, probably because it's a rare and arguable case; EDIT: as pointed out by Raphaël, you can convert key_hash to contract and then to address using IMPLICIT_ACCOUNT ; ADDRESS
3. As was mentioned, key_hash is blake2b hash of key. You would need a key for checking a signature for instance;
4. Allow me to link wikipedia https://ru.wikipedia.org/wiki/EdDSA. A bright example is a multisig contract;
5. Check out the new Michelson documentation https://michelson.nomadic-labs.com/

To sum up:

• key represents a public key (a point on the elliptic curve)
• key_hash is blake2b hash of key
• address is a general representation of Tezos accounts, including both - tz and KT addresses
• signature is a result of signing a message with a private key using the elliptic curve digital signature scheme.

Answer 2

Why can I convert between address and contract. But not between address and key_hash?

There is the (IMPLICIT_ACCOUNT) instruction to go from key_hash to address. For the other direction, there was (a feature request) but it was closed because no use case has been presented to motivate it.