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I came across a number of somewhat similar solutions, which are based on the knowledge factor related to a symmetric key in particular:

  • If a party was able to generate correct message authentication code, be it in form of HMAC...
  • If a party was able to encrypt a piece of plaintext which decrypts to a message of expected structure...

... it means they are in posession of a symmetric key K, which in turn implies that this must be the party XYZ, unless the key has been compromised.

What is the common name for such authentication schemes?

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The generic term is proof of possession.

It's most commonly used for a private key, where a prover needs to convince a verifier that the prover knows a certain private key. The most natural way to do this is for the verifier to send a challenge to the prover, and the prover signs this challenge with the private key. The verifier uses the public key to verify the signature. Only a party who knows the private key can produce a valid signature. The challenge should be unique, because otherwise an adversary who intercepted a response could replay the signed message without knowing the private key. It's also possible to generate a proof of possession by having the verifier send a challenge encrypted with the public key and the prover decrypt it and send it back.

From RFC 2797 — Certificate Management Messages over CMS:

"POP" is an acronym for "Proof of Possession". POP refers to a value that can be used to prove that the private key corresponding to a public key is in the possession and can be used by an end-entity.

More generally, the term can be used with symmetric keys as well. For example JWT defines a proof of possession protocol for both asymmetric and symmetric keys.

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  • I have found a definition which I like most: "Proof-of-possession is a means of proving that a party sending a message is in possession of a particular cryptographic key. This is used as a proof that the correct party is sending the message, under the assumption that only that sender has possession the key." Source: The Increasing Importance of Proof-of-Possession to the Web by Michael B. Jones
    – user237016
    Commented Jan 16, 2021 at 15:57
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This is known as a Zero-Knowledge Proof.

From Wikipedia:

In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that they know a value x, without conveying any information apart from the fact that they know the value x.

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  • Thanks for pointing me at ZKP. However, what is interesting to me, is that despite ZKP-based authentication being used in some shape or form quite often, the community refrains from giving it a common name.
    – user237016
    Commented Nov 1, 2020 at 9:38
  • No, the examples in the question are not zero-knowledge. Zero-knowledge doesn't just mean that the whole value of x isn't disclosed, it's a much stronger condition.
    – Gilles 'SO- stop being evil'
    Commented Nov 1, 2020 at 11:36

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