Digital Signature or MAC Yielding Non-Binary Verification Predicate

Cryptography Asked on December 24, 2021

Is there a digital signature or MAC scheme in which, the verification algorithm returns not ${text{Valid},text{Invalid}}$, but a discrete (finite or infinite) set of result such as ${text{Valid-for-A}, text{Valid-for-B}, text{Valid-for-C}, text{Invalid-for-All}}$?

This is a curiosity question. There is no limit on the nature of the scheme, it can be symmetric or asymmetric, classical, or post-quantum.


To explain why could potentially be "Valid-for-{A,B,C}":

  1. In PKC there could be 3 (or any number of) private keys derived from a master private key (possibly using some form of key-escrow), that can be identified and verified by the "master" public key. An application of such scheme could be "bandwidth-efficient group member authentication".

  2. In symmetric-key cryptography, it could be an multi-party broadcast domain authenticated encryption, in which ciphertext verification don’t require computing the tag with each of the peers’ key – the recipiant instead somehow use the shared key to "decrypt" or "derive" the peer’s key. Same application as above.

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