There's the well-known question on whether to sign or encrypt first. However, if instead a message is to be ring-signed such that either recipient could be the actual signer, is there any scheme that combines signing and encrypting in one "atomic" step?
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Yes, like there are conventional signcryption schemes combining digital signatures with encryption into a single primitive, there are also ring signcryption schemes that realize the same for ring signatures and encryption. Look for instance here or just ask Google scholar.