Is there a common terminology to designate parties in authentication protocols?
For example, we typically use prover and verifier to designate parties with zero-knowledge proofs.
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Yes, it seems so: User and Principal/Party
In Protocols For Authentication And Key Establishment, published this year and written by Colin Boyd, Anish Mathuria, and Douglas Stebila, it says this in Section 1.2.2:
In the following, we use the term user to mean an entity who will use the session key for subsequent communication. We also use the term principal or party to mean an entity who will engage in the protocol. For example, in a protocol which uses a key server (often called an authentication server) there are users who will obtain the session key while the server is a principal but not a user.
These terms occur throughout the the international standard ISO/IEC documentation. Just one example is ISO/IEC 11770-2 Server-Based Protocols, in the section about key establishment mechanisms.