Which method requires a client to authenticate and has the capability to function without encryption?

WEP (Wired Equivalent Privacy) inherently uses encryption as part of its security mechanism, although it is severely flawed.

PSK (Pre-Shared Key), used in WPA/WPA2/WPA3 Personal, requires a key for both authentication and encrypts all traffic.

"Open" authentication in wireless networks means that clients are allowed to associate with the access point without requiring any pre-shared key or credentials. While a client still "authenticates" in the sense of establishing an association, this method explicitly allows for data transfer without encryption (or with optional encryption, but not mandatory as part of the "open" authentication type itself).

WebAuth (Web Authentication) typically redirects clients to a web portal for authentication and can be combined with or without encryption, but the method itself is about the web-based authentication, not its fundamental ability to function without encryption while still requiring client authentication in the sense of associating.