Registered in 2007 for "encrypted admin requests" — a vendor administration channel, not a public protocol.
IANA carries two names for 1138: the original encrypted_admin and encrypted-admin, which IANA assigned later as the well-formed replacement, both described as "encrypted admin requests". There is no published protocol, so the registration tells you only that the vendor intended an administrative channel with transport encryption. Nmap sees it open on a negligible fraction of hosts.
Do not expose
Administration planes do not belong on the internet even when they are encrypted; put it behind a VPN and identify the application while you are there.
$ sudo lsof -nP -iTCP:1138 -sTCP:LISTENSeen this on your network? Beige Box scans your Wi-Fi and shows every open port on every device — and its Ports tool links straight back here.
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Corrections or a missing port? Reply @rimrocksystems.