Passwordless remote access to a restricted shell

Passwordless remote access to a restricted shell

For, um, historic reasons, we have a C program for HPUX which accepts
telnet connections, and runs a home-grown REPL that restricts the commands
available.
Rather than port this code to Linux, I'd like to get effectively the same
functionality using standard tools.
Simple, you say - just make a user with bash --restricted as its default
shell.
However we want the restricted shell to have an effective userid of
"user1", and for it to be accessible without a password. Meanwhile we'd
like "user1" to behave normally when accessed in the conventional manner.
I think it would be OK -- desirable even -- if SSH was the comms protocol
instead of telnet.
Any ideas?