SSH Login Without a Password

I have in the past used a public key authentication without a password to log into a Mac on our local network for a scheduled backup from a Linux machine. The Mac was retired and we got a new Mac Mini (M1, 2020) with Mac OS 11, that I wanted to run the same backup, but I cannot get it to work.

It's an easy thing to do on most Unix system, and as I've said, I have it running on the old machine, which was running 10.13. I tried adding the line "RSAAuthentication yes" to the /etc/sshd_config, which someone suggested but no difference. Permissions on all the files are the same as the old machine. No good.

I've searched for suggestions and/or explanations, but most comments and howtos are quite old.

Does anyone do this on OS 11? Is the change a bug or a security measure?

Thanks for any help.