RSA key check failed for file, signature verification failed
While checking your science applications and other files BOINC downloaded from a project's server, it found that the signature file wildly differed from the public key that you got appointed. This can happen when a project makes all new applications and signs them with a whole new key, instead of the old one they started the project with. It can of course also happen when someone nefarious tries to run dubious applications made to look like that of the project.
The quick and dirty solution is to remove the project and adding it again. If you immediately get the error again, suspend this project and try to get into contact with its administrators to tell them about the problem.