A hand-held token can be operated to generate an acoustic signal representing the digital signature generated by a private key of a public key/private key pair. Verifiers that might be located at, e.g., buildings, in vehicles, at bank ATMs, etc. receive the signal and retrieve the corresponding public key to selectively grant access authorization to components served by the verifiers. Methods and systems permit adding and removing a token from the access list of a verifier. Other methods and systems enable the token to be used with several verifiers that are nearby each other, such as might be the case with multiple vehicles owned by the same user and parked nearby each other, without more than one verifier being operated to grant access.