A hand-held token can be operated to generate an acoustic or other wireless signal representing a digital signature produced from the private key of a public key/private key pair, with the public key being confidential in that it is known only to authorized entities, such as bank computers. The signal from the token can be received by, e.g., a receiver at a bank ATM that also requires a PIN for account access. The user enters the PIN into the ATM, and the ATM encrypts the signal from the token with the PIN and sends it on to the bank computer over a link that need not be secure, since even if the PIN is guessed there is no way to verify that it is the correct PIN without also knowing the confidential public key held by the bank computer.