Abstract: A method and apparatus for verifying the identity of an authorized remote user terminal for access to a base computer over a telephone line comprising providing the authorized user terminal with a programmed preselected algorithm, generating a random number at the base computer system to be accessed and transmitting the random number to the remote user terminal, performing the algorithm on the random number at the remote user terminal to calculate a first result, transmitting the first result from the remote user terminal to the base computer system, performing the algorithm on the random number at the base computer system to calculate a second result, comparing the first result and the second result and granting access to the base computer when the first result matches the second result.