Examines the use of pseudorandom numbers as passwords in databank systems that have many inquiry terminals. It shows that various logistically attractive periodic password generation and distribution systems are vulnerable to simple number-theoretic analyses that permit deducing of the passwords of all the inquiry stations. New generation and distribution strategies of the mixed congruential type to reduce such vulnerabilities are proposed and analyzed. It is shown that there is considerably more protection against cracking if the assignment order of passwords to stations is permuted each period. 24 pp. Ref.