Provided are a computer program product, method and system for dynamically providing algorithm-based password/challenge authentication. A page is generated including selectable conversion operators to enable generation of an algorithm that applies at least one selected conversion operator of the selectable conversion operators on a string to generate a password. A created algorithm created using the at least one selected conversion operator in the page is received. The created algorithm is associated with a username for use in authenticating access by a presenter of the username to a computer service.