A method and an apparatus are disclosed that enable an enhanced, interactive voice response (IVR) system to securely authenticate a user at a telecommunications terminal, without some of the disadvantages in the prior art. In particular, after the user at the telecommunications terminal requests access to a resource, the controlling IVR system of the illustrative embodiment issues a random challenge sequence to the user, along with interspersed "camouflage elements" and one or more directions as to how to respond. The user is then free to speak a returned sequence that answers the combined challenge sequence and interspersed camouflage elements; as a result, an eavesdropper overhearing the user hears what sounds like a random number or string. In short, the technique of the illustrative embodiment uses a challenge-response exchange of a substitution cipher interspersed with camouflage elements.