An authenticatable device according to one embodiment includes a reconfigurable physical unclonable function (‘RPUF’) used with one parameter to recover sensitive values (e.g., a secret or a share of a secret) and a different parameter to encode and store values (e.g., challenge-helper pairs) correlated to the sensitive values. In another embodiment, a pair of RPUFs is used instead of a single PUF, with one RPUF used to recover sensitive values and the other RPUF used to encode and store correlated values. In still another embodiment, the desired expiration of values can be enforced by employing redundant RPUFs; when the device is powered on, one (or more than one, but less than all) of the RPUFs is selected and transitioned to a new configuration, invalidating any correlated values previously constructed using the old configuration, and the RPUF that was not reconfigured is used to recover the sensitive value(s) using the remaining correlated value(s).