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Biometric characteristics cannot be changed; therefore, the loss of privacy is permanent if they are ever compromised. This paper presents a two-factor cancelable formulation, where the biometric data are distorted in a revocable but nonreversible manner by first transforming the raw biometric data into a fixed-length feature vector and then projecting the feature vector onto a sequence of random subspaces that were derived from a user-specific pseudorandom number (PRN). This process is revocable and makes replacing biometrics as easy as replacing PRNs. The formulation has been verified under a number of scenarios (normal, stolen PRN, and compromised biometrics scenarios) using 2400 Facial Recognition Technology face images. The diversity property is also examined.