To circumvent problems associated with dependence on traditional security systems on passwords, Personal Identification Numbers (PINs) and tokens, modern security systems adopt biometric traits that are inimitable to each individual for identification and verification. This study presents two different frameworks for secure person identification using cancellable face recognition (CFR) schemes. Exploiting its ability to guarantee irrevocability and rich diversity, both frameworks utilise Random Projection (RP) to encrypt the biometric traits. In the first framework, a hybrid structure combining Intuitionistic Fuzzy Logic (IFL) with RP is used to accomplish full distortion and encryption of the original biometric traits to be saved in the database, which helps to prevent unauthorised access of the biometric data. The framework involves transformation of spatial-domain greyscale pixel information to a fuzzy domain where the original biometric images are disfigured and further distorted via random projections that generate the final cancellable traits. In the second framework, cancellable biometric traits are similarly generated via homomorphic transforms that use random projections to encrypt the reflectance components of the biometric traits. Here, the use of reflectance properties is motivated by its ability to retain most image details, while the guarantee of the non-invertibility of the cancellable biometric traits supports the rationale behind our utilisation of another RP stage in both frameworks, since independent outcomes of both the IFL stage and the reflectance component of the homomorphic transform are not enough to recover the original biometric trait. Our CFR schemes are validated on different datasets that exhibit properties expected in actual application settings such as varying backgrounds, lightings, and motion. Outcomes in terms standard metrics, including structural similarity index metric (SSIM) and area under the receiver operating characteristic curve (AROC), suggest the efficacy of our proposed schemes across many applications that require person identification and verification.