Cancelable biometric schemes are designed to extract an identity-preserving, non-invertible as well as revocable pseudo-identifier from biometric data. Recognition systems need to store only this pseudo-identifier, to avoid tampering and/or stealing of original biometric data during the recognition process. State-of-the-art cancelable schemes generate pseudo-identifiers by transforming the original template using either user-specific salting or many-to-one transformations. In addition to the performance concerns, most of such schemes are modality-specific and prone to reconstruction attacks as there are chances for unauthorized access to security-critical transformation keys. A novel, modality-independent cancelable biometric scheme is proposed to overcome these limitations. In this scheme, a cancelable template (pseudo identifier) is generated as a distance vector between multiple random transformations of the biometric feature vector. These transformations were done by grouping feature vector components based on a set of user-specific random vectors. The proposed scheme nullifies the possibility of template reconstruction as the generated cancelable template contains only the distance values between the different random transformations of the feature vector and it does not store any details of the biometric template. The recognition performance of the proposed scheme is evaluated for face and fingerprint modalities. Equal Error Rate (EER) of 1.5 is obtained for face and 1.7 is obtained for the fingerprint in the worst case.