The need for high-speed and secure multi-biometric systems has grown in the last few decades. The progress in Internet applications and computer networks has prompted new problems with security and privacy. Having a reliable and secure means for storing biometrics is a necessary issue. Hence, data encryption and network security have become significant. Thence, because of the fast progress in network development, humans can easily and arbitrarily distribute or access digital data from networks. Therefore, ownership security has become a significant issue for individuals, and it requires much interest. Thus, there is a significant threat to copyright owners and digital multimedia producers to conserve multimedia from intruder prospection to avert loss in transmitted data. Ten years ago, most modern security systems depended on biometrics. Unfortunately, these systems have suffered for a long time from hacking trials. If the biometric databases have been hacked and stolen, the saved biometrics will be lost forever. Thus, there is a bad need to develop new cancelable biometric systems. In a classical authentication system, a user can easily change a password if it is compromised. However, the user’s biometrics are limited and unique, and if a user biometric is compromised, it will be impossible to change it in a particular system or at least difficult. Cancelable biometrics can be generated with intentional, repeatable distortions of biometric signals based on transforms. Hence, biometric templates are compared in the transform domain. Cancelable biometrics depend on transforming data to replace a single biometric template in the same or different systems. This paper presents a cancelable biometric system that depends on a novel hybrid encryption framework based on the Rubik’ cube technique. It allows simultaneous encryption of multiple images. The suggested hybrid enrollment stage begins with chaotic Baker map permutation in the Cipher FeedBack (CFB) operation mode, Advanced Encryption Standard (AES) or Ron's Code (RC6) algorithm as a first stage for encrypting the multiple images, separately. After that, the output encrypted images are passed to the second encryption stage via Rubik’s cube technique. Chaotic, RC6, or AES encrypted face images are utilized as the Rubik’s cube faces. For the RC6 and AES algorithms, they add a degree of diffusion, while the chaotic algorithm adds a degree of permutation. Moreover, the Rubik’s cube technique adds more permutations to the encrypted images, simultaneously. The encrypted images are used in the cancelable biometric system. The simulation results prove that the hybrid proposed encryption framework is efficient. Moreover, it has strong robustness and security.