We have devised a novel Multi-Identity Based Fully Homomorphic Encryption (MIBFHE) system by integrating Multi-Key Fully Homomorphic Encryption (MKFHE) with Identity-Based Encryption (IBE). This innovative approach leverages a streamlined MKFHE construction technique called the "decomposition method," which simplifies the encryption process and reduces computational demands. Concurrently, we have tailored an IBE scheme to enhance compatibility and efficiency within our MIBFHE framework. Our MIBFHE scheme facilitates secure computations directly on encrypted data from the initial encryption phase, eliminating the need for separate ciphertext generation. This efficiency enhancement significantly mitigates the computational overhead traditionally associated with such encryption systems. Moreover, our scheme ensures robust security against cryptographic attacks, validated under the Learning with Errors (LWE) assumption in the random oracle model. Furthermore, our analysis demonstrates that the MIBFHE scheme optimally manages access control by associating computations with user identities rather than intricate public key infrastructure. This approach not only simplifies key management but also enhances the scalability and practicality of deploying homomorphic encryption in real-world applications.

Keywords: Multi-Identity Based Fully Homomorphic Encryption, MIBFHE, Multi-Key Fully Homomorphic Encryption, MKFHE, Identity-Based Encryption, IBE, decomposition method, efficiency, secure computations, Learning with Errors, LWE assumption, access control, scalability.