Multiple to One Fully Homomorphic Encryption Scheme over the Integers

Fully homomorphic encryption allows any operation evaluation on encrypted data without decryption. The existing integer-based homomorphic encryption schemes are designed only for two participants namely one party encryption one party decryption (one-to-one), whose computational efficiency is generally low, plaintext space is small, so it can not be applied to big data, cloud computing and other actual scene. Therefore, a full homomorphic encryption scheme with multi-party encryption, one party decryption (multiple to one) is presented. The scheme simplifies the key generation process on the basis of guaranteeing the security, but also gives the range of the number of encrypted parties that can be decrypted accurately in the process of homomorphic operation. Meanwhile, in the random oracle model, the security of the new scheme is proved based on approximate Greatest Common Divisor (GCD) problem. Numerical analysis demonstrates that the presented scheme can not only extend the data traffic, but also improve the efficiency by comparing with the existing schemes. Simulation results show that proposed scheme is more practical in the range of integer, and meets the requirements of the users to the system response. Finally, the plaintext space is expanded to 3 bit, comparing and analysing the experiment with the scheme of 1 bit.