With the rapid development of Internet of Things (IoT), grave questions of privacy protection are raised. This greatly impacts the large-scale applications of IoT. Fully homomorphic encryption (FHE) can provide privacy protection for IoT. But, its efficiency needs to be greatly improved. Nowadays, Gentry’s bootstrapping technique is still the only known method of obtaining a “pure” FHE scheme. And it is also the key for the low efficiency of FHE scheme due to the complexity homomorphic decryption. In this paper, the bootstrapping technique of Halevi and Shoup (EUROCRYPT 15) is improved. Firstly, by introducing a definition of “load capacity”, we optimize the parameter range for which their bootstrapping technique works. Next we generalize their ciphertext modulus from closing to a power of two to more general situations. This enables the method to be applied in a larger number of situations. Moreover, this paper also shows how to introduce SIMD homomorphic computation techniques into the new method, to improve the efficiency of recryption.
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