Optimized relinearization algorithm of the multikey homomorphic encryption scheme

Abstract

Multikey homomorphic encryption (MKHE) supports arbitrary homomorphic evaluation on the ciphertext of different users and thus can be applied to scenarios involving multiusers (e.g., cloud computing and artificial intelligence) to protect user privacy. CDKS19 is the current most efficient MKHE scheme, and its relinearization process consumes most of the time of homomorphic evaluation. In this study, an optimized relinearization algorithm of CDKS19 is proposed. This algorithm reorganizes the evaluation key during the key generation process, decreases the complexity of relinearization, and reduces the error growth rate during homomorphic evaluation. First, we reduce the scale of the evaluation key by increasing its modulus instead of using a gadget vector to decompose the user's public key and extend the ciphertext of homomorphic multiplication. Second, we use rescaling technology to optimize the relinearization algorithm; thus, the error bound of the ciphertext is reduced, and the homomorphic operation efficiency is improved. Lastly, the average-case error estimation on the variances of polynomial coefficients and the upper bound of the canonical embedding map are provided. Results show that our scheme reduces the scale of the evaluation key, the error variance, and the computational cost of the relinearization process. Our scheme can effectively perform the homomorphic multiplication of ciphertexts.

PSO with Mixed Strategy for Global Optimization

“…Canonical PSO. In the optimization process, the velocity vector V i for the ith particle in the population is updated using (1) given in [2] iteratively through the guidance of pbest i and gbest.…”

“…In recent years, optimization algorithms are applied more and more widely in various felds [1]. One of the most famous ones is PSO.…”

Ensuring privacy and confidentiality of data on the cloud using an enhanced homomorphism scheme

“…Ensuring Privacy and Confidentiality of Data on the Cloud… Yang et, al. [29], proposed an optimized re-linearization scheme of CDKS19 to ensure cloud data privacy. Their proposed scheme reduces the linearization complexity thereby decreasing the homomorphism evaluation process through the reorganization of the evaluation key in the key generation process.…”

“…From Table 1, it can be observed that authors [21], [22], [23], [24], [25], [27], [28], [29], and [38] have their algorithms producing predictable, high execution and linear execution time, contrarily, Loyka et al 2018 [26], proposed an algorithm, using homomorphism scheme based on an affine cipher, which produced similar nonlinear results as the proposed Enhanced Homomorphism Scheme when text only was executed as shown in table 6, but the encryption and decryption time for numbers only was linear as shown in Table 7, whiles that of EHS is nonlinear which makes the work of Loyka et al (2018) to be defeated by the works of [34], [35], and [36] that execution time depends on the size of security key used for the execution process. From, this it can be concluded that the proposed Enhanced Homomorphism scheme's execution time is not dependent on data size but on the secret key used for the encryption as proposed by authors [34], [35], and [36].…”