Efficient Fully Homomorphic Encryption with Large Plaintext Space

Abstract

The security of multimedia content and personal privacy for big data has triggered widespread concern in the society. Fully homomorphic encryption (FHE), which can homomorphically compute arbitrary functions on the encrypted data without knowing the secret key, is valuable in protecting user’s data security. However, most of the FHE schemes only take single-bit of ciphertext as the input, which makes the evaluation process complicated. In EUROCRYPT’2015, Ducas and Micciancio proposed an FHE scheme FHEW with the plaintext space Z 2 , and gave an assumption of extending the plaintext space to Z t . In this paper, we optimize the decryption algorithm of FHEW in bootstrapping, and propose an FHE scheme with large plaintext space Z t . Firstly, we optimize the rounding function of the decryption algorithm in FHEW to the msdExtract algorithm, which can homomorphically extract the most significant digit of the plaintext. Secondly, we design the msdExtract algorithm by employing the homomorphic accumulator, and present the process of general bootstrapping. Finally, based on the msdExtract algorithm, we extend the plaintext space of our scheme to Z t , comparing to Z 2 in FHEW. The security of our scheme is based on the basic LWE scheme and FHEW. What’s more, our scheme can perform the evaluation more conveniently with large plaintext space, and can be applied to more scenarios.