An Effective NTRU-Based Fully Homomorphic Encryption Scheme

Fully homomorphic encryption (FHE) supports arbitrary computations on ciphertexts without decryption to protect users’ privacy. However, currently, there are still some shortcomings in research studies FHE. For example, the NTRU-based FHE scheme constructed using approximate eigenvector method requires complex matrix multiplications, and power-of-two cyclotomic ring cannot prevent subfield attacks. To address these problems, this paper proposed a based power-of-prime made following improvements: (1) is immune attacks; (2) multiplications replaced with matrix-vector modify ciphertext forms structures, so as gain advantages storage, transportation, computations; (3) single instruction multiple data (SIMD) technology introduced, operations executed through Chinese remainder theorem, further improving computation storage efficiency. The of form vector, no key exchange required for operations. In addition, can eliminate decisional small polynomial ratio (DSPR) assumption under certain conditions only relies learning errors (RLWE) assumption. standard security model prove that secure against chosen-plaintext (IND-CPA) Compared similar schemes, improves efficiency at least by factor l φ x / d + 1 quadratically decreases noise growth rate.