An Improved Leveled Fully Homomorphic Encryption Scheme over the Integers

Abstract

A scale-invariant leveled fully homomorphic encryption (FHE) scheme over the integers is proposed by Coron et al. in PKC 2014, where the ciphertext noise increases linearly after each homomorphic multiplication. Then based on Coron’s variant of the approximate greatest common divisor problem, we construct a more efficient leveled FHE scheme over the integers without the modulus switching technique, which could resist chosen plaintext attacks. The inner product operation in our homomorphic multiplication is eliminated by multiplying the multiplication key directly. The homomorphic multiplication in our scheme is realized by the more simplified multiplication key, in which the number of integers is decreased from \(O(\varTheta \cdot \eta )\) to O(1) compared with Coron’s scheme. Simulation results and analysis show that our scheme’s performance of multiplication key and homomorphic multiplication is much more efficient than that of Coron’s scheme.