Experiments with the Plaintext Space in Gentry’S Somewhat Homomorphic Scheme

In this paper we propose an improvement of the implementation of the original Gentry-Halevi somewhat homomorphic scheme. We suggest to choose a bigger plaintext space, by changing the underlying ideal from I = (2) to I = (p) for some bigger prime p. Our analysis shows that bigger plaintext space will improve the homomorphic computation of the somewhat homomorphic scheme while it only slightly increases the complexity of the key generation procedure. The encryption and decryption functions have the same complexity. We provide also some experimental computations that support the analysis.