In this paper we propose an interesting improvement of the im-plementation of the original Gentry-Halevi somewhat homomorphic scheme. Wesuggest to choose a bigger plaintext space, by changing the underlying ideal from$I = (2) to I = (p)$for some bigger prime $p$.Our analysis show that bigger plaintext space will improve the homomor-phic computation of the somewhat homomorphic scheme while it only slightlyincreases the complexity of the key generation procedure. The encryption and de-cryption functions have the same complexity. We provide also some experimentalcomputations that support the analysis.
@article{199,
title = {Experiments with the plaintext space in Gentry's somewhat homomorphic scheme},
journal = {Tatra Mountains Mathematical Publications},
volume = {51},
year = {2012},
doi = {10.2478/tatra.v53i0.199},
language = {EN},
url = {http://dml.mathdoc.fr/item/199}
}
Mikuš, Michal. Experiments with the plaintext space in Gentry’s somewhat homomorphic scheme. Tatra Mountains Mathematical Publications, Tome 51 (2012) . doi : 10.2478/tatra.v53i0.199. http://gdmltest.u-ga.fr/item/199/