An IND-CPA cryptosystem from Demytko´s primitive

An encryption scheme should satisfy semantic security or indistinguishability of encryptions against chosen plaintext attack (IND-CPA). We propose an elliptic curve scheme over the ring Z(n²), which is efficient and semantically secure in the standard model. It is based on factoring, and it has expansion factor 2 (previous schemes with these features present expansion factors greater than or equal to 4). Demytko´s primitive has been used to obtain efficiency and probabilistic encryption. Semantic security of this scheme is based on a new decisional assumption, namely, the decisional small root assumption. Confidence in this assumption is also discussed.