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 /spl Zopf/(n/sup 2/), 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.