An efficient semantically secure elliptic curve cryptosystem based on KMOV

We propose an elliptic curve scheme over the ring Zn2 , which is efficient and semantically secure in the standard model. There appears to be no previous elliptic curve cryptosystem based on factoring that enjoys both of these properties. The KMOV scheme has been used as an underlying primitive to obtain efficiency and probabilistic encryption. Semantic security of the scheme is based on a new decisional assumption, namely, the Decisional Small-x eMultiples assumption. Confidence on this assumption is also discussed.

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