Cryptology ePrint Archive: Report 2002/037

An efficient semantically secure elliptic curve cryptosystem based on KMOV

David Galindo and Sebasti\`a Mart\'{\i}n and Paz Morillo and Jorge L. Villar

Abstract: We propose an elliptic curve scheme over the ring $\entq$, 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. 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-$x$ $e$-Multiples Assumption. Confidence on this assumption is also discussed.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem, semantic security.

Date: received 22 Mar 2002, last revised 27 Nov 2002

Contact author: dgalindo at mat upc es

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Note: Revision.

Version: 20021127:174152 (All versions of this report)

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