Cryptology ePrint Archive: Report 2002/083

A semantically secure elliptic curve RSA scheme with small expansion factor

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, and it has expansion factor 2 (previous schemes with similar features present expansion factors greater or equal than 4). Demytko's RSA type 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 Root Assumption. Confidence on this assumption is also discussed.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem, semantic security, expansion factor, Demytko's scheme.

Date: received 27 Jun 2002

Contact author: dgalindo at mat upc es

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Version: 20020627:175440 (All versions of this report)

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