Hybrid Damgård Is CCA1-Secure under the DDH Assumption

In 1991, Damgard proposed a simple public-key cryptosystem that he proved CCA1-secure under the Diffie-Hellman Knowledge assumption. Only in 2006, Gjosteen proved its CCA1-security under a more standard but still new and strong assumption. The known CCA2-secure public-key cryptosystems are considerably more complicated. We propose a hybrid variant of Damgard's public-key cryptosystem and show that it is CCA1-secure if the used symmetric cryptosystem is CPA-secure, the used MAC is unforgeable, the used key-derivation function is secure, and the underlying group is a DDH group. The new cryptosystem is the most efficient known CCA1-secure hybrid cryptosystem based on standard assumptions.

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