Chosen Ciphertext Secure Public Key Encryption with a Simple Structure

In this paper, we present a new public key encryption schemewith an easy-to-understand structure. More specifically, in theproposed scheme, for fixed group elements g 1 ,...,g 𝓁 in the public keya sender computes only $g_1^r,\ldots,g_\ell^r$ for encryption wherer is a single random number. Due to this simple structure,its security proof becomes very short (and one would easilyunderstand the simulator's behavior for simultaneously dealing withembedding a hard problem and simulating a decryption oracle). Ourproposed scheme is provably chosen-ciphertext secure under the gapDiffie-Hellman assumption (without random oracles). A drawback ofour scheme is that its ciphertext is much longer than knownpractical schemes. We also propose a modification of our schemewith improved efficiency.

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