An Efficient Two-Party Public Key Cryptosystem Secure Against Adaptive Chosen Ciphertext Attack

We propose an efficient two-party key cryptosystem that is secure against adaptive chosen ciphertext attack, under the Decision Diffle-Hellman (DDH) assumption. Specifically, we show that the two parties together can decrypt ciphertexts, but neither can alone. Our system is based on the Cramer-Shoup cryptosystem. Previous results on effecient threshold cryptosystems secure against an adaptive chosen ciphertext attack required either (1) a strict majority of uncorrupted decryption servers, and thus do not apply to the two-party scenario, or (2) the random oracle assumption, and thus were not proven secure in the "standard" model.