Lossy Encryption: Constructions from General Assumptions and Efficient Selective Opening Chosen Ciphertext Security

Lossy encryption was originally studied as a means of achieving efficient and composable oblivious transfer. Bellare, Hofheinz and Yilek showed that lossy encryption is also selective opening secure. We present new and general constructions of lossy encryption schemes and of cryptosystems secure against selective opening adversaries.

We show that

every

re-randomizable encryption scheme gives rise to efficient encryptions secure against a selective opening adversary. We show that statistically-hiding 2-round Oblivious Transfer implies Lossy Encryption and so do smooth hash proof systems. This shows that private information retrieval and homomorphic encryption

both

imply Lossy Encryption, and thus Selective Opening Secure Public Key Encryption. Applying our constructions to well-known cryptosystems, we obtain selective opening secure commitments and encryptions from the

Decisional Diffie-Hellman

,

Decisional Composite Residuosity

and

Quadratic Residuosity

assumptions.

In an indistinguishability-based model of chosen-ciphertext selective opening security, we obtain secure schemes featuring short ciphertexts under standard number theoretic assumptions. In a simulation-based definition of chosen-ciphertext selective opening security, we also handle non-adaptive adversaries by adapting the Naor-Yung paradigm and using the perfect zero-knowledge proofs of Groth, Ostrovsky and Sahai.