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.

[1]  Moni Naor,et al.  Cryptography and Game Theory: Designing Protocols for Exchanging Information , 2008, TCC.

[2]  Donald Beaver,et al.  Plug and Play Encryption , 1997, CRYPTO.

[3]  Moni Naor,et al.  Efficient oblivious transfer protocols , 2001, SODA '01.

[4]  Yuval Ishai,et al.  Sufficient Conditions for Collision-Resistant Hashing , 2005, TCC.

[5]  Sanjit Chatterjee,et al.  Generalization of the Selective-ID Security Model for HIBE Protocols , 2006, Public Key Cryptography.

[6]  Hugo Krawczyk,et al.  Chameleon Signatures , 2000, NDSS.

[7]  Ronald Cramer,et al.  A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack , 1998, CRYPTO.

[8]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[9]  Elizabeth D Mann.  Private access to distributed information , 1998 .

[10]  Brent Waters,et al.  Lossy Trapdoor Functions and Their Applications , 2011, SIAM J. Comput..

[11]  Jonathan Katz,et al.  Adaptively-Secure, Non-interactive Public-Key Encryption , 2005, TCC.

[12]  Donald Beaver,et al.  Cryptographic Protocols Provably Secure Against Dynamic Adversaries , 1992, EUROCRYPT.

[13]  Michael K. Reiter,et al.  Alternatives to Non-malleability: Definitions, Constructions, and Applications (Extended Abstract) , 2004, TCC.

[14]  Manoj Prabhakaran,et al.  Rerandomizable RCCA Encryption , 2007, CRYPTO.

[15]  Hovav Shacham,et al.  Short Group Signatures , 2004, CRYPTO.

[16]  Ivan Damgård,et al.  A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System , 2001, Public Key Cryptography.

[17]  Dennis Hofheinz.  Possibility and Impossibility Results for Selective Decommitments , 2010, Journal of Cryptology.

[18]  Amit Sahai,et al.  Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[19]  Yael Tauman Kalai.  Smooth Projective Hashing and Two-Message Oblivious Transfer , 2005, EUROCRYPT.

[20]  Mihir Bellare,et al.  Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening , 2009, EUROCRYPT.

[21]  Ronald Cramer,et al.  Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption , 2001, EUROCRYPT.

[22]  Gil Segev,et al.  Chosen-Ciphertext Security via Correlated Products , 2009, SIAM J. Comput..

[23]  Brent Waters,et al.  Identity-Based Encryption Secure against Selective Opening Attack , 2011, TCC.

[24]  Moni Naor,et al.  Magic Functions: In Memoriam: Bernard M. Dwork 1923--1998 , 2003, JACM.

[25]  Eike Kiltz,et al.  Encryption Schemes Secure against Chosen-Ciphertext Selective Opening Attacks , 2010, EUROCRYPT.

[26]  Rafail Ostrovsky,et al.  Replication is not needed: single database, computationally-private information retrieval , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[27]  Rafail Ostrovsky,et al.  Deniable Encryption , 1997, IACR Cryptol. ePrint Arch..

[28]  Jens Groth,et al.  Rerandomizable and Replayable Adaptive Chosen Ciphertext Attack Secure Cryptosystems , 2004, TCC.

[29]  David Cash,et al.  The Twin Diffie-Hellman Problem and Applications , 2008, EUROCRYPT.

[30]  Rafail Ostrovsky,et al.  Single Database Private Information Retrieval Implies Oblivious Transfer , 2000, EUROCRYPT.

[31]  Gil Segev,et al.  Efficient Lossy Trapdoor Functions based on the Composite Residuosity Assumption , 2008, IACR Cryptol. ePrint Arch..

[32]  Yael Tauman Kalai,et al.  Smooth Projective Hashing and Two-Message Oblivious Transfer , 2005, Journal of Cryptology.

[33]  Yehuda Lindell,et al.  A Simpler Construction of CCA2-Secure Public-Key Encryption under General Assumptions , 2006, Journal of Cryptology.

[34]  Mihir Bellare,et al.  Encryption Schemes Secure under Selective Opening Attack , 2009, IACR Cryptol. ePrint Arch..

[35]  Dan Boneh,et al.  Efficient Selective-ID Secure Identity Based Encryption Without Random Oracles , 2004, IACR Cryptol. ePrint Arch..

[36]  Moni Naor,et al.  Adaptively secure multi-party computation , 1996, STOC '96.

[37]  Daniel Bleichenbacher,et al.  Chosen Ciphertext Attacks Against Protocols Based on the RSA Encryption Standard PKCS #1 , 1998, CRYPTO.

[38]  Jonathan Katz,et al.  Chosen-Ciphertext Security from Identity-Based Encryption , 2004, SIAM J. Comput..

[39]  Rafail Ostrovsky,et al.  Perfect Non-Interactive Zero Knowledge for NP , 2006, IACR Cryptol. ePrint Arch..

[40]  Rui Zhang,et al.  Tweaking TBE/IBE to PKE Transforms with Chameleon Hash Functions , 2007, ACNS.

[41]  Serge Fehr,et al.  On Notions of Security for Deterministic Encryption, and Efficient Constructions without Random Oracles , 2008, CRYPTO.

[42]  Rafail Ostrovsky,et al.  Robust Non-interactive Zero Knowledge , 2001, CRYPTO.

[43]  Moti Yung,et al.  Questionable Encryption and Its Applications , 2005, Mycrypt.

[44]  A. Juels,et al.  Universal Re-encryption for Mixnets , 2004, CT-RSA.

[45]  Eike Kiltz,et al.  Chosen-Ciphertext Security from Tag-Based Encryption , 2006, TCC.

[46]  Oded Goldreich,et al.  More Constructions of Lossy and Correlation-Secure Trapdoor Functions , 2011, Journal of Cryptology.

[47]  Hugo Krawczyk,et al.  Relaxing Chosen-Ciphertext Security , 2003, CRYPTO.

[48]  Moni Naor,et al.  Public-key cryptosystems provably secure against chosen ciphertext attacks , 1990, STOC '90.

[49]  Moni Naor,et al.  Magic functions , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[50]  Rafail Ostrovsky,et al.  Non-interactive and non-malleable commitment , 1998, STOC '98.

[51]  Moni Naor,et al.  Non-malleable cryptography , 1991, STOC '91.

[52]  Brent Waters,et al.  A Framework for Efficient and Composable Oblivious Transfer , 2008, CRYPTO.

[53]  Daniel R. Simon,et al.  Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack , 1991, CRYPTO.

[54]  Dennis Hofheinz,et al.  All-But-Many Lossy Trapdoor Functions , 2012, EUROCRYPT.

[55]  Jonathan Katz,et al.  Improved Efficiency for CCA-Secure Cryptosystems Built Using Identity-Based Encryption , 2005, CT-RSA.