On Homomorphic Encryption and Chosen-Ciphertext Security

Chosen-Ciphertext (IND-CCA) security is generally considered the right notion of security for a cryptosystem. Because of its central importance much effort has been devoted to constructing IND-CCA secure cryptosystems. In this work, we consider constructing IND-CCA secure cryptosystems from (group) homomorphic encryption. Our main results give natural and efficient constructions of IND-CCA secure cryptosystems from any homomorphic encryption scheme that satisfies weak cyclic properties, either in the plaintext, ciphertext or randomness space. Our results have the added benefit of being simple to describe and analyze.

[1]  Steven Myers,et al.  Towards a Separation of Semantic and CCA Security for Public Key Encryption , 2007, TCC.

[2]  Jonathan Katz,et al.  Chosen-Ciphertext Security from Identity-Based Encryption , 2006 .

[3]  Oded Goldreich,et al.  More Constructions of Lossy and Correlation-Secure Trapdoor Functions , 2010, Journal of Cryptology.

[4]  Marc Fischlin,et al.  Topics in Cryptology – CT-RSA 2009 , 2009 .

[5]  Jacques Stern,et al.  Advances in Cryptology — EUROCRYPT ’99 , 1999, Lecture Notes in Computer Science.

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

[7]  Craig Gentry,et al.  Fully homomorphic encryption using ideal lattices , 2009, STOC '09.

[8]  Rafail Ostrovsky,et al.  Extended-DDH and Lossy Trapdoor Functions , 2012, Public Key Cryptography.

[9]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[10]  Taher El Gamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, IEEE Trans. Inf. Theory.

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

[12]  Aggelos Kiayias,et al.  BiTR: Built-in Tamper Resilience , 2011, IACR Cryptol. ePrint Arch..

[13]  Kaisa Nyberg,et al.  Advances in Cryptology — EUROCRYPT'98 , 1998 .

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

[15]  T. Elgamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

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

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

[18]  Adam O'Neill,et al.  Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles , 2008, CRYPTO.

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

[20]  Aggelos Kiayias,et al.  Multi-query Computationally-Private Information Retrieval with Constant Communication Rate , 2010, Public Key Cryptography.

[21]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2005, STOC '05.

[22]  Scott Yilek,et al.  Chosen-Ciphertext Security from Slightly Lossy Trapdoor Functions , 2010, Public Key Cryptography.

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

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

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

[26]  Anderson C. A. Nascimento,et al.  A CCA2 Secure Public Key Encryption Scheme Based on the McEliece Assumptions in the Standard Model , 2009, CT-RSA.

[27]  Aggelos Kiayias,et al.  Traitor Tracing with Constant Transmission Rate , 2002, EUROCRYPT.

[28]  Hugo Krawczyk,et al.  Advances in Cryptology - CRYPTO '98 , 1998 .

[29]  Stefan Katzenbeisser,et al.  A Cleaner View on IND-CCA1 Secure Homomorphic Encryption using SOAP , 2010, IACR Cryptol. ePrint Arch..

[30]  Jacques Stern,et al.  A new public key cryptosystem based on higher residues , 1998, CCS '98.

[31]  Tibor Jager,et al.  Simple and Efficient Public-Key Encryption from Computational Diffie-Hellman in the Standard Model , 2010, Public Key Cryptography.

[32]  Aggelos Kiayias,et al.  Traceable Signatures , 2004, EUROCRYPT.

[33]  Bart Preneel,et al.  Advances in cryptology - EUROCRYPT 2000 : International Conference on the Theory and Application of Cryptographic Techniques, Bruges, Belgium, May 14-18, 2000 : proceedings , 2000 .

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

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

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

[37]  Arto Salomaa,et al.  Public-Key Cryptography , 1991, EATCS Monographs on Theoretical Computer Science.

[38]  Ronald Cramer,et al.  A Twist on the Naor-Yung Paradigm and Its Application to Efficient CCA-Secure Encryption from Hard Search Problems , 2010, TCC.

[39]  Josh Benaloh,et al.  Dense Probabilistic Encryption , 1999 .

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

[41]  Joan Feigenbaum,et al.  Advances in Cryptology-Crypto 91 , 1992 .

[42]  Brent Waters,et al.  Lossy trapdoor functions and their applications , 2008, SIAM J. Comput..

[43]  Chris Peikert,et al.  Public-key cryptosystems from the worst-case shortest vector problem: extended abstract , 2009, STOC '09.

[44]  Rafail Ostrovsky,et al.  Lossy Encryption: Constructions from General Assumptions and Efficient Selective Opening Chosen Ciphertext Security , 2011, ASIACRYPT.

[45]  Dan Boneh,et al.  Evaluating 2-DNF Formulas on Ciphertexts , 2005, TCC.

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

[47]  Alfred Menezes,et al.  Topics in Cryptology – CT-RSA 2005 , 2005 .

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

[49]  Tatsuaki Okamoto,et al.  A New Public-Key Cryptosystem as Secure as Factoring , 1998, EUROCRYPT.

[50]  Martijn Stam.  Beyond Uniformity: Better Security/Efficiency Tradeoffs for Compression Functions , 2008, CRYPTO.