Abstract
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.
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Keywords
- Homomorphic Encryption
- Oblivious Transfer
- Private Information Retrieval
- Homomorphic Encryption Scheme
- Randomness Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Armknecht, F., Katzenbeisser, S., Peter, A.: Group homomorphic encryption. IACR ePrint Archive 2010/501 (2010)
Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2007)
Benaloh, J.C.: Dense probabilistic encryption. In: Proceedings of the Workshop on Selected Areas in Cryptography, pp. 120–128 (1994)
Bellare, M., Fischlin, M., O’Neill, A., Ristenpart, T.: Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 360–378. Springer, Heidelberg (2008)
Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF Formulas on Ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)
Boneh, D., Katz, J.: Improved Efficiency for CCA-Secure Cryptosystems Built Using Identity-Based Encryption. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 87–103. Springer, Heidelberg (2005)
Canetti, R., Halevi, S., Katz, J.: Chosen-Ciphertext Security from Identity-Based Encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004)
Cramer, R., Hofheinz, D., Kiltz, E.: A Twist on the Naor-Yung Paradigm and Its Application to Efficient CCA-Secure Encryption from Hard Search Problems. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 146–164. Springer, Heidelberg (2010)
Di Crescenzo, G., Malkin, T., Ostrovsky, R.: Single Database Private Information Retrieval Implies Oblivious Transfer. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 122–138. Springer, Heidelberg (2000)
Cramer, R., Shoup, V.: A Practical Public Key Cryptosystem Provably Secure against Adaptive Chosen Ciphertext Attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)
Cramer, R., Shoup, V.: Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002); Full version available at http://eprint.iacr.org Cryptology ePrint Archive, Report 2001/085
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. In: STOC 1991, pp. 542–552 (1991)
Damgård, I., Jurik, M.: A Generalisation, a Simplification and Some Applications of Paillier’s Probabilistic Public-key System. In: Kim, K.-C. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)
Dowsley, R., Müller-Quade, J., Nascimento, A.C.A.: A CCA2 Secure Public Key Encryption Scheme Based on the McEliece Assumptions in the Standard Model. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 240–251. Springer, Heidelberg (2009)
Freeman, D.M., Goldreich, O., Kiltz, E., Rosen, A., Segev, G.: More Constructions of Lossy and Correlation-Secure Trapdoor Functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 279–295. Springer, Heidelberg (2010)
El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985)
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC 2009, pp. 169–178. ACM, New York (2009)
Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28, 270–299 (1984)
Gertner, Y., Malkin, T., Myers, S.: Towards a Separation of Semantic and CCA Security for Public Key Encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 434–455. Springer, Heidelberg (2007)
Haralambiev, K., Jager, T., Kiltz, E., Shoup, V.: Simple and Efficient Public-Key Encryption from Computational Diffie-Hellman in the Standard Model. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 1–18. Springer, Heidelberg (2010)
Hemenway, B., Libert, B., Ostrovsky, R., Vergnaud, D.: Lossy Encryption: Constructions from General Assumptions and Efficient Selective Opening Chosen Ciphertext Security. In: Lee, D.H. (ed.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 70–88. Springer, Heidelberg (2011)
Hemenway, B., Ostrovsky, R.: Extended-DDH and Lossy Trapdoor Functions. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 627–643. Springer, Heidelberg (2012)
Ishai, Y., Kushilevitz, E., Ostrovsky, R.: Sufficient Conditions for Collision-Resistant Hashing. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 445–456. Springer, Heidelberg (2005)
Kushilevitz, E., Ostrovsky, R.: Replication is not needed: Single database, computationally-private information retrieval. In: FOCS 1997, pp. 364–373. ACM, New York (1997)
Mann, E.: Private access to distributed information. Master’s thesis, Technion - Israel Institute of Technology (1998)
Mol, P., Yilek, S.: Chosen-Ciphertext Security from Slightly Lossy Trapdoor Functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 296–311. Springer, Heidelberg (2010)
Naccache, D., Stern, J.: A new public key cryptosystem based on higher residues. In: CCS 1998: Proceedings of the 5th ACM Conference on Computer and Communications Security, pp. 59–66. ACM Press, New York (1998)
Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: STOC 1990, pp. 427–437 (1990)
Okamoto, T., Uchiyama, S.: A New Public-Key Cryptosystem as Secure as Factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 308–318. Springer, Heidelberg (1998)
Paillier, P.: Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: STOC 2009: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, pp. 333–342. ACM, New York (2009)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: STOC 2008: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 187–196. ACM, New York (2008)
Regev, O.: On lattices, learning with errors, random linear codes and cryptography. In: STOC 2005, pp. 84–93. ACM (2005)
Rackoff, C., Simon, D.R.: Non-interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992)
Rosen, A., Segev, G.: Efficient lossy trapdoor functions based on the composite residuosity assumption. Cryptology ePrint Archive, Report 2008/134 (2008)
Rosen, A., Segev, G.: Chosen-Ciphertext Security via Correlated Products. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 419–436. Springer, Heidelberg (2009)
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Hemenway, B., Ostrovsky, R. (2012). On Homomorphic Encryption and Chosen-Ciphertext Security. In: Fischlin, M., Buchmann, J., Manulis, M. (eds) Public Key Cryptography – PKC 2012. PKC 2012. Lecture Notes in Computer Science, vol 7293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30057-8_4
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