Encryption Schemes Secure against Chosen-Ciphertext Selective Opening Attacks
Imagine many small devices send data to a single receiver, encrypted using the receiver’s public key. Assume an adversary that has the power to adaptively corrupt a subset of these devices. Given the information obtained from these corruptions, do the ciphertexts from uncorrupted devices remain secure?
Recent results suggest that conventional security notions for encryption schemes (like IND-CCA security) do not suffice in this setting. To fill this gap, the notion of security against selective-opening attacks (SOA security) has been introduced. It has been shown that lossy encryption implies SOA security against a passive, i.e., only eavesdropping and corrupting, adversary (SO-CPA). However, the known results on SOA security against an active adversary (SO-CCA) are rather limited. Namely, while there exist feasibility results, the (time and space) complexity of currently known SO-CCA secure schemes depends on the number of devices in the setting above.
In this contribution, we devise a new solution to the selective opening problem that does not build on lossy encryption. Instead, we combine techniques from non-committing encryption and hash proof systems with a new technique (dubbed “cross-authentication codes”) to glue several ciphertext parts together. The result is a rather practical SO-CCA secure public-key encryption scheme that does not suffer from the efficiency drawbacks of known schemes. Since we build upon hash proof systems, our scheme can be instantiated using standard number-theoretic assumptions such as decisional Diffie-Hellman DDH), decisional composite residuosity (DCR), and quadratic residuosity (QR). Besides, we construct a conceptually very simple and comparatively efficient SO-CPA secure scheme from (slightly enhanced) trapdoor one-way permutations.
We stress that our schemes are completely independent of the number of challenge ciphertexts, and we do not make assumptions about the underlying message distribution (beyond being efficiently samplable). In particular, we do not assume efficient conditional re-samplability of the message distribution. Hence, our schemes are secure in arbitrary settings, even if it is not known in advance how many ciphertexts might be considered for corruptions.
KeywordsEncryption Scheme Challenge Ciphertext Decryption Oracle Choose Ciphertext Attack Decryption Query
- 2.Bellare, M., Desai, A., Pointcheval, D., Rogaway, P.: Relations among notions of security for public-key encryption schemes. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 26–45. Springer, Heidelberg (1998)Google Scholar
- 4.Bellare, M., Waters, B., Yilek, S.: Identity-based encryption secure under selective opening attack (manuscript, 2010)Google Scholar
- 5.Bellare, M., Yilek, S.: Encryption Schemes Secure under Selective Opening Attack. Cryptology ePrint Archive, Report 2009/101 (2009)Google Scholar
- 9.Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd FOCS, October 2001, pp. 136–145. IEEE Computer Society Press, Los Alamitos (2001)Google Scholar
- 10.Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: 28th ACM STOC, pp. 639–648. ACM Press, New York (1996)Google Scholar
- 11.Canetti, R., Dwork, C., Naor, M., Ostrovsky, R.: Deniable encryption. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 90–104. Springer, Heidelberg (1997)Google Scholar
- 12.Canetti, R., Krawczyk, H., Nielsen, J.B.: Relaxing chosen-ciphertext security. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 565–582. Springer, Heidelberg (2003)Google Scholar
- 13.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)Google Scholar
- 20.Hemenway, B., Libert, B., Ostrovsky, R., Vergnaud, D.: Lossy encryption: Constructions from general assumptions and efficient selective opening chosen ciphertext security. Cryptology ePrint Archive, Report 2009/088 (2009)Google Scholar
- 21.Hofheinz, D.: Possibility and impossibility results for selective decommitments. IACR ePrint Archive (2008)Google Scholar
- 24.Katz, J., Ostrovsky, R.: Round-optimal secure two-party computation. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 335–354. Springer, Heidelberg (2004)Google Scholar
- 26.Kurosawa, K., Desmedt, Y.: A new paradigm of hybrid encryption scheme. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 426–442. Springer, Heidelberg (2004)Google Scholar
- 27.Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: 22nd STOC. ACM Press, New York (1990)Google Scholar
- 29.Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: 40th STOC, pp. 187–196. ACM Press, New York (2008)Google Scholar
- 30.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)Google Scholar