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Journal of Cryptology

Deterministic Public-Key Encryption for Adaptively-Chosen Plaintext Distributions

Ananth Raghunathan, Gil Segev, Salil Vadhan

Published Mar 21, 2018• 6 citations
Publisher
DOI
10.1007/s00145-018-9287-y

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Bellare, Boldyreva, and O’Neill (CRYPTO ’07) initiated the study of deterministic public-key encryption as an alternative in scenarios where randomized encryption has inherent drawbacks. Theresultinglineofresearchhassofarguaranteedsecurityonlyforadversarially-chosenplaintext distributions that are independent of the public key used by the scheme. In most scenarios, however, it is typically not realistic to assume that adversaries do not take the public key into account when attacking a scheme. We show that it is possible to guarantee meaningful security even for plaintext distributions that depend on the public key. We extend the previously proposed notions of security, allowing adversaries to adaptively choose plaintext distributions after seeing the public key, in an interactive manner. The onlyrestrictionswemakearethat: (1) plaintextdistributionsareunpredictable (as is essential in deterministic public-key encryption), and (2) the number of plaintext distributions from which each adversary is allowed to adaptively choose is upper bounded by 2 p, where p can be any predetermined polynomial in the security parameter. For example, with p = 0 we capture plaintext distributions that are independent of the public key, and with p = O(slogs)
Deterministic public-key encryption, encrypting a plaintext into a unique ciphertext without involving any randomness, was introduced by Bellare, Boldyreva, and O'Neill (CRYPTO 2007) as a realistic alternative to some inherent drawbacks in randomized public-key encryption. Bellare, Kiltz, Peikert and Waters (EUROCRYPT 2012) bring deterministic public-key encryption to the identity-based setting, and propose deterministic identity-based encryption scheme (DIBE). Although the construc- tions of chosen plaintext attack (CPA) secure DIBE scheme have been studied intensively, the construction of chosen ciphertext attack (CCA) secure DIBE scheme is still challenging problems. In this paper, we introduce the notion of identity-based all-but-one trapdoor functions (IB-ABO-TDF), which is an extension version of all-but-one lossy trapdoor function in the public-key setting. We give a instantiation of IB-ABO-TDF under decisional linear assumption. Based on an identity-based lossy trapdoor function and our IB-ABO-TDF, we present a generic construction of CCA-secure DIBE scheme.