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CCA-Secure Deterministic Identity-Based Encryption Scheme

Bo Yang, Kaitai Liang, Liang Xue, Meijuan Huang, Xiaoyi Yang, Yi Zhao

Published Apr 7, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.3217/jucs-025-03-0245

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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.
Functional encryption (FE) can implement fine-grained control to encrypted plaintext via permitting users to compute only some specified functions on the encrypted plaintext using private keys with respect to those functions. Recently, many FEs were put forward; nonetheless, most of them cannot resist chosen-ciphertext attacks (CCAs), especially for those in the secret-key settings. This changed with the work, i.e., a generic transformation of public-key functional encryption (PK-FE) from chosen-plaintext (CPA) to chosen-ciphertext (CCA), where the underlying schemes are required to have some special properties such as restricted delegation or verifiability features. However, examples for such underlying schemes with these features have not been found so far. Later, a CCA-secure functional encryption from projective hash functions was proposed, but their scheme only applies to inner product functions. To construct such a scheme, some nontrivial techniques will be needed. Our key contribution in this work is to propose CCA-secure functional encryptions in the PKE and SK environment, respectively. In the existing generic transformation from (adaptively) simulation-based CPA- (SIM-CPA-) secure ones for deterministic functions to (adaptively) simulation-based CCA- (SIM-CCA-) secure ones for randomized functions, whether the schemes were directly applied to CCA settings for deterministic functions is not implied. We give an affirmative answer and derive a SIM-CCA-secure scheme for deterministic functions by making some modifications on it. Again, based on this derived scheme, we also propose an (adaptively) indistinguishable CCA- (IND-CCA-) secure SK-FE for deterministic functions. The final results show that our scheme can be instantiated under both nonstandard assumptions (e.g., hard problems on multilinear maps and indistinguishability obfuscation (IO)) and under standard assumptions (e.g., DDH, RSA, LWE, and LPN).
We propose a generic construction that yields efficient identity-based encryption (IBE) schemes secure against chosen ciphertext attack (CCA) in the standard model. Our construction extends Kiltz et al.'s (Eurocrypt '09) method of constructing CCA-secure public-key encryption schemes via randomness extraction to the identity-based setting. The main idea of our construction is to transform ‘|ϵ1\epsilon _1ϵ1​|-almost |$\kappa ∣−entropic’andvalid/invalidciphertextindistinguishable(VI−IND)identity−basedhashproofsystemtotheonethatsatisfiesthestronger‘∣|-entropic’ and valid/invalid ciphertext indistinguishable (VI-IND) identity-based hash proof system to the one that satisfies the stronger ‘|∣−entropic’andvalid/invalidciphertextindistinguishable(VI−IND)identity−basedhashproofsystemtotheonethatsatisfiesthestronger‘∣\epsilon _2$|-universal’ and VI-IND property. This transformation is realized by a randomness extractor based on the 4-wise hash function. We demonstrate that our generic construction can produce CCA-secure IBE schemes whose efficiency is comparable with the most efficient but non-generic CCA-secure IBE schemes without random oracles in the literature.
Abstract We initiate the study of one-wayness under correlated products. We are interested in identify-ing necessary and sufficient conditions for a function f and a distribution on inputs (x1,..., xk),so that the function ( f (x1),..., f (xk)) is one-way. The main motivation of this study is theconstruction of public-key encryption schemes that are secure against chosen-ciphertext attacks (CCA). We show that any collection of injective trapdoor functions that is secure under a verynatural correlated product can be used to construct a CCA-secure public-key encryption scheme. The construction is simple, black-box, and admits a direct proof of security.We provide evidence that security under correlated products is achievable by demonstrating that lossy trapdoor functions (Peikert and Waters, STOC '08) yield injective trapdoor functionsthat are secure under the above mentioned correlated product. Although we currently base security under correlated products on existing constructions of lossy trapdoor functions, weargue that the former notion is potentially weaker as a general assumption. Specifically, there is no fully-black-box construction of lossy trapdoor functions from trapdoor functions that aresecure under correlated products.
Abstract. We use hybrid encryption with Fuzzy Identity-Based Encryption (Fuzzy-IBE) schemes, and present the first and efficient fuzzy identity-based key encapsulation mechanism (Fuzzy-IB-KEM) schemes which are chosen-ciphertext secure (CCA) without random oracle in the selective-ID model. To achieve these goals, we consider Fuzzy-IBE schemes as consisting of separate key and data encapsulation mechanisms (KEM-DEM), and then give the definition of Fuzzy-IB-KEM. Our main idea is to enhance Sahai and Waters ' "large universe " construction, chosen-plaintext secure (CPA) Fuzzy-IBE, by adding some redundant information to the ciphertext to make it CCA-secure.
We initiate the study of one-wayness under correlated products. We are interested in identifying necessary and sufficient conditions for a function f and a distribution on inputs (x1,…,xk)(x_1,\dots,x_k)(x1​,…,xk​) so that the function (f(x1),…,f(xk))(f(x_1),\dots,f(x_k))(f(x1​),…,f(xk​)) is one-way. The main motivation of this study is the construction of public-key encryption schemes that are secure against chosen-ciphertext attacks (CCAs). We show that any collection of injective trapdoor functions that is secure under a very natural correlated product can be used to construct a CCA-secure public-key encryption scheme. The construction is simple, black-box, and admits a direct proof of security. It can be viewed as a simplification of the seminal work of Dolev, Dwork, and Naor [SIAM J. Comput., 30 (2000), pp. 391–437], while relying on a seemingly incomparable assumption. We provide evidence that security under correlated products is achievable by demonstrating that lossy trapdoor functions [Peikert and Waters, Proceedings of the 40th Annual ACM Symposium on Theory of Computing, 2008, pp. 187–196] yield injective trapdoor functions that are secure under the above-mentioned correlated product. Although we currently base security under correlated products on existing constructions of lossy trapdoor functions, we argue that the former notion is potentially weaker as a general assumption. Specifically, there is no fully black-box construction of lossy trapdoor functions from trapdoor functions that are secure under correlated products.
An anonymous identity based encryption (anonymous IBE) scheme requires that an adversary can not determine the identity of the recipient from a ciphertext encrypted by the corresponding public key. The anonymity was formalized in previous works [1], [13], and this can be considered under chosen plaintext attack and adaptive chosen ciphertext attack, yielding two notions of security, ID-II-CPA and ID-II-CCA, where II denotes “indistinguishability of identities.” However, how to obtain an ID-II-CCA secure anonymous IBE in the random oracle model is still a challenging problem. We firstly propose a new notion of plaintext awareness in the two identities setting, called PATI. Secondly, we prove that the IBE scheme is ID-II-CCA secure if it is PATI secure. Finally, we propose the first generic conversion for anonymous IBE from ID-II-CPA to ID-II-CCA in the random oracle model.