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From Selective to Full Security: Semi-Generic Transformations in the Standard Model.

Michel Ferreira Abdalla, Dario Fiore, Vadim Lyubashevsky

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

In this paper, we propose an efficient, standard model, semi-generic transformation of selectivesecure (Hierarchical) Identity-Based Encryption schemes into fully secure ones. The main step is a procedure that uses admissible hash functions (whose existence is implied by collision-resistant hash functions) to convert any selective-secure wildcarded identity-based encryption (WIBE) scheme into a fully secure (H)IBE scheme. Since building a selective-secure WIBE, especially with a selective-secure HIBE already in hand, is usually much less involved than directly building a fully secure HIBE, this transform already significantly simplifies the latter task. This black-box transformation easily extends to schemes secure in the Continual Memory Leakage (CML) model of Brakerski et al. (FOCS 2010), which allows us obtain a new fully secure IBE in that model. We furthermore show that if a selective-secure HIBE scheme satisfies a particular security notion, then it can be generically transformed into a selective-secure WIBE. We demonstrate that several current schemes already fit this new definition, while some others that do not obviously satisfy

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In this paper, we propose an efficient, standard model, semi-generic transformation of selectivesecure (Hierarchical) Identity-Based Encryption schemes into fully secure ones. The main step is a procedure that uses admissible hash functions (whose existence is implied by collision-resistant hash functions) to convert any selective-secure wildcarded identity-based encryption (WIBE) scheme into a fully secure (H)IBE scheme. Since building a selective-secure WIBE, especially with a selective-secure HIBE already in hand, is usually much less involved than directly building a fully secure HIBE, this transform already significantly simplifies the latter task. This black-box transformation easily extends to schemes secure in the Continual Memory Leakage (CML) model of Brakerski et al. (FOCS 2010), which allows us obtain a new fully secure IBE in that model. We furthermore show that if a selective-secure HIBE scheme satisfies a particular security notion, then it can be generically transformed into a selective-secure WIBE. We demonstrate that several current schemes already fit this new definition, while some others that do not obviously satisfy
We prove that there is no fully black-box construction of collision-resistant hash functions (CRH) from hierarchical identity-based encryption (HIBE) with arbitrary polynomial number of identity levels. As a corollary we obtain a series of separations showing that none of the primitives implied by HIBE in a black-box way (e.g., IBE, CCA-secure public-key encryption) can be used in a black-box way to construct fully homomorphic encryption or any other primitive that is known to imply CRH in a black-box way. To the best of our knowledge, this is the first limitation proved for the power of HIBE. Our proof relies on the reconstruction paradigm of Gennaro and Trevisan (FOCS 2000) and Haitner et al. (FOCS 2007) and extends their techniques for one-way and trapdoor permu-tations to the setting of HIBE. A technical challenge for our separation of HIBE stems from the adaptivity of the adversary who is allowed to obtain keys for different identities before she selects the attacked identity. Our main technical contribution is to show how to achieve com-
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.
Receiver selective opening (RSO) security considers the security of encryption schemes under the scenario of a single sender and multiple receivers, where an adversary is allowed to adaptively corrupt some receivers’ secret keys. RSO security has been proven to be more secure than indistinguishability-based security notions. A lot of research has focused on RSO security in terms of public-key encryption and identity-based encryption (IBE); however, hierarchical IBE (HIBE), which is a generalization of IBE, is still lacking in the study, and how to obtain such a construction remains an open problem. To address this gap, we initiate a study of RSO security on HIBE in this work. Precisely, we first formalize the definition of simulation-based RSO against identity-chosen-plaintext/ciphertext attacks in the k-challenge setting (SIM-ID-RSO k_kk​ -CPA/CCA) for HIBE. We then present generic SIM-ID-RSO k_kk​ -CCA secure HIBE constructions by introducing the double secret key paradigm. Specifically, we show that a SIM-ID-RSO k_kk​ -CCA secure HIBE scheme can be obtained from an IND-ID-CPA secure HIBE scheme as well as a one-time signature scheme that satisfies strong unforgeability. Through our general construction, we can derive various concrete schemes based on different hard assumptions (e.g., lattice-based and pairing-based SIM-ID-RSO k_kk​ -CCA secure HIBE schemes) according to usage requirements.
We propose two efficient Identity-Based threshold decryption schemes.They are proved secure against chosen ciphertext attacks under the standard decisional bilinear Diffie-Hellman assumption.The first one is constructed from(one of) the Selective ID-Based Encryption(Selective-IBE) scheme proposed by Boneh and Boyen recently,yet the second one is transformed from the Full ID-Based Encryption(Full-IBE) scheme obtained by Waters.As the based IBE schemes,the attacker in the first proposal has to choose the challenge identity before the common parameter is generated.while the attacker in the second one could choose the identity adaptively.To the best of our knowledge,previous related schemes could only be proved secure in the random oracle model.
Abstract We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length. The security reductions of previous HIBEs lose at least a factor of Q, which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation.