Abstract
The key escrow problem is one of the main barriers to the widespread real-world use of identity-based encryption (IBE). Specifically, a key generation center (KGC), which generates secret keys for a given identity, has the power to decrypt all ciphertexts. At PKC 2009, Chow defined a notion of security against the KGC, that relies on assuming that it cannot discover the underlying identities behind ciphertexts. However, this is not a realistic assumption since, in practice, the KGC manages an identity list and hence it can easily guess the identities corresponding to given ciphertexts. Chow later closed the gap between theory and practice by introducing a new entity called an identity-certifying authority (ICA) and proposed an anonymous key-issuing protocol. Essentially, this allows the users, KGC, and ICA to interactively generate secret keys without users ever having to reveal their identities to the KGC. Unfortunately, the proposed protocol did not include a concrete security definition, meaning that all of the subsequent works following Chow lack the formal proofs needed to determine whether or not it delivers a secure solution to the key escrow problem.
In this paper, based on Chow’s work, we formally define an IBE scheme that resolves the key escrow problem and provide formal definitions of security against corrupted users, KGC, and ICA. Along the way, we observe that if we are allowed to assume a fully trusted ICA, as in Chow’s work, then we can construct a trivial (and meaningless) IBE scheme that is secure against the KGC. Finally, we present a lattice-based construction in our new security model based on the Gentry–Peikert–Vaikuntanathan (GPV) IBE scheme (STOC 2008) and Rückert’s lattice-based blind signature scheme (ASIACRYPT 2010).
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Notes
- 1.
Note that without an ICA this can never be secure since a malicious user can obtain \(\mathsf{sk}_{\mathsf{ID}}\) for any \(\mathsf{ID}\) without identification. Recall that in practice KGC implicitly authenticates the users to which it provides \(\mathsf{sk}_\mathsf{ID}\).
- 2.
We note that another potential path to resolving the key escrow problem may be to consider distributed KGCs. Specifically, it may be possible to use the threshold variant of GPV IBE scheme by Bendlin et al. [4] to obtain a lattice-based IBE scheme secure against the key escrow problem. We leave this as potential future direction.
- 3.
We note that the sampling algorithm \(\mathsf{CTSamp}\) does not necessarily have to be identical to the one we defined in the IND-ANON-CPA security. This is true for the subsequent IND-ANON-ICA security.
- 4.
In the same paper [10], Chow acknowledged this issue and introduced an anonymous key-issuing protocol to close the gap between the assumption and reality, however, he did not give any formal definition of ACI-KGC for IBE where secret keys are generated with this protocol.
- 5.
Looking ahead, this will be implicit in our definition since the \(\mathsf{IBE.Enc}\) algorithm is independent of \((\mathsf{vk},\mathsf{ik})\).
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Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers JP16K00198, JP17K12697, and JP17J05603, and was supported by JST CREST Grant Number JPMJCR19F6, Japan.
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Emura, K., Katsumata, S., Watanabe, Y. (2019). Identity-Based Encryption with Security Against the KGC: A Formal Model and Its Instantiation from Lattices. In: Sako, K., Schneider, S., Ryan, P. (eds) Computer Security – ESORICS 2019. ESORICS 2019. Lecture Notes in Computer Science(), vol 11736. Springer, Cham. https://doi.org/10.1007/978-3-030-29962-0_6
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