Abstract
In this paper, we introduce a new framework for constructing public-key encryption (PKE) schemes resilient to joint post-challenge/after-the-fact leakage and tampering attacks in the bounded leakage and tampering (BLT) model, introduced by Damgård et al. (Asiacrypt 2013). All the prior formulations of PKE schemes considered leakage and tampering attacks only before the challenge ciphertext is made available to the adversary. However, this restriction seems necessary, since achieving security against post-challenge leakage and tampering attacks in its full generality is impossible, as shown in previous works. In this paper, we study the post-challenge/after-the-fact security for PKE schemes against bounded leakage and tampering under a restricted yet meaningful and reasonable notion of security, namely, the split-state leakage and tampering model. We show that it is possible to construct secure PKE schemes in this model, tolerating arbitrary (but bounded) leakage and tampering queries; thus overcoming the previous impossibility results.
To this end, we formulate a new notion of security, which we call entropic post-challenge IND-CCA-BLT secure PKE. We first define a weaker notion called entropic restricted post-challenge IND-CCA-BLT secure PKE, which can be instantiated using the (standard) DDH assumption. We then show a generic compiler from our entropic restricted notion to the entropic notion of security using a simulation-extractable non-interactive zero-knowledge argument system. This requires an untamperable common reference string, as in previous works. Finally, we demonstrate the usefulness of our entropic notion of security by giving a simple and generic construction of post-challenge IND-CCA-BLT secure PKE scheme in the split-state leakage and tampering model. This also settles the open problem posed by Faonio and Venturi (Asiacrypt 2016).
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Notes
- 1.
However, note that, the tampering functions may be identity functions with respect to ciphertexts \(c \ne c^*\), where \(c^*\) is the challenge ciphertext. This also emulates access to the (original) decryption oracle to the adversary.
- 2.
For our construction the secret key is split into only two parts/splits, which is the optimal.
- 3.
When \(T_i(sk) = sk\), and the adversary gets access to the tampering oracle with respect to \(c^*\), it is emulating the scenario when it gets decryption oracle access with respect to sk on \(c^*\), which is anyway disallowed in the IND-CCA-2 security game.
- 4.
Recall when we write \(\mathsf {Dec}(\widetilde{sk}_\theta ,\cdot , \cdot )\), the second coordinate is the placeholder for ciphertexts input by the adversary; whereas the third coordinate is the placeholder for labels.
- 5.
In our construction, we will show that \(\mathcal {F}(t_{\mathsf {post}}) = t_{\mathsf {post}} \log p\), i.e., for each post-challenge tampering query we have to leak only one element of the base group \(\mathbb {G}\) of prime order p. This single element is sufficient to simulate polynomially many (modified) decryption queries with respect to each tampering query.
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Acknowledgments
We acknowledge the reviewers for their helpful comments. The authors are grateful to the project “Information Security Education and Awareness Program” of Ministry of Information Technology, Government of India for providing partial support.
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Chakraborty, S., Rangan, C.P. (2019). Public Key Encryption Resilient to Post-challenge Leakage and Tampering Attacks. In: Matsui, M. (eds) Topics in Cryptology – CT-RSA 2019. CT-RSA 2019. Lecture Notes in Computer Science(), vol 11405. Springer, Cham. https://doi.org/10.1007/978-3-030-12612-4_2
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