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Forward Security Under Leakage Resilience, Revisited

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Cryptology and Network Security (CANS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14342))

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Abstract

As both notions employ the same key-evolution paradigm, Bellare et al. (CANS 2017) study combining forward security with leakage resilience. The idea is for forward security to serve as a hedge in case at some point the full key gets exposed from the leakage. In particular, Bellare et al. combine forward security with continual leakage resilience, dubbed FS+CL. Our first result improves on Bellare et al.’s FS+CL secure PKE scheme by building one from any continuous leakage-resilient binary-tree encryption (BTE) scheme; in contrast, Bellare et al. require extractable witness encryption. Our construction also preserves leakage rate of the underlying BTE scheme and hence, in combination with existing CL-secure BTE, yields the first FS+CL secure encryption scheme with optimal leakage rate from standard assumptions.

We next explore combining forward security with other notions of leakage resilience. Indeed, as argued by Dziembowski et al. (CRYPTO 2011), it is desirable to have a deterministic key-update procedure, which FS+CL does not allow for arguably pathological reasons. To address this, we combine forward security with entropy-bounded leakage (FS+EBL). We construct FS+EBL non-interactive key exchange (NIKE) with deterministic key update based on indistinguishability obfuscation (\(i\mathcal {O}\)), and DDH or LWE. To make the public keys constant size, we rely on the Superfluous Padding Assumption (SuPA) of Brzuska and Mittelbach (ePrint 2015) without auxiliary information, making it more plausible. SuPA notwithstanding, the scheme is also the first FS-secure NIKE from \(i\mathcal {O}\) rather than multilinear maps. We advocate a future research agenda that uses FS+EBL as a hedge for FS+CL, whereby a scheme achieves the latter if key-update randomness is good and the former if not.

H. Karthikeyan—Work done while at New York University, New York, USA.

C. P. Rangan—Research partially supported by KIAC research grant.

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Notes

  1. 1.

    We stress that our scheme supports an exponential number of time periods; however, the adversary can only run for a polynomial number of them. Hence we incur a polynomial security loss in making this guess.

  2. 2.

    Recall that in HIBE the tree can have an arbitrary degree.

  3. 3.

    Note that, this model where the adversary specifies the target node \(w^*\) ahead of time is weaker than the model where the adversary may choose the target adaptively (analogous to the adaptive security of HIBE schemes). However, as we will show, this model already suffices to construct of a FS+CL encryption scheme.

  4. 4.

    In particular, the adversary receives the secret keys of all the nodes that are siblings of all the nodes that are on the path from the root node to the target node \(w^*\).

  5. 5.

    This is equivalent to a definition where, in each round, the adversary asks for multiple leakage functions adaptively, such that the output length of all these functions sum up to \(\lambda (\kappa )\).

  6. 6.

    If the adversary is allowed to ask leakage queries after receiving the challenge ciphertext, it can encode the entire decryption algorithm of \(C^*\) as a function on a secret key, and thus win the game trivially.

  7. 7.

    The original CHK transform [12] is used to construct a forward-secure PKE scheme starting from a BTE scheme.

  8. 8.

    Recall that \(\mathcal {A}_{\mathsf {clr\text {-}bte}}\) receives the secret keys of all the nodes that are right siblings of the nodes that lie on the path P from the root node to \(w^{i^*}\).

  9. 9.

    Our construction will achieve security for arbitrary polynomial T.

  10. 10.

    A \((\kappa ,k,m)\)-lossy function maps an input from \(x \in \{0,1\}^\kappa \) to an output \(y \in \{0,1\}^m\). In the lossy mode, the image size of the function is at most \(2^{\kappa -k}\) with high probability.

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Author information

Authors and Affiliations

  1. Visa Research, Palo Alto, CA, USA

    Suvradip Chakraborty

  2. J.P. Morgan AI Research, New York, USA

    Harish Karthikeyan

  3. Manning College of Information and Computer Sciences, University of Massachusetts Amherst, Amherst, USA

    Adam O’Neill

  4. Kotak Mahindra, IISc Bangalore, Bengaluru, India

    C. Pandu Rangan

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  1. Suvradip Chakraborty
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  4. C. Pandu Rangan
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Correspondence to Suvradip Chakraborty .

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  1. University of North Carolina, Greensboro, NC, USA

    Jing Deng

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

  3. Augusta University, Augusta, GA, USA

    Alexander A. Schwarzmann

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Chakraborty, S., Karthikeyan, H., O’Neill, A., Rangan, C.P. (2023). Forward Security Under Leakage Resilience, Revisited. In: Deng, J., Kolesnikov, V., Schwarzmann, A.A. (eds) Cryptology and Network Security. CANS 2023. Lecture Notes in Computer Science, vol 14342. Springer, Singapore. https://doi.org/10.1007/978-981-99-7563-1_1

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