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\(\textsf{LR}\)-\(\textsf{OT}\): Leakage-Resilient Oblivious Transfer

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Security and Cryptography for Networks (SCN 2024)

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Abstract

Oblivious Transfer (\(\textsf{OT}\)) is a fundamental cryptographic primitive, becoming a crucial component of a practical secure protocol. \(\textsf{OT}\) is typically implemented in software, and one way to accelerate its running time is by using hardware implementations. However, such implementations are vulnerable to side-channel attacks (SCAs). On the other hand, protecting interactive protocols against SCA is highly challenging because of their longer secrets (which include inputs and randomness), more complicated design, and running multiple instances. Consequently, there are no truly practical leakage-resistant \(\textsf{OT}\) protocols yet.

In this paper, we introduce two tailored indistinguishability-based security definitions for leakage-resilient \(\textsf{OT}\), focusing on protecting the sender’s state. Second, we propose a practical semi-honest secure \(\textsf{OT}\) protocol that achieves these security levels while minimizing the assumptions on the protocol’s building blocks and the use of a secret state. Finally, we extend our protocol to support sequential composition and explore efficiency-security tradeoffs.

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Notes

  1. 1.

    Recall that in the security definitions of encryption schemes with leakage, we assume that the adversary knows the challenge ciphertext but has at most some leakage information about the key, here the adversary knows the key and has some information about the challenge ciphertext.

  2. 2.

    For example, if the oracle implements an encryption scheme \(\textsf{Enc}_k(m)\), and the adversary plays a \(\textsf{CPA}\)-game with leakage, the public input is m, chosen by the adversary, while the secret input is the key k. Thus, \(\mathcal {I}^{sec}=\mathcal {K}\), the key-space of the encryption scheme, while \(\mathcal {I}^{pub}=\mathcal {M}\), the message space.

  3. 3.

    Should not be confuse with secret-sharing, here a share merely describe part of the message.

  4. 4.

    In our model, these values are not deleted, but since the corresponding memory cells are not accessed anymore, they cannot be leaked.

  5. 5.

    It is well known that computation with asymmetric primitives leaks far more on each secret-bit of (say) the key as compared to symmetric primitives.

  6. 6.

    We are also inspired by the definition of security in the presence of leakage of the XOR of a pseudorandom value with a message block [9], where we give the leakage of the generation of the random block.

  7. 7.

    If k is unpredictable, then passing through an ideal cipher gives random outputs.

  8. 8.

    It is enough to XOR z with one share and keep all other shares to have an additive output sharing.

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Acknowledgments

Francesco Berti and Itamar Levi were founded by the Israel Science Foundation (ISF) grant 2569/21. Carmit Hazay was partially supported by the Algorand Centres of Excellence programme managed by Algorand Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Algorand Foundation, and the United States-Israel Binational Science Foundation (BSF) through Grant No. 2020277.

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  1. Bar-Ilan University, Ramat-Gan, Israel

    Francesco Berti, Carmit Hazay & Itamar Levi

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  1. Francesco Berti
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  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

  2. Télécom Paris, Paris, France

    Duong Hieu Phan

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Berti, F., Hazay, C., Levi, I. (2024). \(\textsf{LR}\)-\(\textsf{OT}\): Leakage-Resilient Oblivious Transfer. In: Galdi, C., Phan, D.H. (eds) Security and Cryptography for Networks. SCN 2024. Lecture Notes in Computer Science, vol 14973. Springer, Cham. https://doi.org/10.1007/978-3-031-71070-4_9

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