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International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2020: Advances in Cryptology – ASIACRYPT 2020 pp 653–685Cite as

Cryptography from One-Way Communication: On Completeness of Finite Channels

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12493)

Abstract

Garg et al. (Crypto 2015) initiated the study of cryptographic protocols over noisy channels in the non-interactive setting, namely when only one party speaks. A major question left open by this work is the completeness of finite channels, whose input and output alphabets do not grow with the desired level of security. In this work, we address this question by obtaining the following results:

  1. 1.

    Completeness of Bit-ROT with Inverse Polynomial Error. We show that bit-ROT (i.e., Randomized Oblivious Transfer channel, where each of the two messages is a single bit) can be used to realize general randomized functionalities with inverse polynomial error. Towards this, we provide a construction of string-ROT from bit-ROT with inverse polynomial error.

  2. 2.

    No Finite Channel is Complete with Negligible Error. To complement the above, we show that no finite channel can be used to realize string-ROT with negligible error, implying that the inverse polynomial error in the completeness of bit-ROT is inherent. This holds even with semi-honest parties and for computational security, and is contrasted with the (negligible-error) completeness of string-ROT shown by Garg et al.

  3. 3.

    Characterization of Finite Channels Enabling Zero-Knowledge Proofs. An important instance of secure computation is zero-knowledge proofs. Noisy channels can potentially be used to realize truly non-interactive zero-knowledge proofs, without trusted common randomness, and with non-transferability and deniability features that cannot be realized in the plain model. Garg et al. obtain such zero-knowledge proofs from the binary erasure channel (BEC) and the binary symmetric channel (BSC). We complete the picture by showing that in fact any non-trivial channel suffices.

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Notes

  1. 1.

    In more detail, the sender can generate an anonymous \(\$100\) bill by letting the input be \(m\,=\,\)(Sender-name, 100) and the transmitted message be (m, id) for a random identifier id picked by the functionality. Consider the scenario where multiple \(\$100\) bills are sent to different receivers. The id is needed to prevent double spending. Anonymity comes from the fact that the sender doesn’t learn id, so it cannot associate a particular \(\$100\) bill with the receiver to whom it was sent.

  2. 2.

    Indeed, an \(\mathsf {OWSC} / {\mathcal {C}}\) ZK-PoK protocol is equivalent to an information-theoretic UC-secure protocol for the ZK functionality in the \(\mathcal {C}\)-hybrid model, with an additional requirement that the protocol involves a single invocation of \(\mathcal {C}\) and no other communication.

  3. 3.

    Note that the conceptually simpler approach of applying NIZK proofs is not applicable here, since in the setting of secure computation over noisy channels there is no public transcript to which such a proof can apply.

  4. 4.

    The notions of redundancy and core were defined more generally in [21], in the context of 2-party functionalities where both parties have inputs and outputs. Here we present simpler definitions that suffice for the case of channels.

  5. 5.

    This is essentially identical to the Von Neumann extractor trick.

  6. 6.

    In [17], an encoding scheme was used to argue that with some probability, the bits sent through the BSC are “erased.” But this encoding turns out to be redundant, as a BSC implicitly guarantees erasure: Concretely, a BSC with error probability p can be simulated by post-processing a BEC with erasure probability 2p. The post-processing corresponds to decoding the erasure symbol as a uniformly random bit.

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Acknowledgements

We thank the anonymous Asiacrypt reviewers for their careful reading and many helpful comments. This Research was supported by Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India, and in part by the International Centre for Theoretical Sciences (ICTS) during a visit for participating in the program-Foundational Aspects of Blockchain Technology (ICTS/Prog-fabt2020/01). In addition, S. Agrawal was supported by the DST “Swarnajayanti” fellowship, and Indo-French CEFIPRA project; Y. Ishai was supported by ERC Project NTSC (742754), NSF-BSF grant 2015782, ISF grant 2774/20, and BSF grant 2018393; E. Kushilevitz was supported by ISF grant 2774/20, BSF grant 2018393, and NSF-BSF grant 2015782; V. Narayanan and V. Prabhakaran were supported by the Department of Atomic Energy, Government of India, under project no. RTI4001, DAE OM No. 1303/4/2019/R&D-II/DAE/1969 dated 7.2.2020; M. Prabhakaran was supported by the Dept. of Science and Technology, India via the Ramanujan Fellowship; A. Rosen was supported in part by ISF grant No. 1399/17 and Project PROMETHEUS (Grant 780701).

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Authors and Affiliations

  1. Indian Institute of Technology Madras, Chennai, India

    Shweta Agrawal

  2. Technion, Haifa, Israel

    Yuval Ishai & Eyal Kushilevitz

  3. Tata Institute of Fundamental Research, Mumbai, India

    Varun Narayanan & Vinod Prabhakaran

  4. Indian Institute of Technology Bombay, Mumbai, India

    Manoj Prabhakaran

  5. IDC Herzliya, Herzliya, Israel

    Alon Rosen

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  1. Shweta Agrawal
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  2. Yuval Ishai
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  6. Vinod Prabhakaran
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  7. Alon Rosen
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Correspondence to Varun Narayanan .

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  1. Network Security Research Institute (NICT), Tokyo, Japan

    Shiho Moriai

  2. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Agrawal, S. et al. (2020). Cryptography from One-Way Communication: On Completeness of Finite Channels. In: Moriai, S., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2020. ASIACRYPT 2020. Lecture Notes in Computer Science(), vol 12493. Springer, Cham. https://doi.org/10.1007/978-3-030-64840-4_22

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  • DOI: https://doi.org/10.1007/978-3-030-64840-4_22

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