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Non-Interactive Anonymous Router with Quasi-Linear Router Computation

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14371))

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Abstract

Anonymous routing is an important cryptographic primitive that allows users to communicate privately on the Internet, without revealing their message contents or their contacts. Until the very recent work of Shi and Wu (Eurocrypt’21), all classical anonymous routing schemes are interactive protocols, and their security rely on a threshold number of the routers being honest. The recent work of Shi and Wu suggested a new abstraction called Non-Interactive Anonymous Router (NIAR), and showed how to achieve anonymous routing non-interactively for the first time. In particular, a single untrusted router receives a token which allows it to obliviously apply a permutation to a set of encrypted messages from the senders. Shi and Wu’s construction suffers from two drawbacks: 1) the router takes time quadratic in the number of senders to obliviously route their messages; and 2) the scheme is proven secure only in the presence of static corruptions.

In this work, we show how to construct a non-interactive anonymous router scheme with sub-quadratic router computation, and achieving security in the presence of adaptive corruptions. To get this result, we assume the existence of indistinguishability obfuscation and one-way functions. Our final result is obtained through a sequence of stepping stones. First, we show how to achieve the desired efficiency, but with security under static corruption and in a selective, single-challenge setting. Then, we go through a sequence of upgrades which eventually get us the final result. We devise various new techniques along the way which lead to some additional results. In particular, our techniques for reasoning about a network of obfuscated programs may be of independent interest.

P. Soni—Work was done partially when the author was visiting Carnegie Mellon University.

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Notes

  1. 1.

    Throughout the paper, we use \(O_\lambda (\cdot )\) to hide \({\textsf{poly}} (\lambda )\) multiplicative factors where \(\lambda \) denotes the security parameter.

  2. 2.

    In this sense, our adaptive corruption result is also interesting in the context of function-hiding MCFE since how to get function-hiding MCFE under adaptive corruption was not known earlier. The recent work of Shi and Vanjani [52] showed a function-hiding MCFE scheme for inner-product computation under static corruption, relying on standard bilinear group assumptions.

  3. 3.

    Informally speaking, SPB signatures have a special single-point binding property which states that it is possible to generate a special verification key w.r.t. a message \(m^*\) s.t. it only accepts a single signature for \(m^*\). Similarly, SPB hash functions have a special single-point binding property which states that it is possible to generate a special hash key w.r.t. a message \(m^*\) s.t. no hash collisions exist on \(m^*\).

  4. 4.

    Our formal proof in the technical sections actually first proves single, selective-challenge, static security only for an adversary subject to the following restrictions: it must corrupt all receivers, and submit two permutations that differ by a single inversion. We prove that even this weaker version is sufficient for our upgrade all the way to full security under adaptive corruption.

  5. 5.

    To be more precise there are \(c \cdot n\) wires in each layer for constant \(c \ge 2\), but for simplicity we assume \(c = 2\) as this is achieved by our proposed instantiation.

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Acknowledgements

Elaine Shi was supported by a DARPA SIEVE grant, a Packard Fellowship, a grant from Algorand Foundation, NSF awards under the grant numbers 2128519 and 2044679, and a grant from ONR under the award number N000142212064. Brent Waters was supported by NSF CNS-1908611, CNS-2318701 and Simons Investigator award.

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Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    Rex Fernando, Elaine Shi & Nikhil Vanjani

  2. University of Utah, Salt Lake City, USA

    Pratik Soni

  3. University of Texas at Austin, Austin, USA

    Brent Waters

  4. NTT Research, Sunnyvale, USA

    Brent Waters

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  1. Rex Fernando
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  2. Elaine Shi
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  3. Pratik Soni
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  4. Nikhil Vanjani
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Correspondence to Rex Fernando .

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  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Fernando, R., Shi, E., Soni, P., Vanjani, N., Waters, B. (2023). Non-Interactive Anonymous Router with Quasi-Linear Router Computation. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14371. Springer, Cham. https://doi.org/10.1007/978-3-031-48621-0_3

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