Abstract
Reverse firewalls were introduced at Eurocrypt 2015 by Miro-nov and Stephens-Davidowitz, as a method for protecting cryptographic protocols against attacks on the devices of the honest parties. In a nutshell: a reverse firewall is placed outside of a device and its goal is to “sanitize” the messages sent by it, in such a way that a malicious device cannot leak its secrets to the outside world. It is typically assumed that the cryptographic devices are attacked in a “functionality-preserving way” (i.e. informally speaking, the functionality of the protocol remains unchanged under this attacks). In their paper, Mironov and Stephens-Davidowitz construct a protocol for passively-secure two-party computations with firewalls, leaving extension of this result to stronger models as an open question.
In this paper, we address this problem by constructing a protocol for secure computation with firewalls that has two main advantages over the original protocol from Eurocrypt 2015. Firstly, it is a multiparty computation protocol (i.e. it works for an arbitrary number n of the parties, and not just for 2). Secondly, it is secure in much stronger corruption settings, namely in the active corruption model. More precisely: we consider an adversary that can fully corrupt up to \(n-1\) parties, while the remaining parties are corrupt in a functionality-preserving way.
Our core techniques are: malleable commitments and malleable non-interactive zero-knowledge, which in particular allow us to create a novel protocol for multiparty augmented coin-tossing into the well with reverse firewalls (that is based on a protocol of Lindell from Crypto 2001).
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Notes
- 1.
Since we use a NIZK proof system, we need to assume a trusted setup algorithm which generates a common reference string (CRS) to be used by all the parties. We assume that the CRS is hardwired inside the code of each party.
- 2.
Informally, the exfiltration-resistant property stipulates that the corrupt implementation of party does not leak any information through the firewall. Weak exfiltration-resistance guarantees the same property when the party is corrupted in a functionality-maintaining way (and not arbitrarily).
- 3.
One can modify the zero-knowledge proofs for the Graph Hamiltonicity problem or the 3-Coloring problem to obtain cm-IZK proofs by replacing the commitments with homomorphic commitments, similar to our coin-tossing protocol.
- 4.
Although the protocol of Lindell [24] is constant round, its round-complexity is greater than 4 due to the use of (constant-round) zero-knowledge proofs. We use NIZK arguments in a natural way to shrink the round-complexity of the protocol to 3, albeit introducing a trusted setup assumption, as required for NIZK protocols.
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Acknowledgments
We would like to thank the anonymous reviewers for their helpful comments and suggestions. The work was initiated while the first author was in IIT Madras, India. Part of this work was done while the author was visiting the University of Warsaw. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (682815 - TOCNeT) and from the Foundation for Polish Science under grant TEAM/2016-1/4 founded within the UE 2014–2020 Smart Growth Operational Program. The last author was supported by the Independent Research Fund Denmark project BETHE and the Concordium Blockchain Research Center, Aarhus University, Denmark.
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Chakraborty, S., Dziembowski, S., Nielsen, J.B. (2020). Reverse Firewalls for Actively Secure MPCs. In: Micciancio, D., Ristenpart, T. (eds) Advances in Cryptology – CRYPTO 2020. CRYPTO 2020. Lecture Notes in Computer Science(), vol 12171. Springer, Cham. https://doi.org/10.1007/978-3-030-56880-1_26
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