Abstract
Zero-knowledge shuffle arguments are a useful tool for constructing mix-nets which enable anonymous communication. We propose a new shuffle argument using a novel technique that probabilistically checks that each weighted set of input elements corresponds to some weighted set of output elements, with weights from the same set as the input element weights. We achieve this using standard discrete log assumptions and the shortest integer solution (SIS) assumption. Our shuffle argument has prover and verifier complexity linear in the size of the shuffled set, and communication complexity logarithmic both in the shuffled set size and security parameter.
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Notes
- 1.
Brands [10] called it the FindRep assumption and its known to be tightly equivalent to the discrete logarithm assumption.
- 2.
If non-trivial DLRELs are known between the input elements and the value h, there are attacks that succeed with overwhelming probability.
- 3.
Essentially finding a DLREL that holds both between the original commitments and the rerandomized ones, is related to solving a linear equation with \(N\) variables with two equations.
- 4.
The number v here depends on our SIS-assumption. If a cheating prover wants to use some known non-trivial discrete relation between the inputs, the relation has to be “short” and same across every rerandomization, meaning that effectively using it would break the SIS-assumption. We will expand on this more formally later.
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Acknowledgment
This research is supported by the National Research Foundation, Singapore under its Strategic Capability Research Centres Funding Initiative. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore.
Author Toomas Krips was partly supported by the Estonian Research Council, ETAG, through grant PRG 946.
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Abdolmaleki, B., Fauzi, P., Krips, T., Siim, J. (2024). Shuffle Arguments Based on Subset-Checking. 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_16
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