Abstract
Card-based protocols provide secure multi-party computation using a deck of physical cards, via a series of operations such as shuffling and turning over cards, which are supposed to be executed by humans. Although almost all existing protocols have been designed to be perfectly secure, operative errors by humans would cause information leakage. In this paper, we propose a technique for analyzing information leakage due to operative errors in card-based protocols. To be specific, we introduce a concept, which we call a “probability trace,” and propose a new diagram for displaying how much information leaks, by enhancing the KWH diagram proposed by Koch, Walzer, and Härtel. By applying our diagram to a card-based protocol with an operative error, we can precisely reveal the leakage of players’ inputs from the protocol output. We also discuss an application of the diagram to human-error-free implementations of the existing six-card AND protocol.
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Notes
- 1.
We omit the description of \(\mathcal {F}\) if the distribution is uniform.
- 2.
If the back of the card is symmetric, it is possible to make the back asymmetric by putting a mark on it.
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Acknowledgments
This work was supported by JSPS KAKENHI Grant Number JP17K00001.
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Mizuki, T., Komano, Y. (2018). Analysis of Information Leakage Due to Operative Errors in Card-Based Protocols. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_21
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DOI: https://doi.org/10.1007/978-3-319-94667-2_21
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