Abstract
In 1989, den Boer presented the first card-based protocol, called the “five-card trick” that securely computes the AND function using a deck of physical cards via a series of actions such as shuffling and turning over cards. This protocol enables a couple to confirm their mutual love without revealing their individual feelings. During such a secure computation protocol, it is important to keep any information about the inputs secret. Almost all existing card-based protocols are secure under the assumption that all players participating in a protocol are semi-honest or covert, i.e., they do not deviate from the protocol if there is a chance that they will be caught when cheating. In this paper, we consider a more malicious attack in which a player as an active adversary can reveal cards illegally without any hesitation. Against such an actively revealing card attack, we define the t-secureness, meaning that no information about the inputs leaks even if at most t cards are revealed illegally. Subsequently, we design a 1-secure AND protocol. Thus, our contribution is the construction of the first formal framework to handle actively revealing card attacks and their countermeasures.
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- 1.
It is well known that humans can implement a random cut securely [13].
- 2.
We can specify the boundary between commitments by the color of consecutive cards. For example, if we obtain a sequence \(\clubsuit \clubsuit \heartsuit \clubsuit \heartsuit \clubsuit \heartsuit \heartsuit \), we can place delimiters in the middle of each of \(\clubsuit \clubsuit \) and \(\heartsuit \heartsuit \) as \(\clubsuit |\clubsuit \heartsuit \clubsuit \heartsuit \clubsuit \heartsuit |\heartsuit \); hence, we have \(\clubsuit \heartsuit |\clubsuit \heartsuit |\clubsuit \heartsuit |\heartsuit \clubsuit \).
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Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers JP17K00001 and JP19J21153. We would like to thank the anonymous reviewers for their fruitful comments.
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Takashima, K., Miyahara, D., Mizuki, T., Sone, H. (2019). Card-Based Protocol Against Actively Revealing Card Attack. In: Martín-Vide, C., Pond, G., Vega-Rodríguez, M. (eds) Theory and Practice of Natural Computing. TPNC 2019. Lecture Notes in Computer Science(), vol 11934. Springer, Cham. https://doi.org/10.1007/978-3-030-34500-6_6
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