Abstract
Consider the holiday season, where there are n players who would like to exchange gifts. That is, we would like to generate a random permutation having no fixed point. It is known that such a random permutation can be obtained in a hidden form by using a number of physical cards of four colors with identical backs, guaranteeing that it has no fixed point (without revealing the permutation itself). This paper deals with such a problem and improves the known result: whereas the known protocol needs \(O(n^2)\) cards of four colors, our efficient protocol uses only \(O(n \log n)\) cards of two colors.
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Notes
- 1.
Throughout this paper, we say that a card has the same “color” as another one if they have the same pattern on their face sides.
- 2.
Note that we cannot use a standard deck of playing cards because each of them has a unique pattern on its face side.
- 3.
All logarithms are base 2 throughout this paper.
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Acknowledgments
We thank the anonymous referees whose comments helped us to improve the presentation of the paper. This work was supported by JSPS KAKENHI Grant Number 26330001.
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Ishikawa, R., Chida, E., Mizuki, T. (2015). Efficient Card-Based Protocols for Generating a Hidden Random Permutation Without Fixed Points. In: Calude, C., Dinneen, M. (eds) Unconventional Computation and Natural Computation. UCNC 2015. Lecture Notes in Computer Science(), vol 9252. Springer, Cham. https://doi.org/10.1007/978-3-319-21819-9_16
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