Evaluating card-based protocols in terms of execution time
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Evaluating card-based protocols in terms of execution time Daiki Miyahara1,2
· Itaru Ueda1 · Yu-ichi Hayashi3
· Takaaki Mizuki4
· Hideaki Sone4
© The Author(s) 2020
Abstract Card-based cryptography is an attractive and unconventional computation model; it provides secure computing methods using a deck of physical cards. It is noteworthy that a card-based protocol can be easily executed by non-experts such as high school students without the use of any electric device. One of the main goals in this discipline is to develop efficient protocols. The efficiency has been evaluated by the number of required cards, the number of colors, and the average number of protocol trials. Although these evaluation metrics are simple and reasonable, it is difficult to estimate the total number of operations or execution time of protocols based only on these three metrics. Therefore, in this paper, we consider adding other metrics to estimate the execution time of protocols more precisely. Furthermore, we actually evaluate some of the important existing protocols using our new criteria. Keywords Cryptography · Card-based protocols · Real-life hands-on cryptography · Secure multiparty computations
1 Introduction
♣ and a red card ♥ , a Boolean value can be expressed as:
Card-based protocols are unconventional computing methods using a deck of physical cards; their advantage is that they can be executed by humans practically (e.g., [4,8,11,16]). To illustrate this, let us explain how to manipulate Boolean values based on a two-colored deck of cards. Given a black card
♣ ♥ = 0, ♥ ♣ = 1.
An earlier version of this paper was presented at the 17th International Conference on Unconventional Computation and Natural Computation, Fontainebleau, France, June 25–29, 2018, and appeared in Proc. UCNC 2018, Lecture Notes in Computer Science, vol. 10867, Springer, pp.145–158, 2018 [7].
B
Daiki Miyahara [email protected] Takaaki Mizuki [email protected]
1
Graduate School of Information Sciences, Tohoku University, 6–3 Aramaki-Aza-Aoba, Aoba, Sendai 980-8578, Japan
2
National Institute of Advanced Industrial Science and Technology, 2–3–26, Aomi, Koto-ku, Tokyo 135-0064, Japan
3
Graduate School of Science and Technology, Nara Institute of Science and Technology, 8916–5 Takayama, Ikoma, Nara 630–0192, Japan
4
Cyberscience Center, Tohoku University, 6–3 Aramaki-Aza-Aoba, Aoba, Sendai 980-8578, Japan
(1)
Following this encoding, for example, two players, Alice and Bob, can each put two cards face down on a table, representing their private bits a and b, respectively: ? ?
? ? .
a
(2)
b
Here, we assume that the backs ? of all cards are indistinguishable and that the fronts ♣ or ♥ are also indistinguishable if the cards have the same color. We call the left pair of two face-down cards in (2) a commitment to a. Similarly, the right pair of two face-down cards are a commitment to b. Typically, given two input commitments to a, b ∈ {0, 1}, as in (2), a card
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