The Five-Card Trick Can Be Done with Four Cards

Mizuki, Takaaki; Kumamoto, Michihito; Sone, Hideaki

doi:10.1007/978-3-642-34961-4_36

Cited by 73 publications

(19 citation statements)

References 7 publications

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“…On the other hand, PP enables players' malicious behaviors. 4 Our protocols suppose the semi-honest model, which assumes all players follow the protocols.…”

Section: Private Modelmentioning

confidence: 99%

Secure Computation for Threshold Functions with Physical Cards: Power of Private Permutations

et al. 2022

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Card-based cryptography is a variant of multi-party computation using physical cards like playing cards. There are two models on card-based cryptography, called public and private models. The public model assumes that all operations are executed publicly, while the private model allows the players private operations called private permutations (PP, for short). Much of the existing card-based protocols were developed under the public model. Under the public model, 2n cards are necessary for every protocol with n-bit input since at least two cards are required to express a bit. In this paper, we propose n-bit input protocols with fewer than 2n cards by utilizing PP, which shows the power of PP. In particular, we show that a protocol for (n-bit input) threshold function can be realized with only $$n+1$$ n + 1 cards by reducing the threshold function to the majority voting. Toward this end, we first offer that two-bit input protocols for logic gates can be realized with fewer than four cards. Furthermore, we construct a new protocol for three-input majority voting with only four cards by observing the relationship between AND/OR operations. This protocol can be easily extended to more participants, and to the protocol for threshold functions.

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“…On the other hand, PP enables players' malicious behaviors. 4 Our protocols suppose the semi-honest model, which assumes all players follow the protocols.…”

Section: Private Modelmentioning

confidence: 99%

Secure Computation for Threshold Functions with Physical Cards: Power of Private Permutations

et al. 2022

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“…Mizuki et al [7] later improved the five-card trick protocol so that it requires only four cards instead of five. While both protocols are useful, the format of the output value a ∧ b is different from the format of the inputs a and b (♣♥ for 0 and ♥♣ for 1).…”

Section: The Five-card Trickmentioning

confidence: 99%

AND Protocols Using only Uniform Shuffles

Ruangwises

Itoh

2019

Lecture Notes in Computer Science

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Secure multi-party computation using a deck of playing cards has been a subject of research since the "five-card trick" introduced by den Boer in 1989. One of the main problems in card-based cryptography is to design committed-format protocols to compute a Boolean AND operation subject to different runtime and shuffle restrictions by using as few cards as possible. In this paper, we introduce two AND protocols that use only uniform shuffles. The first one requires four cards and is a restart-free Las Vegas protocol with finite expected runtime. The second one requires five cards and always terminates in finite time.

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“…den Boer [2] first showed a five-card protocol to securely calculate logical AND of two inputs. Since then, many protocols have been proposed to realize primitives to calculate any logical functions [14,18,24,37,42,48,49,62,63] and specific computations such as a specific class of logical functions [1,7,13,19,23,25,31,33,43,46,54,58,61,68], universal computation such as Turing machines [6,16], millionaires' problem [27,40,47], voting [32,41,44,69,70], random permutation [8,10,11,39], grouping [9], ranking [66], lottery [64], proof of knowledge of a puzzle solution [3, 5, 12, 21, 26, 28, 29, 50-53, 55-57, 59], and so on. This paper considers calculations of logical functions and a copy operation under the malicious model since any logical function can be realized with a combination of these calculations.…”

Section: Introductionmentioning

confidence: 99%

Card-Based Cryptographic Protocols with Malicious Players Using Private Operations

Manabe

Ono

2022

New Gener. Comput.

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This paper shows new card-based cryptographic protocols using private operations that are secure against malicious players. Physical cards are used in card-based cryptographic protocols instead of computers. Operations that a player executes in a place where the other players cannot see are called private operations. Using several private operations, calculations of two variable Boolean functions and copy operations were realized with the minimum number of cards. Though private operations are very powerful in card-based cryptographic protocols, there is a problem that it is very hard to prevent malicious actions during private operations. Though most card-based protocols are discussed in the semi-honest model, there might be cases when the semi-honest model is not enough. Thus, this paper shows new protocols that are secure against malicious players. We show logical XOR, logical AND, n-variable Boolean function, and copy protocols. We can execute any logical computations with a combination of these protocols. We use envelopes as an additional tool that can be easily prepared and used by people.

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The Five-Card Trick Can Be Done with Four Cards

Cited by 73 publications

References 7 publications

Secure Computation for Threshold Functions with Physical Cards: Power of Private Permutations

Secure Computation for Threshold Functions with Physical Cards: Power of Private Permutations

AND Protocols Using only Uniform Shuffles

Card-Based Cryptographic Protocols with Malicious Players Using Private Operations

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