Toward Finite-Runtime Card-Based Protocol for Generating a Hidden Random Permutation without Fixed Points

Hashimoto, Yuji; Nuida, Koji; Shinagawa, Kazumasa; Inamura, Masaki; Hanaoka, Goichiro

doi:10.1587/transfun.e101.a.1503

Cited by 13 publications

(5 citation statements)

References 14 publications

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“…No player can prepare the same envelopes in his/her pocket and exchange them for the envelopes used in the protocol. Such envelopes are used in some cardbased protocols [8,45,58,63].…”

Section: Envelopesmentioning

confidence: 99%

“…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%

“…Envelopes are used in [38] to realize cryptographic protocols that do not use physical cards. In card-based cryptographic protocols, envelopes are used in [8,45,58,63] to realize some kind of shuffles that are not easy to be executed by people.…”

Section: Introductionmentioning

confidence: 99%

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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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“…No player can prepare the same envelopes in his/her pocket and exchange them for the envelopes used in the protocol. Such envelopes are used in some cardbased protocols [8,45,58,63].…”

Section: Envelopesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Card-Based Cryptographic Protocols with Malicious Players Using Private Operations

Manabe

Ono

2022

New Gener. Comput.

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“…In 2018, Hashimoto et al [4] proposed the first finite-runtime protocol for generating a uniformly distributed random derangement by using the properties of the types of permutations. While their proposed protocol is innovative, its feasibility to be performed by humans has not been studied, as it requires a shuffle operation with a nonuniform probability distribution.…”

Section: Introductionmentioning

confidence: 99%

Efficient Generation of a Card-Based Uniformly Distributed Random Derangement

Murata

Miyahara

Mizuki

et al. 2021

Lecture Notes in Computer Science

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Consider a situation, known as Secret Santa, where n players wish to exchange gifts such that each player receives exactly one gift and no one receives a gift from oneself. Each player only wants to know in advance for whom he/she should purchase a gift. That is, the players want to generate a hidden uniformly distributed random derangement. (Note that a permutation without any fixed points is called a derangement.) To solve this problem, in 2015, Ishikawa et al. proposed a simple protocol with a deck of physical cards. In their protocol, players first prepare n piles of cards, each of which corresponds to a player, and shuffle the piles. Subsequently, the players verify whether the resulting piles have fixed points somehow: If there is no fixed point, the piles serve as a hidden random derangement; otherwise, the players restart the shuffle process. Such a restart occurs with a probability of approximately 0.6. In this study, we consider how to decrease the probability of the need to restart the shuffle based on the aforementioned protocol. Specifically, we prepare more piles of cards than the number n of players. This potentially helps us avoid repeating the shuffle, because we can remove fixed points even if they arise (as long as the number of remaining piles is at least n). Accordingly, we propose an efficient protocol that generates a uniformly distributed random derangement. The probability of the need to restart the shuffle can be reduced to approximately 0.1.

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“…den Boer [2] first showed a five-card protocol to securely calculate AND of two inputs. Since then, many protocols have been proposed to calculate logical functions [4,5,21,24,27,30,40,44,47] and specific computations such as computations on three inputs [32,33,43], calculation of symmetric functions [41], millionaires' problem [18,29,37], voting [22,28,51], random permutation [6,8,9], grouping [7], matching [17], ranking [48], zero-knowledge proof of puzzle solutions [3,16,19,42] and so on. Most of the protocols assume a semi-honest model, that is, players obey the rule of the protocol but try to obtain secret values.…”

Section: Introductionmentioning

confidence: 99%

Card-Based Cryptographic Logical Computations Using Private Operations

Ono

Manabe

2020

New Gener. Comput.

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This paper proposes new card-based cryptographic protocols to calculate logic functions with the minimum number of cards using private operations under the semi-honest model. Though various card-based cryptographic protocols were shown, the minimum number of cards used in the protocol has not been achieved yet for many problems. Operations executed by a player where the other players cannot see are called private operations. Private operations have been introduced in some protocols to solve a particular problem or to input private values. However, the effectiveness of introducing private operations to the calculation of general logic functions has not been considered. This paper introduces three new private operations: private random bisection cuts, private reverse cuts, and private reveals. With these three new operations, we show that all of AND, XOR, and copy protocols are achieved with the minimum number of cards by simple three-round protocols. This paper then shows a protocol to calculate any logical functions using these private operations. Next, we consider protocols with malicious players.

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Toward Finite-Runtime Card-Based Protocol for Generating a Hidden Random Permutation without Fixed Points

Cited by 13 publications

References 14 publications

Card-Based Cryptographic Protocols with Malicious Players Using Private Operations

Card-Based Cryptographic Protocols with Malicious Players Using Private Operations

Efficient Generation of a Card-Based Uniformly Distributed Random Derangement

Card-Based Cryptographic Logical Computations Using Private Operations

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