Card-Based Cryptographic Protocols Using a Minimal Number of Cards

Koch, Alexander; Walzer, Stefan; Härtel, Kevin

doi:10.1007/978-3-662-48797-6_32

Cited by 86 publications

(54 citation statements)

References 9 publications

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“…Previously, the bounds in Table 2 were all tight except in the third row (restart-free Las Vegas, uniform) where the trivial lower bound was four (since we need at least two cards for a commitment of each player's bit) but the upper bound was five (protocol of Abe et al [1]), and the sixth row (finite, uniform) where the lower bound was five [5] but the upper bound was six (protocol of Mizuki and Sone [9]).…”

Section: Our Contributionmentioning

confidence: 98%

“…In this paper we use a KWH-tree, a tool developed by Koch et al [5], to help verify the correctness and security of the protocol. X 00 , X 01 , X 10 , and X 11 denote the probabilities of (a, b) being (0, 0), (0, 1), (1, 0), and (1, 1), respectively, with shorthands X 0 = X 00 + X 01 + X 10 and X 1 = X 11 being used.…”

Section: Proof Of Correctness and Securitymentioning

confidence: 99%

“…More recently in 2009, Mizuki and Sone[9] developed an AND protocol using only six cards. This was an important milestone since their protocol was the first one that has finite runtime.Koch et al[5] investigated a novel way of shuffles that are not uniform or closed. That reduced the number of cards to five for finite protocol, and four for Las Vegas protocol with finite expected runtime.…”

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confidence: 99%

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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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Section: Our Contributionmentioning

confidence: 98%

Section: Proof Of Correctness and Securitymentioning

confidence: 99%

mentioning

confidence: 99%

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AND Protocols Using only Uniform Shuffles

Ruangwises

Itoh

2019

Lecture Notes in Computer Science

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“…We also use x to denote not only an element in Z 4 but also the front side card, as long as it is clear from the context. The important property is that [2]] and [ [3]] have the identical face ■ .…”

Section: Regular Polygon Cardsmentioning

confidence: 99%

Card-Based Protocols Using Regular Polygon Cards

Shinagawa

Mizuki

Schuldt

et al. 2017

IEICE Trans. Fundamentals

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SUMMARY Cryptographic protocols enable participating parties to compute any function of their inputs without leaking any information beyond the output. A card-based protocol is a cryptographic protocol implemented by physical cards. In this paper, for constructing protocols with small numbers of shuffles, we introduce a new type of cards, regular polygon cards, and a new protocol, oblivious conversion. Using our cards, we construct an addition protocol on non-binary inputs with only one shuffle and two cards. Furthermore, using our oblivious conversion protocol, we construct the first protocol for general functions in which the number of shuffles is linear in the number of inputs. key words: card-based protocol, regular polygon cards

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“…(The Five-Card Trick [1] does not enjoy this property since it outputs the value of x ∧ y.) The state-of-the-art protocols are summarized as follows: In the above encoding scheme ( ♣ ♡ = 0, ♡ ♣ = 1), Mizuki and Sone [9] constructed a six-card COPY protocol and a four-card XOR protocol, and Koch [9], and Koch, Walzer and Härtel [4] constructed a five-card AND protocol; see Table 1. There are a five-card COPY protocol [13] and a four-card AND protocol [4], however, these protocols are Las-Vegas protocols, i.e., their computational times are finite only in expectation.…”

Section: Introductionmentioning

confidence: 99%

Secure Computation Protocols Using Polarizing Cards

Shinagawa

Mizuki

Schuldt

et al. 2016

IEICE Trans. Fundamentals

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It is known that, using just a deck of cards, an arbitrary number of parties with private inputs can securely compute the output of any function of their inputs. In 2009, Mizuki and Sone constructed a sixcard COPY protocol, a four-card XOR protocol, and a six-card AND protocol, based on a commonly used encoding scheme in which each input bit is encoded using two cards. However, up until now, there are no known results to construct a set of COPY, XOR, and AND protocols based on a twocard-per-bit encoding scheme, which all can be implemented using only four cards. In this paper, we show that it is possible to construct four-card COPY, XOR, and AND protocols using polarizing plates as cards and a corresponding two-card-per-bit encoding scheme. Our protocols use a minimum number of cards in the setting of two-card-per-bit encoding schemes since four cards are always required to encode the inputs. Moreover, we show that it is possible to construct two-card COPY, two-card XOR, and three-card AND protocols based on a one-card-per-bit encoding scheme using a common reference polarizer which is a polarizing material accessible to all parties.

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Card-Based Cryptographic Protocols Using a Minimal Number of Cards

Cited by 86 publications

References 9 publications

AND Protocols Using only Uniform Shuffles

AND Protocols Using only Uniform Shuffles

Card-Based Protocols Using Regular Polygon Cards

Secure Computation Protocols Using Polarizing Cards

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