A formalization of card-based cryptographic protocols via abstract machine

Mizuki, Takaaki; Shizuya, Hiroki

doi:10.1007/s10207-013-0219-4

Cited by 79 publications

(29 citation statements)

References 11 publications

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“…We call a protocol is secure if it leaks no information for any run of the protocol (in other words, random variables I and V denoting the inputs and the visible sequence trace, respectively, are stochastically independent, where the visible sequence trace means what can be observed on the table). See [6][7][8] for the more formal definitions based on abstract machine and information theory.…”

Section: Correctness and Securitymentioning

confidence: 99%

Six-Card Finite-Runtime XOR Protocol with Only Random Cut

Toyoda

Miyahara

Mizuki

et al. 2020

Proceedings of the 7th ACM Workshop on ASIA Public-Key Cryptography

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Executing a card-based cryptographic protocol is an attractive way to perform secure multiparty computation (MPC) with a deck of physical cards. Crèpeau and Kilian at CRYPTO 1993 proposed cardbased AND and XOR protocols that can deal with a logical conjunction and exclusive-or of variables. Their protocols use a familiar shuffling action called a random cut that can be easily implemented by humans, while the numbers of required cards and shuffles are not small enough to be efficient and the protocols are Las Vegas algorithms, i.e., they are not finite-runtime. Several researchers have improved upon the protocols for a quarter of a century. Eventually, there are many AND protocols in the literature, some of which are quite efficient and practical to execute. By contrast, there are only three XOR protocols including the Crèpeau-Kilian protocol mentioned above. In this paper, we design an efficient XOR protocol using only random cuts; the numbers of required cards and shuffles are six and two (which is fixed), respectively. Our proposed XOR protocol is the first construction of a finite-runtime XOR protocol if we restrict ourselves to use only random cuts. CCS CONCEPTS • Security and privacy → Cryptography.

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Section: Correctness and Securitymentioning

confidence: 99%

Six-Card Finite-Runtime XOR Protocol with Only Random Cut

Toyoda

Miyahara

Mizuki

et al. 2020

Proceedings of the 7th ACM Workshop on ASIA Public-Key Cryptography

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“…The feasibility of card-based cryptographic MPC is due to [dB89; CK93;NR98], with a formal model given by [MS14]. The only two papers looking at standard deck solutions are [NR99;M16].…”

Section: Related Workmentioning

confidence: 99%

Card-Based Cryptography Meets Formal Verification

Koch

Schrempp

Kirsten

2019

Lecture Notes in Computer Science

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Card-based cryptography provides simple and practicable protocols for performing secure multi-party computation (MPC) with just a deck of cards. For the sake of simplicity, this is often done using cards with only two symbols, e.g., ♣ and ♡. Within this paper, we target the setting where all cards carry distinct symbols, catering for use-cases with commonly available standard decks and a weaker indistinguishability assumption. As of yet, the literature provides for only three protocols and no proofs for non-trivial lower bounds on the number of cards. As such complex proofs (handling very large combinatorial state spaces) tend to be involved and error-prone, we propose using formal verification for finding protocols and proving lower bounds. In this paper, we employ the technique of software bounded model checking (SBMC), which reduces the problem to a bounded state space, which is automatically searched exhaustively using a SAT solver as a backend. Our contribution is twofold: (a) We identify two protocols for converting between different bit encodings with overlapping bases, and then show them to be card-minimal. This completes the picture of tight lower bounds on the number of cards with respect to runtime behavior and shuffle properties of conversion protocols. For computing AND, we show that there is no protocol with finite runtime using four cards with distinguishable symbols and fixed output encoding, and give a four-card protocol with an expected finite runtime using only random cuts. (b) We provide a general translation of proofs for lower bounds to a bounded model checking framework for automatically finding card-and length-minimal protocols and to give additional confidence in lower bounds. We apply this to validate our method and, as an example, confirm our new AND protocol to have a shortest run for protocols using this number of cards.

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“…In the formal computation model of card-based protocols developed by Mizuki and Shizuya [8], a shuffle of the deck is mathematically defined by a pair (Π, F ), where Π is a set of permutations and F is a probability distribution on Π. We call the shuffle uniform if F is a uniform distribution, and closed if Π is a subgroup (of the symmetric group) [1].…”

Section: Properties Of Protocolsmentioning

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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A formalization of card-based cryptographic protocols via abstract machine

Cited by 79 publications

References 11 publications

Six-Card Finite-Runtime XOR Protocol with Only Random Cut

Six-Card Finite-Runtime XOR Protocol with Only Random Cut

Card-Based Cryptography Meets Formal Verification

AND Protocols Using only Uniform Shuffles

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