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Lecture notes in computer science

Card-Based Protocol Against Actively Revealing Card Attack

Ken Takashima, Daiki Miyahara, Takaaki Mizuki, Hideaki Sone

Published Jan 1, 2019• 7 citations
Publisher
DOI
10.1007/978-3-030-34500-6_6

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Abstract In 1989, den Boer presented the first card-based protocol, called the “five-card trick,” that securely computes the AND function using a deck of physical cards via a series of actions such as shuffling and turning over cards. This protocol enables a couple to confirm their mutual love without revealing their individual feelings. During such a secure computation protocol, it is important to keep any information about the inputs secret. Almost all existing card-based protocols are secure under the assumption that all players participating in a protocol are semi-honest or covert, i.e., they do not deviate from the protocol if there is a chance that they will be caught when cheating. In this paper, we consider a more malicious attack in which a player as an active adversary can reveal cards illegally without any hesitation. Against such an actively revealing card attack, we define the t-secureness, meaning that no information about the inputs leaks even if at most t cards are revealed illegally. We then actually design t-secure AND protocols. Thus, our contribution is the construction of the first formal framework to handle actively revealing card attacks as well as their countermeasures.

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Abstract In 1989, den Boer presented the first card-based protocol, called the “five-card trick,” that securely computes the AND function using a deck of physical cards via a series of actions such as shuffling and turning over cards. This protocol enables a couple to confirm their mutual love without revealing their individual feelings. During such a secure computation protocol, it is important to keep any information about the inputs secret. Almost all existing card-based protocols are secure under the assumption that all players participating in a protocol are semi-honest or covert, i.e., they do not deviate from the protocol if there is a chance that they will be caught when cheating. In this paper, we consider a more malicious attack in which a player as an active adversary can reveal cards illegally without any hesitation. Against such an actively revealing card attack, we define the t-secureness, meaning that no information about the inputs leaks even if at most t cards are revealed illegally. We then actually design t-secure AND protocols. Thus, our contribution is the construction of the first formal framework to handle actively revealing card attacks as well as their countermeasures.
We construct statistical zero-knowledge authentication protocols for smart cards based on general assumptions. The main protocol is only secure against active attacks, but we present a modication based on trapdoor commitments that can resist concurrent attacks as well. Both protocols are instantiated using lattice-based primitives, which are conjectured to be secure against quantum attacks. We illustrate the practicality of our main protocol on smart cards in terms of storage, computation, communication, and round complexities. Furthermore, we compare it to other lattice-based authentication protocols, which are either zero-knowledge or have a similar structure. The comparison shows that our protocol improves the best previous protocol.
Card-based cryptography, as first proposed by den Boer [den Boer, 1989], enables secure multiparty computation using only a deck of playing cards. Many protocols as of yet come with an “honest-but-curious” disclaimer. However, modern cryptography aims to provide security also in the presence of active attackers that deviate from the protocol description. In the few places where authors argue for the active security of their protocols, this is done ad-hoc and restricted to the concrete operations needed, often using additional physical tools, such as envelopes or sliding cover boxes. This paper provides the first systematic approach to active security in card-based protocols. The main technical contribution concerns shuffling operations. A shuffle randomly permutes the cards according to a well-defined distribution but hides the chosen permutation from the players. We show how the large and natural class of uniform closed shuffles, which are shuffles that select a permutation uniformly at random from a permutation group, can be implemented using only a linear number of helping cards. This ensures that any protocol in the model of Mizuki and Shizuya [Mizuki and Shizuya, 2014] can be realized in an actively secure fashion, as long as it is secure in this abstract model and restricted to uniform closed shuffles. Uniform closed shuffles are already sufficient for securely computing any circuit [Mizuki and Sone, 2009]. In the process, we develop a more concrete model for card-based cryptographic protocols with two players, which we believe to be of independent interest.