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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.

Actively revealing card attack on card-based protocols