Card-Based Protocols Using Regular Polygon Cards

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

Card-based Protocols Using Triangle Cards

Suppose that three boys and three girls attend a party. Each boy and girl have a crush on exactly one of the three girls and three boys, respectively. The following dilemma arises: On one hand, each person thinks that if there is a mutual affection between a girl and boy, the couple should go on a date the next day. On the other hand, everyone wants to avoid the possible embarrassing situation in which their heart is broken "publicly." In this paper, we solve the dilemma using novel cards called triangle cards. The number of cards required is only six, which is minimal in the case where each player commits their input at the beginning of the protocol. We also construct multiplication and addition protocols based on triangle cards. Combining these protocols, we can securely compute any function f: {0,1,2}^n --> {0,1,2}

Secure Grouping Protocol Using a Deck of Cards

We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about how the remaining parties are divided (except for certain public predetermined constraints, such as the number of parties in each group). In this paper, we construct an information-theoretically secure protocol using a deck of physical cards to solve the problem, which is jointly executable by the parties themselves without a trusted third party. Despite the non-triviality and the potential usefulness of the secure grouping, our proposed protocol is fairly simple to describe and execute. Our protocol is based on algebraic properties of conjugate permutations. A key ingredient of our protocol is our new techniques to apply multiplication and inverse operations to hidden permutations (i.e., those encoded by using face-down cards), which would be of independent interest and would have various potential applications

Using Five Cards to Encode Each Integer in Z/6Z\mathbb{Z}/6\mathbb{Z}

Research in secure multi-party computation using a deck of playing cards, often called card-based cryptography, dates back to 1989 when Den Boer introduced the "five-card trick" to compute the logical AND function. Since then, many protocols to compute different functions have been developed. In this paper, we propose a new encoding scheme using five cards to encode each integer in $\mathbb{Z}/6\mathbb{Z}$. Using this encoding scheme, we develop protocols that can copy a commitment with 13 cards, add two integers with 10 cards, and multiply two integers with 16 cards. All of our protocols are the currently best known protocols in terms of the required number of cards. Our encoding scheme can also be generalized to encode integers in $\mathbb{Z}/n\mathbb{Z}$ for other values of $n$ as well

The Landscape of Computing Symmetric nn-Variable Functions with 2n2n Cards

Secure multi-party computation using a physical deck of cards, often called card-based cryptography, has been extensively studied during the past decade. Many card-based protocols to securely compute various Boolean functions have been developed. As each input bit is typically encoded by two cards, computing an $n$-variable Boolean function requires at least $2n$ cards. We are interested in optimal protocols that use exactly $2n$ cards. In particular, we focus on symmetric functions, where the output only depends on the number of 1s in the inputs. In this paper, we formulate the problem of developing $2n$-card protocols to compute $n$-variable symmetric Boolean functions by classifying all such functions into several NPN-equivalence classes. We then summarize existing protocols that can compute some representative functions from these classes, and also solve some of the open problems by developing protocols to compute particular functions in the cases $n=4$, $5$, $6$, and $7$

An Improved Physical ZKP for Nonogram

Nonogram is a logic puzzle consisting of a rectangular grid with an objective to color every cell black or white such that the lengths of blocks of consecutive black cells in each row and column are equal to the given numbers. In 2010, Chien and Hon developed the first physical zero-knowledge proof for Nonogram, which allows a prover to physically show that he/she knows a solution of the puzzle without revealing it. However, their protocol requires special tools such as scratch-off cards and a machine to seal the cards, which are difficult to find in everyday life. Their protocol also has a nonzero soundness error. In this paper, we propose a more practical physical zero-knowledge proof for Nonogram that uses only a deck of regular paper cards and also has perfect soundness.Comment: This paper has appeared at COCOA 202

Physical Zero-Knowledge Proof for Ball Sort Puzzle

Ball sort puzzle is a popular logic puzzle consisting of several bins containing balls of multiple colors. Each bin works like a stack; a ball has to follow the last-in first-out order. The player has to sort the balls by color such that each bin contains only balls of a single color. In this paper, we propose a physical zero-knowledge proof protocol for the ball sort puzzle using a deck of playing cards, which enables a prover to physically show that he/she knows a solution with $t$ moves of the ball sort puzzle without revealing it. Our protocol is the first zero-knowledge proof protocol for an interactive puzzle involving moving objects.Comment: arXiv admin note: text overlap with arXiv:2302.0123

RF Localization in Indoor Environment

In this paper indoor localization system based on the RF power measurements of the Received Signal Strength (RSS) in WLAN environment is presented. Today, the most viable solution for localization is the RSS fingerprinting based approach, where in order to establish a relationship between RSS values and location, different machine learning approaches are used. The advantage of this approach based on WLAN technology is that it does not need new infrastructure (it reuses already and widely deployed equipment), and the RSS measurement is part of the normal operating mode of wireless equipment. We derive the Cramer-Rao Lower Bound (CRLB) of localization accuracy for RSS measurements. In analysis of the bound we give insight in localization performance and deployment issues of a localization system, which could help designing an efficient localization system. To compare different machine learning approaches we developed a localization system based on an artificial neural network, k-nearest neighbors, probabilistic method based on the Gaussian kernel and the histogram method. We tested the developed system in real world WLAN indoor environment, where realistic RSS measurements were collected. Experimental comparison of the results has been investigated and average location estimation error of around 2 meters was obtained

Card-Based ZKP Protocols for Takuzu and Juosan

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