Crypto Santa

Ryan, Peter Y. A.

doi:10.1007/978-3-662-49301-4_33

Cited by 2 publications

(1 citation statement)

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“…Since then, several solutions with physical tools have been proposed. (Refer to [17] for the non-physical solutions.) As practical protocols, Heather et al [6] proposed a protocol with envelopes and fill-in-the-blank cards in 2014; Ibaraki et al [7] proposed a protocol with two sequences of cards representing player IDs and gift IDs in 2016.…”

Section: Introductionmentioning

confidence: 99%

Efficient Generation of a Card-Based Uniformly Distributed Random Derangement

Murata

Miyahara

Mizuki

et al. 2021

Lecture Notes in Computer Science

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Consider a situation, known as Secret Santa, where n players wish to exchange gifts such that each player receives exactly one gift and no one receives a gift from oneself. Each player only wants to know in advance for whom he/she should purchase a gift. That is, the players want to generate a hidden uniformly distributed random derangement. (Note that a permutation without any fixed points is called a derangement.) To solve this problem, in 2015, Ishikawa et al. proposed a simple protocol with a deck of physical cards. In their protocol, players first prepare n piles of cards, each of which corresponds to a player, and shuffle the piles. Subsequently, the players verify whether the resulting piles have fixed points somehow: If there is no fixed point, the piles serve as a hidden random derangement; otherwise, the players restart the shuffle process. Such a restart occurs with a probability of approximately 0.6. In this study, we consider how to decrease the probability of the need to restart the shuffle based on the aforementioned protocol. Specifically, we prepare more piles of cards than the number n of players. This potentially helps us avoid repeating the shuffle, because we can remove fixed points even if they arise (as long as the number of remaining piles is at least n). Accordingly, we propose an efficient protocol that generates a uniformly distributed random derangement. The probability of the need to restart the shuffle can be reduced to approximately 0.1.

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Section: Introductionmentioning

confidence: 99%