TY - JOUR

T1 - Toward finite-runtime card-based protocol for generating a hidden random permutation without fixed points

AU - Hashimoto, Yuji

AU - Nuida, Koji

AU - Shinagawa, Kazumasa

AU - Inamura, Masaki

AU - Hanaoka, Goichiro

N1 - Publisher Copyright:
© 2018 The Institute of Electronics, Information and Communication Engineers.

PY - 2018/9

Y1 - 2018/9

N2 - In the research area of card-based secure computation, one of the long-standing open problems is a problem proposed by Crépeau and Kilian atCRYPTO1993. This is to develop an efficient protocol using a deck of physical cards that generates uniformly at random a permutation with no fixed points (called a derangement), where the resulting permutation must be secret against the parties in the protocol. All the existing protocols for the problem have a common issue of lacking a guarantee to halt within a finite number of steps. In this paper, we investigate feasibility and infeasibility for the problem where both a uniformly random output and a finite runtime is required. First, we propose a way of reducing the original problem, which is to sample a uniform distribution over an inefficiently large set of the derangements, to another problem of sampling a non-uniform distribution but with a significantly smaller underlying set. This result will be a base of a newapproach to the problem. On the other hand, we also give (assuming the abc conjecture), under a certain formal model, an asymptotic lower bound of the number of cards for protocols solving the problem using uniform shuffles only. This result would give a supporting evidence for the necessity of dealing with non-uniform distributions such as in the aforementioned first part of our result.

AB - In the research area of card-based secure computation, one of the long-standing open problems is a problem proposed by Crépeau and Kilian atCRYPTO1993. This is to develop an efficient protocol using a deck of physical cards that generates uniformly at random a permutation with no fixed points (called a derangement), where the resulting permutation must be secret against the parties in the protocol. All the existing protocols for the problem have a common issue of lacking a guarantee to halt within a finite number of steps. In this paper, we investigate feasibility and infeasibility for the problem where both a uniformly random output and a finite runtime is required. First, we propose a way of reducing the original problem, which is to sample a uniform distribution over an inefficiently large set of the derangements, to another problem of sampling a non-uniform distribution but with a significantly smaller underlying set. This result will be a base of a newapproach to the problem. On the other hand, we also give (assuming the abc conjecture), under a certain formal model, an asymptotic lower bound of the number of cards for protocols solving the problem using uniform shuffles only. This result would give a supporting evidence for the necessity of dealing with non-uniform distributions such as in the aforementioned first part of our result.

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U2 - 10.1587/transfun.E101.A.1503

DO - 10.1587/transfun.E101.A.1503

M3 - Article

AN - SCOPUS:85053858153

VL - E101A

SP - 1503

EP - 1511

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 9

ER -