Research Article
Verifiable Rational Secret Sharing Scheme in Mobile Networks
En Zhang,
1,2,3
Peiyan Yuan,
1,3
and Jiao Du
4
1
College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, China
2
State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences,
Beijing 100093, China
3
Engineering Lab of Intelligence Business & Internet of ings, Xinxiang, Henan 453007, China
4
College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
Correspondence should be addressed to En Zhang; zhangenzdrj@.com
Received January ; Revised May ; Accepted May
Academic Editor: Francesco Gringoli
Copyright © En Zhang et al. is is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
With the development of mobile network, lots of people now have access to mobile phones and the mobile networks give users
ubiquitous connectivity. However, smart phones and tablets are poor in computational resources such as memory size, processor
speed, and disk capacity. So far, all existing rational secret sharing schemes cannot be suitable for mobile networks. In this paper,
we propose a veriable rational secret sharing scheme in mobile networks. e scheme provides a noninteractively veriable proof
for the correctness of participants’ share and handshake protocol is not necessary; there is no need for certicate generation,
propagation, and storage in the scheme, which is more suitable for devices with limited size and processing power; in the scheme,
every participant uses her encryption on number of each round as the secret share and the dealer does not have to distribute any
secret share; every participant cannot gain more by deviating the protocol, so rational participant has an incentive to abide by the
protocol; nally, every participant can obtain the secret fairly (means that either everyone receives the secret, or else no one does)
in mobile networks. e scheme is coalition-resilient and the security of our scheme relies on a computational assumption.
1. Introduction
1.1. Background. Secret sharing is playing a more and more
important role in modern cryptography. In classical (,)
secret sharing schemes [, ], a secret can be shared among
participants. At least or more participants can reconstruct
the secret, but −1or fewer participants cannot obtain
anything about the secret. Recently, a series of secret sharing
schemes were proposed in [–]. However, the works in [–
] cannot prevent the dealer or players from cheating. For
example, in Shamir’s scheme, we assume that one party does
not broadcast his share, while exactly −1other players reveal
their shares. He can still reconstruct the secret although his
cheatingcanbedetectedbythescheme[–].
Motivated by the desire to develop more realistic mod-
els, the cryptographic community has signicant interest
in exploring protocols for rational secret sharing. Halpern
and Teague [] rstly introduced the notion of rational
secret sharing. ey pointed out that there exist many
Nash equilibriums which, in some sense, are unreasonable.
erefore, they focus on one particular renement of Nash
equilibrium that is determined by iterated deletion of weakly
dominated strategies. However, their protocols cannot work
foroutofsecretsharingandrequiretheonlinedealer.
Later, a series of rational secret sharing schemes [–]
wereproposed.However,noneofthemarefullysatisfactory.
e works in [–] rely on secure multiparty computation
which is strong. Kol and Naor’s scheme [] has information
theoretic security. However, their scheme fails to resist against
coalitions. e works in [, ]requiretheinvolvementof
some trusted external parties during the reconstruction phase
which is dicult to nd. e solution in []constructsa
rationalschemebasedonrepeatedgames.However,every
player has high probability to learn the secret in his last
round. e works of Lepinski et al. [, ]andIzmalkov
et al. [, ] can guarantee fairness, prevent coalitions, and
eliminate side information. However, their solutions rely on
physical assumption such as secure envelopes and ballot
Hindawi Publishing Corporation
Mobile Information Systems
Volume 2015, Article ID 462345, 7 pages
http://dx.doi.org/10.1155/2015/462345