Nonlinear Dyn (2014) 78:1293–1300
DOI 10.1007/s11071-014-1515-x
ORIGINAL PAPER
Cryptanalysis and enhancement of a chaotic maps-based
three-party password authenticated key exchange protocol
Xuexian Hu · Zhenfeng Zhang
Received: 7 July 2013 / Accepted: 5 June 2014 / Published online: 28 June 2014
© Springer Science+Business Media Dordrecht 2014
Abstract Recently, Lee et al. (Nonlinear Dyn,
73(1–2):125–132, 2013) proposed a three party pass-
word authenticated key exchange with user anonymity
by utilizing extended chaotic maps. They claimed that
their protocol is more secure than previously proposed
schemes. In this paper, our analysis shows that Lee
et al.’s protocol suffers from two kinds of attacks:
(1) man-in-the-middle attack, and (2) user anonymity
attack. To overcome these weakness, we propose an
enhanced protocol that can resist the attacks described
and yet with comparable efficiency.
Keywords Chaotic maps · Key exchange protocol ·
Anonymity · Man-in-the-middle attack
1 Introduction
In order to guarantee the security of communica-
tion over an insecure network, it is essential that
cryptographically strong session keys are established
through key exchange protocols, based on various
X. Hu (
B
) · Z. Zhang
Trusted Computing and Information Assurance Laboratory,
Institute of Software, Chinese Academy of Sciences,
Beijing, People’s Republic of China
e-mail: xuexian_hu@hotmail.com
Z. Zhang
e-mail: zfzhang@tca.iscas.ac.cn
X. Hu
State Key Laboratory of Mathematical Engineering and
Advanced Computing, Zhengzhou, People’s Republic of China
authentication means. Password-based authenticated
key exchange (PAKE) protocols allow parties to gen-
erate a common session key based on a shared low-
entropy, human-memorable password without requir-
ing a complex public-key infrastructure. Three-party
password authenticated key exchange (3PAKE) proto-
col is a special kind of PAKE protocol, in which each
user shares a password with the trusted server, and two
users establish a common session key with the aid of the
server. This solution is quite realistic in practice since
it provides each user with the capability of communi-
cating securely with other parties while only requiring
it to remember a single password.
In 2007, Lu and Cao [1] proposed a simple three-
party password-based key exchange protocol, called S-
3PAKE protocol, based on chosen-basis computational
Diffie–Hellman assumption of Abdalla and Pointcheval
[2]. However, it is found that S-3PAKE is vulnerable
to various attacks such as man-in-the-middle attacks
[3,4], undetectable on-line dictionary attacks [4,5], and
off-line dictionary attacks [6–8]. As a replacement of S-
3PAKE protocol, Huang [9] presented a simple 3PAKE
protocol, which is more efficient than previously pro-
posed schemes. Nevertheless, Huang et al.’s protocol
is also vulnerable to a number of attacks, such as unde-
tectable on-line dictionary attack and key compromise
impersonation attack[10,11].
To enhance the efficiency and security, as well as
to provide user anonymity, Lee et al. [12] presented a
three-party password authenticated key exchange pro-
tocol, based on extended Chebyshev chaotic maps. It is
123