Chebyshev Chaotic Map Research Articles

An Improved AES Encryption Algorithm Based on the Hénon and Chebyshev Chaotic Map

An Improved AES Encryption Algorithm Based on the Hénon and Chebyshev Chaotic Map

Attacks and improvements to chaotic map‐based RFID authentication protocol

AbstractBecause of its low cost and ease of deployment, radio frequency identification (RFID) technology offers great potential for all applications that require identification. Main obstacle for wide adoption of this technology is the concerns about its security and privacy issues. Many RFID authentication protocols have been proposed to provide desired security and privacy level for RFID systems. Recently, Benssalah et al. have proposed a chaotic map‐based RFID security protocol. In this paper, we analyze the security of this protocol and discover its vulnerabilities. We show that message generation arises some weaknesses, and this protocol is vulnerable to tracking, tag impersonation, and de‐synchronization attacks. The success probabilities of the proposed attacks are significant, and their complexities are polynomial. Furthermore, we propose an RFID authentication protocol. Our protocol utilizes the Chebyshev chaotic map hard problem and conforms to the EPCglobal Class 1 Generation 2 (EPC C1‐G2) standard. Our protocol eliminates the weaknesses of the protocol of Benssalah et al. Copyright © 2015 John Wiley & Sons, Ltd.

A Chebyshev-Map Based One-Way Authentication and Key Agreement Scheme for Multi-Server Environment

One-way authentication and key agreement scheme can achieve strong user anonymity and transmitted data confidentiality over insecure public communication channel, which is very useful for the user who cares about his/her identity information. In conventional networks, Public Key Infrastructure (PKI) is a very useful component to design one-way authentication key agreement scheme. However, it will consume large amounts of computing resources. Therefore, it is inappropriate to PKI in a resource-constrained environment. In this paper, we proposed a new one-way authentication and key agreement scheme based on Chebyshev chaotic map. Compared with the related research activities, our proposed scheme has not only the high efficiency and unique functions, but also robust to various attacks and achieves perfect forward secrecy. Security and performance analyses demonstrate that the proposed scheme can solve various types of security problems and can meet the requirements of computational complexity for lowpower mobile devices.

An efficient three-party password-based key agreement protocol using extended chaotic maps**Project supported by the National Natural Science Foundation of China (Grant No. 61462033).

Three-party password-based key agreement protocols allow two users to authenticate each other via a public channel and establish a session key with the aid of a trusted server. Recently, Farash et al. [Farash M S, Attari M A 2014 “An efficient and provably secure three-party password-based authenticated key exchange protocol based on Chebyshev chaotic maps”, Nonlinear Dynamics 77(7): 399–411] proposed a three-party key agreement protocol by using the extended chaotic maps. They claimed that their protocol could achieve strong security. In the present paper, we analyze Farash et al.’s protocol and point out that this protocol is vulnerable to off-line password guessing attack and suffers communication burden. To handle the issue, we propose an efficient three-party password-based key agreement protocol using extended chaotic maps, which uses neither symmetric cryptosystems nor the server’s public key. Compared with the relevant schemes, our protocol provides better performance in terms of computation and communication. Therefore, it is suitable for practical applications.

Aggregated-Proof Based Hierarchical Authentication Scheme for the Internet of Things

The Internet of Things (IoT) is becoming an attractive system paradigm to realize interconnections through the physical, cyber, and social spaces. During the interactions among the ubiquitous things, security issues become noteworthy, and it is significant to establish enhanced solutions for security protection. In this work, we focus on an existing U2IoT architecture (i.e., unit IoT and ubiquitous IoT), to design an aggregated-proof based hierarchical authentication scheme (APHA) for the layered networks. Concretely, 1) the aggregated-proofs are established for multiple targets to achieve backward and forward anonymous data transmission; 2) the directed path descriptors, homomorphism functions, and Chebyshev chaotic maps are jointly applied for mutual authentication; 3) different access authorities are assigned to achieve hierarchical access control. Meanwhile, the BAN logic formal analysis is performed to prove that the proposed APHA has no obvious security defects, and it is potentially available for the U2IoT architecture and other IoT applications.

Cryptanalysis and improvement of a three‐party password‐based authenticated key exchange protocol with user anonymity using extended chaotic maps

SummaryThree‐party password‐authenticated key exchange (3PAKE) protocols allow two clients to agree on a secret session key through a server via a public channel. 3PAKE protocols have been designed using different arithmetic aspects including chaotic maps. Recently, Lee et al. proposed a 3PAKE protocol using Chebyshev chaotic maps and claimed that their protocol has low computation and communication cost and can also resist against numerous attacks. However, this paper shows that in spite of the computation and communication efficiency of the Lee et al. protocol, it is not secure against the modification attack. To conquer this security weakness, we propose a simple countermeasure, which maintains the computation and communication efficiency of the Lee et al. protocol. Copyright © 2014 John Wiley & Sons, Ltd.

A new three-party-authenticated key agreement scheme based on chaotic maps without password table

Three-party-authenticated key agreement allows two users to establish a common session key through a trusted server via an insecure communication channel. Early authenticated key agreement schemes were mostly based on either pairing operations, hash operations, or modular exponentiation operations. In 2011, Wang and Zhao took a new path and built their three-party-authenticated key agreement scheme on the basis of chaotic maps. By applying Chebyshev chaotic maps, Wang and Zhao succeeded in lifting their scheme up to a higher level of efficiency and security. In this paper, we shall propose a new three-party-authenticated key agreement scheme based on chaotic maps that can do without passwords. Keeping no password table, our new scheme is completely resistant to password guessing attacks. Besides that, our scheme also offers thorough privacy protection to the users, so the user forgery attack can cause no damage. Compared with the schemes currently available including Wang and Zhao’s work, our new scheme obviously provides better security.

A secure chaotic maps and smart cards based password authentication and key agreement scheme with user anonymity for telecare medicine information systems.

Telecare medicine information system (TMIS) is widely used for providing a convenient and efficient communicating platform between patients at home and physicians at medical centers or home health care (HHC) organizations. To ensure patient privacy, in 2013, Hao et al. proposed a chaotic map based authentication scheme with user anonymity for TMIS. Later, Lee showed that Hao et al.'s scheme is in no provision for providing fairness in session key establishment and gave an efficient user authentication and key agreement scheme using smart cards, in which only few hashing and Chebyshev chaotic map operations are required. In addition, Jiang et al. discussed that Hao et al.'s scheme can not resist stolen smart card attack and they further presented an improved scheme which attempts to repair the security pitfalls found in Hao et al.'s scheme. In this paper, we found that both Lee's and Jiang et al.'s authentication schemes have a serious security problem in that a registered user's secret parameters may be intentionally exposed to many non-registered users and this problem causing the service misuse attack. Therefore, we propose a slight modification on Lee's scheme to prevent the shortcomings. Compared with previous schemes, our improved scheme not only inherits the advantages of Lee's and Jiang et al.'s authentication schemes for TMIS but also remedies the serious security weakness of not being able to withstand service misuse attack.

Improved chaotic maps-based password-authenticated key agreement using smart cards

Elaborating on the security of password-based authenticated key agreement, in this paper, the author cryptanalyzes a chaotic maps-based password-authenticated key agreement proposed by Guo and Chang recently. Specifically, their protocol could not achieve strong user anonymity due to a fixed parameter and a malicious adversary is able to derive the shared session key by manipulating the property of Chebyshev chaotic maps. Additionally, the author also presents an improved scheme to eliminate the above weaknesses and still maintain the efficiency.

A revised key agreement protocol based on chaotic maps

Very recently, Chen et al. proposed a security-enhanced key agreement protocol based on Chebyshev chaotic map. They claimed that the proposed protocol can achieve session key agreement shared among the server and user with security and users anonymity. Although, in this paper, we will prove that Chen et al.’s protocol cannot guarantee security and user anonymity against internal adversary who is a legal user. Furthermore, we give some improvements to dominate the mentioned shortcomings. The analysis shows that our proposed improvements are secure and efficient.

Provably secure three-party key agreement protocol using Chebyshev chaotic maps in the standard model

Recently, several key agreement protocols based on Chebyshev chaotic maps have been proposed in the literature. However, they can normally achieve “heuristic” security, that is, once drawbacks are found in these protocols, they are either modified to resist the new attacks, or are discarded. Under these circumstances, it is necessary and significant to define standard security models that can precisely characterize the capabilities of the participants and a potent adversary. Hence, we propose to use public key encryption based on enhanced Chebyshev chaotic maps and pseudo-random function ensembles to construct an efficient three-party key agreement protocol under the standard model, in which the adversary is able to make a wider range of queries and have more freedom than the other proposed schemes. In the design of our protocol, we follow the ideas in the recent key agreement protocol of Yang and Cao’s. The proposed protocol is shown to be provably secure if decisional Diffie–Hellman problem, which is based on Chebyshev chaotic maps, is computationally infeasible. To the best of our knowledge, our protocol is the first provably secure 3PAKE protocol using Chebyshev chaotic maps under the standard model.

An efficient and provably secure three-party password-based authenticated key exchange protocol based on Chebyshev chaotic maps

Three-party password-based authenticated key exchange (3PAKE) protocols allow two clients to establish a secure session key through a server over an insecure channel. Recently, the 3PAKE protocols have been developed based on Chebyshev chaotic maps, in which the clients utilize smart cards to login into the server and employ server’s public key to ensure the identity of the server or symmetric cryptosystems to encrypt the messages. However, this paper describes an efficient chaos-based 3PAKE protocol without smart cards, which requires neither server’s public key nor symmetric cryptosystems. The security of the proposed 3PAKE protocol is proved in the random oracle model using the chaos-based decisional Diffie–Hellman assumption. In comparison with the existing chaos-based 3PAKE protocols, our protocol individually provides better performance in terms of communication, computation, and security aspects, and is supported by the formal proof in the random oracle model.

Security enhancement of the authenticated RFID security mechanism based on chaotic maps

ABSTRACTWith the fast growth of the automatic authentication and asset tracking usage in a wide variety of applications in different fields, government, logistics, transportation and retail are among the most supportive of the radio‐frequency identification (RFID) market. Security is a crucial issue and must be addressed seriously. RFID security must meet the public demand of data protection. Recently, several lightweight RFID authentication protocols conforming to the EPCglobal Class 1 Generation 2 (EPC C1‐G2) standard have been proposed. In this paper, we present efficient attacks against the authenticated RFID security mechanism of Chang et al. based on Chebyshev chaotic maps, which is the first solution that adopted the chaos in the RFID authentication process. It turns out that this protocol has fundamental weaknesses that can be used by an adversary to break the system. We will show that this protocol is vulnerable to tracking attack, secret disclosure attack, impersonation attack and desynchronization attack. The proposed attack techniques are in light of two flaws related to the message generation and the shared‐secret update process, which are not neatly scrutinized. Then, we propose an improved RFID authentication protocol based on the Chebyshev chaotic map hard problem, conforming to the EPC C1‐G2 standard with more flexibility, security and mobility for the RFID application. Copyright © 2014 John Wiley & Sons, Ltd.

A Blind Watermarking Technique for Color Image based on SVD with Circulation

Digital watermarking is a method for protecting copyrighted materials such as digital images. This paper presents a new color watermark embedding technique with circulation, based on non-overlapping Singular Value Decomposition (SVD) for hiding important information in images. First, the real-color original image is decomposed into three components R, G and B. The blue component and the watermark performed by Chebyshev chaotic map are divided into non-overlapping blocks, respectively. Then an SVD is performed on each partitioned blocks. Second, the Singular Values (SVs) of watermark are embedded into the singular value matrix of blue component with circulation. Extracting any consecutive four rows and columns from the blocked watermarked image can get complete watermark information. Every watermark bits have been embedded several times and their embedding position are consecutive in the selected original image. That is why, our proposed scheme is naturally secure to geometric attacks and compound attacks, and it is also strongly robust against common image processing attacks. Index Terms—Copyrighted materials, Circulation, Chebyshev chaotic map, Singular values

DWT and SVD based Watermarking Scheme with Circulation

The major application for watermark is protecting intellectual property rights. In this paper, a watermark scheme with circulation, based on non-overlapping discrete wavelet transform (DWT) and singular value decomposition (SVD), is presented. First, the original host image and watermark image are divided into non-overlapping blocks, respectively and to the former DWT and SVD is applied. Second, the scrambling watermark by Chebyshev chaotic map is embedded into the singular value matrix of original components with circulation. Extracting any consecutive four rows and columns from the blocked watermarked image can get complete watermark information. The quantity of embedded watermark information is large and the original image is not needed for watermark extracting. Both theoretical analysis and experimental results indicate that the proposed method can very effectively resist large degree of geometric attacks and compound attacks, and it is also strongly robust against common image processing attacks.

Image Encryption Algorithm Based on Wavelet Transforms and Dual Chaotic Maps

In view of characteristics of digital image,such as bulk data capacity,high redundancy and poor security, a new image encryption algorithm was put forward by combining chaotic maps with wavelet transform. Mallat algorithm in wavelet transform firstly was used to decompose the original image, leaving only the low-frequency information, and then oversampled Chebyshev chaotic maps were used to achieve space chaos of compressed image, oversampled Logistic chaotic maps were used for encryption. Finally, security analysis of the encryption algorithm are analyzed from the perspective of key space, statistical analysis, key sensitivity analysis and so on. Simulation results show that the method can effectively compress image, the amount of information transmission is low and the key space is large enough to resist the brute-force attack and with good encryption effect .

Cryptanalysis of an image encryption algorithm using Chebyshev generator

Recently, studies of image encryption algorithms have been increasingly based on chaos, but there still exist drawbacks in chaotic cryptosystem that threat the security. In this paper, we make cryptanalysis on an image encryption based on Chebyshev chaotic map and find the following: (1) chosen-plaintext attack can break the scheme. (2) There exist equivalent keys and weak keys for the encryption scheme. (3) The scheme has low sensitivity to the changes of plain image. And we successfully carry out the chosen-plaintext attack. To overcome the drawbacks, a remedial technique is suggested.

Cryptanalysis and improvement of a three-party key agreement protocol using enhanced Chebyshev polynomials

Three-party key agreement protocol is an important cryptographic mechanism for secure communication, which allows two parties authenticate each other with the help of a trusted server. Very recently, Lai et al.’s proposed a novel three-party key agreement protocol using the enhanced Chebyshev chaotic map and claimed their protocol could withstand various attacks. Unfortunately, in this paper, we will show their protocol is vulnerable to the privileged insider attack and the off-line password guessing attack. To solve the problems, we propose an improved three-party key agreement protocol using the enhanced Chebyshev chaotic map. Security analysis and performance analysis show our protocol not only could withstand various attacks, but also has similar performance. Therefore, it is very suitable for practical applications.

A chaotic maps-based authenticated key agreement protocol with strong anonymity

In wireless communication environments, the authenticated key agreement with user anonymity is important. Recently, many chaotic maps-based anonymous authenticated key agreement protocols have been proposed. Tseng et al. applied Chebyshev chaotic maps to propose an anonymous key agreement protocol. Unfortunately, Niu et al. demonstrated that Tseng et al.’s protocol cannot protect the user anonymity and it suffers from insider attacks. Xue et al. improved Tseng et al.’s protocol. However, we have found that their improved protocol still cannot provide strong anonymity and it is vulnerable to the man-in-the-middle attack. To remove these weaknesses, we have proposed a novel chaotic maps-based authenticated key agreement protocol. The proposed protocol cannot only resist these attacks, but also provide strong anonymity.

The Research and Analysis Based on a New Hybrid Chaotic Sequences

The chaos sequence generated by the chaotic map methods usually has unsatisfactory performances. To solve this problem, this paper proposes a novel method with chaos sequence, which blends the Chebyshev chaotic map and one-dimensional chaotic map with infinite collapse in finite interval. Both MATLAB simulations and performance analyses results show that the proposed method has much improved chaotic performances than the single Chebyshev sequence or the chaotic sequence with infinite collapses, by analyzing and simulating the sequence of traversal feature, period doubling properties, Lyapunov exponents, initial value sensitivity, autocorrelation, and the uniformity of sequence.