In cryptographic systems, the encryption process relies on the nonlinear mapping of original data or plaintext to the secure data. The mapping of data is facilitated by the application of the substitution process embedded in the cipher. It is desirable to have resistance against differential cryptanalysis, which assists in providing clues about the composition of keys, and linear secret system, where a simple approximation is created to emulate the original cipher characteristics. In this work, we propose the use of nonlinear functional chaos-based substitution process which employs a continuous time Lorenz system. The proposed substitution system eliminates the need of independent round keys in a substitution-permutation network. The performance of the new substitution box is evaluated by nonlinearity analysis, strict avalanche criterion, bit independence criterion, linear approximation probability, and differential approximation probability.

A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems

Very recently, Lee et al. (C. Lee, C. Chen, C. Wu, S. Huang, An extended chaotic maps-based key agreement protocol with user anonymity, Nonlinear Dynamics, doi:
 10.1007/s11071-011-0247-4
 ) proposed a chaotic maps-based key agreement protocol with user anonymity and claimed their protocol could resist various attacks. In this paper, we will point out that Lee et al.’s protocol suffers from three weaknesses: (1) inability of resisting the privileged insider attack; (2) inability of resisting the denial-of-service attack; and (3) inability of providing anonymity. To overcome the weaknesses, we also proposed an improved protocol. The analysis shows our protocol is more suitable for practical applications.

Cryptanalysis and improvement of an extended chaotic maps-based key agreement protocol

Recently, biometric-based remote user authentication schemes along with passwords have drawn considerable attention in research. In 2011, Das proposed an improvement on an efficient biometric-based remote user authentication scheme using smart cards and claimed his scheme could resist various attacks. However, there are some weaknesses in Das’s scheme such as the privileged insider attack and the off-line password guessing attack. Besides, Das’s scheme also cannot provide user anonymity. To overcome these weaknesses, we shall propose a secure biometric-based remote user authentication with key agreement scheme using extended chaotic maps. The proposed scheme not only can resist the above-mentioned attacks, but also provide user anonymity.

A secure biometric-based remote user authentication with key agreement scheme using extended 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.

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

Due to its high level of security, three-factor authentication combining password, smart card and biometrics has received much interest in the past decades. Recently, Islam proposed a dynamic identity-based three-factor authentication scheme using extended chaotic map which attempts to fulfill three-factor security and resist various known attacks, offering many advantages over existing works. However, in this paper we first show that the process of password verification in the login phase is invalid. Besides this defect, it is also vulnerable to user impersonation attack and off-line password guessing attack, under the condition that the smart card is lost or stolen. Furthermore, it fails to preserve biometric template privacy in the case that the password and the smart card are compromised. To remedy these flaws, we propose a robust three-factor authentication scheme, which not only resists various known attacks, but also provides more desired security features. We demonstrate that our scheme provides mutual authentication using the Burrows–Abadi–Needham logic. Our scheme provides high security strength as well as low computational cost.

Robust extended chaotic maps-based three-factor authentication scheme preserving biometric template privacy

A key agreement protocol is used to derive a shared secure session key by two or more parties, but no party can predetermine the resulting value. Users can securely exchange information over an open network by using the shared session key to encrypt/decrypt secure information. Recently, several key agreement protocols based on chaotic maps are proposed. Xiao et al. proposed a novel key agreement protocol based on chaotic maps and claimed their protocol can resist the known attack which is proposed by Bergamo et al. However, Han et al. and Xiang et al. pointed out that the Xiao et al. protocol is still insecure. To overcome these attacks, we shall propose an extended chaotic maps-based key agreement protocol. The proposed protocol not only can resist these attacks, but also provide mutual authentication and user anonymity.

An extended chaotic maps-based key agreement protocol with user anonymity

Establishing a secure communication of Internet conferences for participants is very important. Before starting the conference, all the participants establish a common conference key to encrypt/decrypt communicated messages. It enables participants to exchange the secure messages. Nevertheless, in the conference, if there are any malicious participants who may try to upset the key generation process causing other legal participants to obtain a different conference key. In this article, we propose an improved conference key agreement with fault-tolerant capability. The proposed scheme can filter malicious participants at the beginning of the conference to ensure that all participants obtain the same conference key. Compare with other schemes, our scheme is more secure and efficient than others. Keywords—Conference key, Diffie-Hellman protocol, key agreement, fault tolerance.

Chia-Ying Wu

Papers

An extended chaotic maps-based key agreement protocol with user anonymity

An Enhanced Fault-Tolerant Conference Key Agreement Protocol