Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic Family Symbolic Dynamics Topological Conjugacy Chaos Structural Stability Sarlovskiis Theorem The Schwarzian Derivative Bifurcation Theory Another View of Period Three Maps of the Circle Morse-Smale Diffeomorphisms Homoclinic Points and Bifurcations The Period-Doubling Route to Chaos The Kneeding Theory Geneaology of Periodic Units Part Two: Higher Dimensional Dynamics Preliminaries from Linear Algebra and Advanced Calculus The Dynamics of Linear Maps: Two and Three Dimensions The Horseshoe Map Hyperbolic Toral Automorphisms Hyperbolicm Toral Automorphisms Attractors The Stable and Unstable Manifold Theorem Global Results and Hyperbolic Sets The Hopf Bifurcation The Hnon Map Part Three: Complex Analytic Dynamics Preliminaries from Complex Analysis Quadratic Maps Revisited Normal Families and Exceptional Points Periodic Points The Julia Set The Geometry of Julia Sets Neutral Periodic Points The Mandelbrot Set An Example: the Exponential Function

An introduction to chaotic dynamical systems (2nd edition), by Robert L. Devaney. Pp 336. £34·95. 1989. ISBN 0-201-13046-7 (Addison-Wesley)

The user authentication scheme has been widely applied to verify the users’ legality. In order to enhance the security, the smart card has widely used in an authentication scheme. Recently, Liu et al. shown that some weaknesses exist in Li et al.’s scheme. An efficient and secure user authentication scheme with a smart card presented by them is more efficient and secure than other schemes. However, the security issues of their scheme proposed by them also exist, so we will demonstrate that their scheme is vulnerable to the replaying attack.

Cryptanalysis of an Efficient and Secure Smart Card Based Password Authentication Scheme

Blockchain-based privacy preserving e-health system for healthcare data in cloud

Recently, Amin proposed an efficient dynamic ID-based remote user password authentication scheme for multi-server environment. They claimed that his scheme resisted different possible attacks include off-line identity guessing attack, off-line password guessing attack, and smart card stolen attack. However, we find some weaknesses of his scheme in this article. We show that his scheme is vulnerable to off-line identity guessing with smart card stolen attack and off-line password guessing with smart card stolen attack.

Cryptanalysis of Efficient Dynamic ID Based Remote User Authentication Scheme in Multi-Server Environment Using Smart Card

An ameliorated two‐factor anonymous key exchange authentication protocol for mobile client‐server environment

Until now, the overwhelming majority of password- authenticated key agreement protocols using chaotic maps are based on three architectures (client/server, two clients/server and multi-server) and four security models (heuristic security, random oracle, ideal cipher and standard model). However, with rapid changes in the modern communication environment such as wireless mesh net- works and cloud storing, it is necessary to put forward a kind more flexible and general architecture to adapt it. So, in our paper, we firstly propose a provable secure two-party in two-realm key agreement protocol using chaotic maps in the standard model. Our proposed protocol is more general and it is easy to expand to many other forms, such as three-party or N-party in different realms. The new protocol resists dictionary attacks mounted by either passive or active network intruders, allowing, in principle, even weak password phrases to be used safely. It also offers perfect forward secrecy, which protects past sessions and passwords against future compromises. Finally, we give the security proof in the standard model and the efficiency analysis of our proposed scheme.

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A Provably Password Authenticated Key Exchange Scheme Based on Chaotic Maps in Different Realm

A One-Way Authentication Key Agreement Scheme with User Anonymity Based on Chaotic maps towards Multi-Server Architecture.

Nowadays, several three-party authenticated key agreement protocols based on Chebyshev chaotic maps have been proposed. Most of them can provide heuristic security, which means that once the weaknesses of these protocols are found, they are either modified or abandoned. Under this circumstance, some protocols which defined in the standard security models have been proposed. These protocols establish a session key to authenticate each other with the help of a trusted server. Usually, users share their passwords and identities with the trusted server in these protocols. Users cannot protect their privacy information. In our paper, we propose a novel authentication key agreement protocol with user anonymity in the standard model, through applying public key encryption based on Chebyshev chaotic maps and pseudorandom function. In the design of our paper, we follow the ideas in the protocol of Lai et al. The proposed protocol not only can achieve various securities, but also can provide user anonymity.

Three-party Authentication Key Agreement Protocol Based on Chaotic Maps in the Standard Model with Privacy Preserving.

The technology of On-Demand Password (ODP), as an instance of authentication or other secure services technologies, is designed to assist the smart phone users accomplishing to forget their password and access any service with servers and thus having a better quality of life while preserving their privacy. The paper firstly proposed a universal and enhanced ODP scheme which can achieve two kinds of services without remembering any password for users: The first is login service which can make users use the ODP which was sent by the registration center (RC) to login certain server, such as E-mail and E-payment service. The other is session service which can let users use the ODP to get a secure session key with certain server, such as consulting service. Furthermore, our enhanced ODP scheme does not need to input the temporary short password which was sent by RC. Because this short password was already in the right place, the user only need to adopt some confirmed way, such as draw lines to confirm. About practical environment, we adopt multi-server architecture which can allow the user to register at the RC once and can access all the permitted services provided by the eligible servers. Then a new universal and enhanced ODP scheme is given based on chaotic maps. Security of the scheme is based on chaotic maps hard problems, a secure one way hash function and a secure symmetric cryptosystem. Compared with the related literatures recently, our proposed scheme can not only own high efficiency and unique functionality, but is also robust to various attacks and achieves perfect forward secrecy. Finally, we give the security proof and the efficiency analysis of our proposed scheme.

Yifeng Zhang

Papers

A Provably Password Authenticated Key Exchange Scheme Based on Chaotic Maps in Different Realm

A One-Way Authentication Key Agreement Scheme with User Anonymity Based on Chaotic maps towards Multi-Server Architecture.

Three-party Authentication Key Agreement Protocol Based on Chaotic Maps in the Standard Model with Privacy Preserving.

A Novel On-Demand Password Scheme Based on BAN Logic.