Chaotic cryptosystems: Cryptanalysis and identifiability (original) (raw)
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Cryptanalytic methods in chaotic cryptosystems
6 pages, 6 figures.-- Communication presented at the 5th World Multiconference on Systemics, Cybernetics and Informatics and 7th International Conference on Information System Analysis and Synthesis (SCI/ISAS 2001, Orlando, Florida, Jul 22-25, 2001). In recent years, telecommunications networks have undergone an explosive growth. As a consequence, there has been a strong demand of information protection mechanisms. Many cryptosystems based on chaos have been proposed, although little or no critical analysis has been made about the security and cryptographic robustness of these algorithms. In this paper we present our tools to examine some of these algorithms from a cryptographic perspective, showing many vulnerabilities that can be exploited to successfully break them. We conclude that most of the chaotic cryptosystems are very insecure and cumbersome, thus, unreliable and impractical for real applications. Peer reviewed
CRYPTANALYSIS OF CHAOTIC CIPHER BASED ON IDENTIFIABILITY CONCEPT
Cryptanalysis of chaotic ciphers based on concept of identifiability is presented and discussed in this paper. Both the ciphers are developed using 2-D chaotic map and parameter of map acts as secret key. The ciphers are developed using Henon and Burger map. Key space analysis of cipher provides the range of keys. The keys are then selected randomly from domain of key space and they are tested for identifiability. Identifiability concept of cryptanalysis is accompanied with other basic cryptanalytic procedures like avalanche effect. Analysis of keys has been accomplished on various texts. It is concluded that identifiability concept of testing the strength of chaotic ciphers, against brute force attack in prior to sending message, proves to be quite advantageous. The developed ciphers are found to have identifiable key and good key sensitivity which concludes that they can resist linear and brute force attacks.
Cryptanalysis of dynamic look-up table based chaotic cryptosystems
Physics Letters A, 2004
In recent years many chaotic cryptosystems based on Baptista's seminal work have been proposed. We analyze the security of two of the newest and most interesting ones, which use a dynamically updated look-up table and also work as stream ciphers. We provide different attack techniques to recover the keystream used by the algorithms. The knowledge of this keystream provides the attacker with the same information as the key and thus the security is broken. We also show that the dependence on the plaintext, and not on the key, of the look-up table updating mechanism facilitates cryptanalysis.
Cryptanalysis of a chaotic encryption system
Physics Letters A, 2000
Recently a new chaotic encryption system has been proposed by E. Alvarez et al. In this paper, several weaknesses of this cryptosystem are pointed out and four successful cryptanalytic attacks are described.
A basic framework for the cryptanalysis of digital chaos-based cryptography
Systems, Signals and …, 2009
Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and efficient use of chaos in the context of cryptography requires a thorough knowledge about the dynamics of the selected chaotic system. Indeed, if the final encryption system reveals enough information about the underlying chaotic system it could be possible for a cryptanalyst to get the key, part of the key or some information somehow equivalent to the key just analyzing those dynamical properties leaked by the cryptosystem. This paper shows what those dynamical properties are and how a cryptanalyst can use them to prove the inadequacy of an encryption system for the secure exchange of information. This study is performed through the introduction of a series of mathematical tools which should be the basic framework of cryptanalysis in the context of digital chaos-based cryptography.
Some hints for the design of digital chaos-based cryptosystems: lessons learned from cryptanalysis
Arxiv preprint arXiv:0812.0765, 2008
In this work we comment some conclusions derived from the analysis of recent proposals in the field of chaos-based cryptography. These observations remark a number of major problems detected in some of those schemes under examination. Therefore, this paper is a list of what to avoid and to pay special attention to when considering chaos as source of new strategies to conceal and protect information.
Performance analysis of Jakimoski–Kocarev attack on a class of chaotic cryptosystems
Physics Letters A, 2003
Recently Jakimoski and Kocarev cryptanalyzed two chaotic cryptosystems without using chaotic synchronization—Baptista cryptosystem and Alvarez cryptosystem. As a result, they pointed out that neither of the two cryptosystems are secure to known-plaintext attacks. In this Letter, we re-study the performance of Jakimoski–Kocarev attack on Baptista cryptosystem and find that it is not efficient enough as a practical attack tool. Furthermore, a simple but effective remedy is presented to resist Jakimoski–Kocarev attack, and the detailed discussion on its performance are given.
Since 1990s chaotic dynamical systems have been widely used to design new strategies to encrypt information. Indeed, the dependency to initial conditions and control parameters, along with the ergodicity of their temporal evolution allow the establishment of chaos as the base of new cryptosystems, i.e., of new schemes of confusion and diffusion of information. However, an optimum design in the context of chaos-based cryptography demands a thorough knowledge not only of the foundations of cryptography, but also of the dynamics and inner structure of chaos. Therefore, any proposal to use chaos in the context of cryptography must respect a series of design rules, in order to avoid the reconstruction of the dynamics of the underlying chaotic system, and to determine an optimum use of the virtues of the chaotic dynamics. Although it is possible to use chaos to design analog cryptosystems based on synchronization techniques, this Thesis is focused on the application of chaotic maps, i.e., chaotic dynamical systems defined in discrete time to cryptography. In this sense, a set of mathematical tools are defined to establish the adequacy of a chaotic map as the base of a cryptosystem, and the requirements that an encryption architecture must satisfy to avoid the dynamical reconstruction of the underlying chaotic map. More precisely, this Thesis provides an extension and systematization of the results derived from the cryptanalysis of chaos-based cryptosystems. The above goal comprises three different stages: 1.- Definition of a set of mathematical tools that allow the selection of the adequate configurations of a dynamical system to implement strategies of confusion and diffusion of information. 2.- Study of the most popular chaotic maps in the field of chaos-based cryptography to determine whether these maps can be used to design new cryptosystems without incurring in security problems. 3.- Summary and conclusions of the first two stages. The aim is to define a set of rules or recommendations as a guide for the design of chaos-based cryptosystems. Recalling the first stage, its main purpose is the search of procedures to infer or estimate the initial conditions and/or the control parameters from the orbits of a chaotic map. Different scenarios are considered depending on whether complete orbits are accesible or it is only possible to work with sampled or discretized versions of the orbits. In all scenarios the goal consist in building bijective functions with respect to the initial conditions and/or the control parameters. The requirements to build these bijective functions are clarified, along with the procedures to guide the estimation of the initial conditions and/or the control parameters. In order to test the set of mathematical tools and the estimation methods, the logistic map and its associated topological conjugate maps are thoroughly studied, since these maps are the most widely used in the design of new digital chaotic cryptosystems. Specially relevant is the study of the symbolic dynamics and order patterns of unimodal maps. The study of this family of chaotic maps leads to a series of very useful results to define a set of recommendations for both the evaluation of the security of chaos-based cryptosystems and the design of encryption schemes based on chaos.
Methods of attacking chaotic encryption and countermeasures
2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221)
Methods of attacking chaotic encryption algorithms have been developed. These methods have been applied to all the published chaotic encryption systems and all these systems are broken in very short computer times. Counter measures have also been developed in order to make chaotic encryption secure. Several examples and results are given.