Cryptanalysis of a chaos-based cryptosystem on DSP (original) (raw)

Chaos-based cryptosystem on DSP

Chaos, Solitons & Fractals, 2009

We present a numeric chaos-based cryptosystem, implemented on a Digital Signal Processor (DSP), which resists all the attacks we have thought of. The encryption scheme is a synchronous stream cipher. Its security arises from the properties of the trajectories in a chaotic attractor, reinforced by the use of a nonlinear non-invertible two-dimensional map, the introduction of jumps between successive points of the orbits and the retaining of only one bit of the representation of real values. We describe the results obtained through a cryptanalytic study, we detail how to adjust the different parameters of the cryptosystem in order to ensure security, and we apply the NIST (National Institute of Standards and Technology) standard tests for pseudo-randomness to our construction. The originality of this work lies in the end in the way we were able to improve the security of our system, so that it is from now on possible to envisage the use, in more general cryptographic purposes, of other recurrences than those classically employed.

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.

Implementation and Practical Problems of Chaos-based Cryptography Revisited

Journal of Information Security and Applications, 2019

Chaos-based cryptography, since its inception, has become a widely published subject. Despite the vast amount of contributions in the area, its applications in real-world scenarios are minimal as compared to conventional cryptography. Chaotic maps have been used in the design of cryptosystems because they depict desirable characteristics such as pseudorandomness, complexity, and sensitivity to parameter changes. Despite these characteristics being analogous to cryptographic requirements, the resulting chaos-based cryptosystems are usually difficult to analyze, inefficient, and have reproducibility issues. In this paper, we highlight some of the problems which deter the practical application of chaos-based cryptosystems. We show that recently published work in reputable journals still do not address these problems and remain only of academic interest. We also perform experiments to depict some of the implementation issues of digital chaos that need to be taken into consideration when designing chaos-based algorithms. We then discuss a number of possible solutions that can be explored to overcome these problems.

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

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

Chaos-Based Cryptography, 2011

The idea of using chaotic transformations in cryptography is explicit in the foundational papers of Shannon on secrecy systems (e.g., [96]). Although the word “chaos” was not minted till the 1970s [71], Shannon clearly refers to this very concept when he proposes the construction of secure ciphers by means of measure-preserving, mixing maps which depend ‘sensitively’ on their parameters. The implementation of Shannon’s intuitions had to wait till the development of Chaos Theory in the 1980s. Indeed, it was around 1990 when the first chaos-based ciphers were proposed (e.g., [78], [46]). Moreover, in 1990 chaos synchronization [91] entered the scene and shortly thereafter, the first applications to secure communications followed [56, 37]. The idea is remarkably simple: mask the message with a chaotic signal and use synchronization at the receiver to filter out the chaotic signal. The realization though had to overcome the desynchronization induced by the message itself. After this initial stage, the number of proposals which exploited the properties of chaotic maps for cryptographical purposes, grew in a spectacular way.

Cryptanalysis of a secure communication scheme combining chaos and noise

This paper studies the security of a secure communication scheme based on two discrete-time intermittently-chaotic systems synchronized via a common random driving signal. Some security defects of the secure communication scheme are revealed: 1) the key space can be remarkably reduced; 2) the decryption is insensitive to the mismatch of the secret key; 3) the key-generation process used in this secure communication scheme is insecure against known/chosen-plaintext attacks. The first two defects mean that the secure communication scheme is not secure enough against brute-force attacks, and the third means that an attacker can easily break the cryptosystem by approximately estimating the secret key once he has a chance to access a fragment of the generated keystream. A direct result of the cryptanalysis given in this paper is the unsuitability of intermittent chaos in the design of secure chaotic cryptosystems.

Encryption using Deterministic Chaos

The concepts of randomness, unpredictability, complexity and entropy form the basis of modern cryptography and a cryptosystem can be interpreted as the design of a key-dependent bijective transformation that is unpredictable to an observer for a given computational resource. For any cryptosystem, including a Pseudo-Random Number Generator (PRNG), encryption algorithm or a key exchange scheme, for example, a cryptanalyst has access to the time series of a dynamic system and knows the PRNG function (the algorithm that is assumed to be based on some iterative process) which is taken to be in the public domain by virtue of the Kerchhoff-Shannon principal, i.e. the enemy knows the system. However, the time series is not a compact subset of a trajectory (intermediate states are hidden) and the iteration function is taken to include a 'secret parameter'-the 'key'. We can think of the sample as being 'random', 'unpredictable' and 'complex'. What do these properties mean mathematically and how do they relate to chaos? This paper focuses on answers to this question, links these properties to chaotic dynamics and consider the issues associated with designing pseudo-random number generators based on chaotic systems. The theoretical backound associated with using chaos for encryption is introduced with regard to randomness and complexity. A complexity and information theortic approach is considered based on a study of the complexity and entropy measures associated with chaotic systems. A study of pseudorandomness is then given which provides the foundations for the numerical methods that need to be realed for the practical implementation of data encryption. We study cryptographic systems using finite-state approximations to chaos or 'pseudochaos' and develop an approach based on the concept of multialgorithmic cryptography that exploits the properties of pseudochaotic algorithms.

Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems

International Journal of Bifurcation and Chaos, 2006

In recent years, a large amount of work on chaos-based cryptosystems have been published. However many of the proposed schemes fail to explain or do not possess a number of features that are fundamentally important to all kind of cryptosystems. As a result, many proposed systems are difficult to implement in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a thorough security analysis. Consequently, it is difficult for other researchers and end users to evaluate their security and performance. This work is intended to provide a common framework of basic guidelines that, if followed, every new cryptosystem would benefit from. The suggested guidelines address three main issues: implementation, key management, and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements. Meanwhile, several recommendations are made regarding some practical aspects of analog chaos-based secure communications, such as channel noise, limited bandwith, and attenuation.

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.