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, could benefit every new cryptosystem. 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.

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Some basic cryptographic requirements for chaos-based cryptosystems

Image encryption using chaotic logistic map

In recent years, a great amount of secure communications systems based on chaotic synchronization have been published. Most of the proposed schemes fail to explain a number of features of fundamental importance to all cryptosystems, such as key definition, characterization, and generation. As a consequence, the proposed ciphers are difficult to realize in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a security analysis. Thus, it is hard for the reader to have a hint about their security. In this work we provide a set of guidelines that every new cryptosystems would benefit from adhering to. The proposed guidelines address these two main gaps, i.e., correct key management and security analysis, to help new cryptosystems be presented in a more rigorous cryptographic way. Also some recommendations are offered regarding some practical aspects of communications, such as channel noise, limited bandwith, and attenuation.

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Cryptographic requirements for chaotic secure communications

A new 1D chaotic system for image encryption

A novel colour image encryption algorithm based on chaos

A new substitution–diffusion based image cipher using chaotic standard and logistic maps

Discrete chaotic cryptography using external key

Cryptography using multiple one-dimensional chaotic maps

During last one and half decade an interesting relationship between chaos and cryptography has been developed, according to which many properties of chaotic systems such as: ergodicity, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems. As a result of this close relationship several chaos-based cryptosystems have been put forward since 1990. In one of the stages of the development of chaotic stream ciphers, the application of discrete chaotic dynamical systems in pseudo random bit generation has been widely studied recently. In this communication, we propose a novel pseudo random bit generator (PRBG) based on two chaotic logistic maps running side-by-side and starting from random independent initial conditions. The pseudo random bit sequence is generated by comparing the outputs of both the chaotic logistic maps. We discuss the suitability of the logistic map by highlighting some of its interesting statistical properties, which make it a perfect choice for such random bit generation. Finally, we present the detailed results of the statistical testing on generated bit sequences, done by the most stringent tests of randomness: the NIST suite tests, to detect the specific characteristics expected of truly random sequences. Povzetek: Predstavljen je psevdo nakljucni generator bitov na osnovi kaoticnega pristopa.

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Narendra K. Pareek

Papers

Image encryption using chaotic logistic map

A new substitution–diffusion based image cipher using chaotic standard and logistic maps

Discrete chaotic cryptography using external key

Cryptography using multiple one-dimensional chaotic maps

A Pseudo Random Bit Generator Based on Chaotic Logistic Map and its Statistical Testing