In their celebrated ”Period three implies chaos” paper, Li and Yorke proved that if a continuous interval map f has a period 3 point then there is an uncountable scrambled set S on which f has very complicated dynamics. One question arises naturally: Can this set S be chosen invariant under f? The answer is positive for turbulent maps and negative otherwise. In this note, we shall use symbolic ...

This paper analyzes the security of the Yi-Tan-Siew chaos-based cipher proposed in [1]. It is found that the claimed key (α,β, γ,K) collapses to be (α, γ) under a differential chosen-plaintext attack, and that an intermediate variable (called noise vector) used in the encryption function does not have a uniform distribution, which will downgrade the security of the cipher. Also, analysis shows ...

Recently, an optimal noncoherent detection technique for chaos-shift-keying digital communication system has been proposed. The computational intensity required, however, increases exponentially with the spreading factor. In this Letter, we propose an approximate-optimal detection technique, whose computational effort increases only linearly with the spreading factor. In particular, we use the ...

It is shown that every unimodal map is realized as a restriction of a simple map defined on the unit disc to a part of its boundary. Our two-dimensional map is called a full-folding map, which is defined generally on a compact metric space. It is a generalization of the full tent map in that it has two homeomorphic inverse maps and thus every non-critical point has two inverse images.

We have recently established a strong connection between the Tent map (also known as Generalized Luroth Series or GLS which is a chaotic, ergodic and lebesgue measure preserving non-linear dynamical system) and Arithmetic coding which is a popular source compression algorithm used in international compression standards such as JPEG2000 and H.264. This was for independent and identically distrib...

In this work, we used a sensor-based True Random Number Generator in order to generate keys for a stream cipher based on a recently published hybrid algorithm mixing Skew Tent Map and a Linear Feedback Shift Register. The stream cipher was implemented and tested in a Field Programmable Gate Array (FPGA) and was able to generate 8-bit width data streams at a clock frequency of 134 MHz, which is ...

In recent years, the chaos based cryptographic algorithms have some optional and efficient ways to develop secure encryption techniques. In this paper, we proposed a modified approach for encryption based on chaotic skew tent maps in order to meet the requirements of the secure transfer. In the projected encryption scheme, an external secret key of 128-bit and two chaotic skew tent maps are emp...

The intriguing characteristics of chaotic maps have prompted researchers to use these sequences in watermarking systems to good effect. In this paper we aim to use a tent map to encrypt the binary logo to achieve a like-noise signal. This approach makes extraction of the watermark signal by potential attacker very hard. Embedding locations are selected based on certain principles. Experimental ...

The properties of chaotic dynamical systems make them useful for channel coding in a variety of practical communication applications. To illustrate this, a novel analog code based on tent map dynamics and having a fast decoding algorithm is developed for use on unknown, multiple, and time-varying signal-to-noise ratio (SNR) channels. This code is shown to be an attractive alternative to both di...