A maximal entropy digital chaotic circuit

Michaels, Alan J.

doi:10.1109/iscas.2011.5937666

Cited by 20 publications

(20 citation statements)

References 11 publications

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“…Since the output of the digital chaotic circuit [10] follows a uniform distribution, independent pairs of the chaotic output (X A ,X B ) are transformed to quadrature Gaussian random variables (X I , X Q ) via the BM transformation [9], which implements the bivariate statistical mapping (1). …”

Section: A Generalized Box-muller Transformationmentioning

confidence: 99%

Performance of Percent Gaussian Orthogonal Signaling Waveforms

Michaels¹,

Lau

2014

2014 IEEE Military Communications Conference

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Recent developments of secure digital chaotic spread spectrum communication systems have been based on the generalized ideals of maximum channel capacity and maximal entropy/security, which result in a Gaussian-distributed noiselike signal that is indistinguishable from naturally occurring (bandlimited) thermal noise. An implementation challenge associated with these waveforms is that the signal peak-toaverage power ratio (PAPR) is approximately that of an i.i.d Gaussian distributed random sequence; with infinite tails in the Gaussian distribution, modeled practically by a Gaussian distribution truncated to ±4.8ı, the peak excursions of the output can be 13-15 dB over that of the average signal power. To address this PAPR constraint, a series of "percent Gaussian" orthogonal signaling waveforms were developed, allowing parameterized waveform selection that compactly trade PAPR improvements with cyclostationary feature content; these waveforms are bounded by the Gaussian distributed digital chaos signal and a constant amplitude zero autocorrelation (CAZAC) signal, all of which deliver security advantages over traditional direct sequence spread spectrum (DSSS) waveforms. This paper presents an underlying model for these "percent Gaussian" waveforms, derives a generalized set of symbol error rate metrics. Discussion of the performance bounds is also presented.

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Section: A Generalized Box-muller Transformationmentioning

confidence: 99%

Performance of Percent Gaussian Orthogonal Signaling Waveforms

Michaels¹,

Lau

2014

2014 IEEE Military Communications Conference

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“…For digital chaotic spread spectrum systems using baseband spreading these random values are circular symmetric complex normal (quadrature Gaussian) random variables. The construction of a chaotic spread symbol modulated with 16QAM constellations can take the form 1 where T is a symbol interval, S[mT] is the m th spread symbol, M is the number of spreading chips 1 per symbols (the spread ratio, assumed to be an integer), τ is chip interval and Q[mT] is the m th 16-QAM formatted symbol of the form , where , {-3,-1,1,3}. A simulated capture of one hundred real-valued 16-QAM data symbols is shown in Figure 1.…”

Section: Extension Of Gaussian Distributed Spreading Sequences Tomentioning

confidence: 99%

“…For 16-QAM symbols, the complementary amplitudes are the same 16-QAM energy-normalized amplitudes applied to yield a constant aggregate expected energy. 1 That is, a symbol with normalized variance | | 2 is paired with an independent signal with normalized variance | ′ | 18 such that the sum of their variances is a constant 20M. The independence of the orthogonal waveforms ensures that the variance of the sum ′ is the sum of the individual variances.…”

Section: Featureless Chaotic Spread Spectrum Techniques For a 16mentioning

confidence: 99%

“…Many of these chaotic signals exhibit colored spectra, providing discernible features that enable their detection independent of the transmitted data. A recent digital chaotic circuit [1] has been shown to exhibit a truly white spectrum in addition to apparent time-domain randomness. This maximal entropy characteristic supports Shannon's criteria for maximal channel capacity communication, low probability of interception/ detection (LPI/LPD), and a compact bandlimited white spectrum.…”

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Featureless chaotic spread spectrum modulation of arbitrary data constellations

Michaels

Chester

2011

2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications

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Chaotic spread spectrum communication systems provide a number of advantages for secure communications due to the apparent randomness of the underlying spreading signal. Many of these chaotic signals exhibit colored spectra, providing discernible features that enable their detection independent of the transmitted data. A recent digital chaotic circuit [1] has been shown to exhibit a truly white spectrum in addition to apparent time-domain randomness. This maximal entropy characteristic supports Shannon's criteria for maximal channel capacity communication, low probability of interception/ detection (LPI/LPD), and a compact bandlimited white spectrum. Such a signal is featureless, susceptible only by energy detection. The disadvantage of such spread communication systems, one shared equally by all spread spectrum systems, is that the channel capacity is constrained by the bandwidth increases required for spreading gain. A traditional approach to increasing bandwidth efficiency is generalizing the modulated digital signaling constellation to include multiple levels of amplitude and phase modulation, which enhances exploitable cyclostationary features unless compensated. This paper presents a framework for adapting the maximal entropy digital chaotic signal to featureless chaotic spread spectrum modulation of arbitrary discrete-time discrete-amplitude data constellations, permitting higher throughputs in chaotic spread spectrum communication systems without sacrificing any of the maximum entropy characteristics that provide LPI/LPD.

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“…Efficient mechanisms for creating arbitrary sequence lengths measured in googols have been constructed [2], with reverse engineering attempts being a combination of prime number factoring and mixed-radix conversions using noisecorrupted samples. Secondary keying processes, such as those used in public-key encryption, and offline monitoring of the overall cyber-physical infrastructure can also be used to pinpoint and timestamp DoS or spoofing attempts, with network node entry (signal acquisition) occurring only according to known protocols.…”

Section: Ia Evaluation Of Phy-layer Encryptionmentioning

confidence: 99%

Physical-layer encryption for enhanced cyber-physical security

Michaels¹,

Allen²

2011

Proceedings of the Seventh Annual Workshop on Cyber Security and Information Intelligence Research

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Communication in wide-area measurement/control systems (WAM/CS) presents simultaneous challenges of achieving low latency, high security, and sufficient data throughputs to meet the overall quality of service requirements. High-value and timecritical information such as that indicating transient instability or attacks on the cyber-physical infrastructure must be delivered to their destination within 5-20 ms of identification [1], eliminating many of the existing commercial communications solutions that employ a traditional net-centric ISO stack-based architecture. This paper focuses on a physical-layer wireless communications technology capable of supporting real-time protection, detection, and reaction processes within the WAM/CS via physical-layer encryption. This PHY-layer encryption adapts a maximum entropy digital chaotic spread spectrum waveform originally developed for secure military communications [2] by employing the underlying spreading sequence as a private key cryptosystem, thus avoiding latencies derived from MAC-layer framing or cryptographic block algorithms. The proposed approach delivers latencies on the order of 500µs per node, allowing significant flexibility in wireless network topology. We present the proposed PHY-layer encryption system in the context of communicating an a monitored "event," evaluate its behavior against the traditional IA objectives, and also consider its integration with related communications techniques to demonstrate its utility as a building block for enhancing cyber-physical security.

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A maximal entropy digital chaotic circuit

Cited by 20 publications

References 11 publications

Performance of Percent Gaussian Orthogonal Signaling Waveforms

Performance of Percent Gaussian Orthogonal Signaling Waveforms

Featureless chaotic spread spectrum modulation of arbitrary data constellations

Physical-layer encryption for enhanced cyber-physical security

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