This paper and its companion are devoted to the evaluation of the impact of chaos-based techniques on communications systems with asynchronous code division multiple access. Sequences obtained by repeating a truncated and quantized chaotic time series are compared with classical m-sequences and Gold sequences by means of a performance index taken from communication theory which is here defined and thoroughly discussed. This analysis reveals that, unlike conventional sequences, chaotic spreading codes can be generated for any number of users and allocated bandwidth. Numerical simulations are reported, showing that systems based on chaotic spreading sequences perform generally better than the conventional ones. Some analytical tools easing the comprehension of these advantages are summarized.

We present a true random number generator which, contrary to other implementations, is not based on the explicit observation of complex micro-cosmic processes but on standard signal processing primitives, freeing the designer from the need for dedicated hardware. The system can be implemented from now ubiquitous analog-to-digital converters building blocks, and is therefore well-suited to embedding. On current technologies, the design permits data rates in the order of a few tens of megabits per second. Furthermore, the absence of predictable, repeatable behaviors increases the system security for cryptographic applications. The design relies on a simple inner model based on chaotic dynamics which, in ideal conditions, can be formally proven to generate perfectly uncorrelated binary sequences. Here, we detail the design and we validate the quality of its output against a couple of test suites standardized by the U.S. National Institute of Standards and Technology, both in the ideal case and assuming implementation errors.

In this paper we review some statistical tests included in the NIST SP 800-22 suite, which is a collection of tests for the evaluation of both true-random (physical) and pseudorandom (algorithmic) number generators for cryptographic applications. The output of these tests is the so-called p-value which is a random variable whose distribution converges to the uniform distribution in the interval [0,1] when testing an increasing number of samples from an ideal generator. Here, we compute the exact non-asymptotic distribution of p-values produced by few of the tests in the suite, and propose some computation-friendly approximations. This allows us to explain why intensive testing produces false-positives with a probability much higher than the expected one when considering asymptotic distribution instead of the true one. We also propose a new approximation for the Spectral Test reference distribution, which is more coherent with experimental results.

The application of chaotic dynamics to signal processing tasks stems from the realization that its complex behavior becomes tractable when observed from a statistical perspective. Here we illustrate the validity of this statement by considering two noteworthy problems-namely, the synthesis of high-electromagnetic compatibility clock signals and the generation of spreading sequences for direct-sequence code-division communication systems, and by showing how the statistical approach to discrete-time chaotic systems can be applied to find their optimal solution. To this aim, we first review the basic mathematical tools both intuitively and formally; we consider the Perron-Frobenius operator its spectral decomposition and its tie to the correlation properties of chaotic sequences. Then, by leveraging on the modeling/approximation of chaotic systems through Markov chains, we introduce a matrix/tensor-based framework where statistical indicators such as high-order correlations can be quantified. We underline how, for many particular cases, the proposed analysis tools can be reversed into synthesis methodologies and we use them to tackle the two above mentioned problems. In both cases, experimental evidence shows that the availability of statistical tools enables the design of chaos-based systems which favorably compare with analogous nonchaos-based counterparts.

We present the design and the validation by means of suitably improved randomness tests of two different implementations of high-performance true-random number generators which use a discrete-time chaotic circuit as their entropy source. The proposed system has been developed from a standard pipeline Analog-to-Digital converter (ADC) design, modified to operate as a set of piecewise-linear chaotic maps. The evolution of each map is observed and quantized to obtain a random bit stream. With this approach it is possible to obtain, on current CMOS technology, a data rate in the order of tens of megabit per second. Furthermore, we can also prove that the design is tamper resistant in the sense that a power analysis cannot leak information regarding the generated bits. This makes the proposed circuit perfectly suitable for embedding in cryptographic systems like smarts cards, even more so if one consider that it could be easily obtained by reconfiguring an existing pipeline ADC. The two prototypes have been designed in a 0.35-μm and 0.18-μm CMOS technology, and have a throughput of, respectively, 40 Mbit/s and 100 Mbit/s. A comparison between measured results and other high-end commercial solutions shows a comparable quality with a operating speed that is one order of magnitude faster.

The idea that compressed sensing may be used to encrypt information from unauthorized receivers has already been envisioned but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper, we apply this simple encoding to define a general private-key encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, which are provided partially corrupted encoding matrices and are thus allowed to decode the acquired signal at provably different levels of recovery quality. The security properties of this scheme are thoroughly analyzed: first, the properties of our multiclass encryption are theoretically investigated by deriving performance bounds on the recovery quality attained by lower-class receivers with respect to high-class ones. Then, we perform a statistical analysis of the measurements to show that, although not perfectly secure, compressed sensing grants some level of security that comes at almost-zero cost and thus may benefit resource-limited applications. In addition to this, we report some exemplary applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal recoveries.