Tommaso Addabbo

A Class of Maximum-Period Nonlinear Congruential Generators Derived From the Rényi Chaotic Map

In this paper, a family of nonlinear congruential generators (NLCGs) based on the digitized Reacutenyi map is considered for the definition of hardware-efficient pseudorandom number generators (PRNGs), and a theoretical framework for their study is presented. The authors investigate how the nonlinear structure of these systems eliminates some of the statistical regularities spoiling the randomness of sequences generated with linear techniques. In detail, in this paper, a necessary condition that the considered NLCGs must satisfy to have maximum period length is given, and a list of such maximum period PRNGs for period lengths up to 231-1 is provided. Referring to the NIST800-22 statistical test suite, two PRNG examples are presented and compared to well-known PRNGs based on linear recurrencies requiring a similar amount of resources for their implementation

The Digital Tent Map: Performance Analysis and Optimized Design as a Low-Complexity Source of Pseudorandom Bits

In this paper, the discretized Tent map is analyzed as a source of pseudorandom bits. To evaluate the performance of the proposed pseudorandom bit generators (PRBGs), different issues were considered, such as the period length, the statistical characteristics of the generated bit sequences, and the hardware complexity required in digital circuit implementations. The results show that, under proper design conditions, the Tent-map-based PRBGs represent a suitable alternative to other traditional low-complexity PRBGs such as the linear feedback shift registers

Invariant Measures of Tunable Chaotic Sources: Robustness Analysis and Efficient Estimation

In this paper, a theoretical approach for studying the robustness of the chaotic statistics of piecewise affine maps with respect to parameter perturbations is discussed. The approach is oriented toward the study of the effects that the nonidealities derived from the circuit implementation of these chaotic systems have on their dynamics. The ergodic behavior of these systems is discussed in detail, adopting the approach developed by Boyarsky and Gora, with particular reference to the family of sawtooth maps, and the robustness of their invariant measures is studied. Although this paper is particularly focused on this specific family of maps, the proposed approach can be generalized to other piecewise affine maps considered in the literature for information and communications technology applications. Moreover, in this paper, an efficient method for estimating the unique invariant density for stochastically stable piecewise affine maps is proposed. The method is an alternative to Monte Carlo methods and to other methods based on the discretization of the Frobenius-Perron operator.

Low-hardware complexity PRBGs based on a piecewise-linear chaotic map

In this brief, a family of discretized one-dimensional chaotic maps derived from the Sawtooth map is analyzed to evaluate its suitability for the integrated implementation of low-complexity digital pseudorandom bit generators (PRBGs). The proposed PRBGs, classifiable as nonlinear congruential generators, are investigated in terms of period length, statistical properties of the generated sequences, hardware complexity, and are compared with traditional PRBGs.

Measurement of Angular Vibrations in Rotating Shafts: Effects of the Measurement Setup Nonidealities

In this paper, the authors discuss a measurement method, based on the zero-crossing demodulation technique of FM signals, to estimate the angular velocity vibrations of a rotating shaft. The demodulation algorithm is applied without any filtering to the direct voltage output issued by some probes sensing the passages of arbitrarily shaped targets installed on the rotating shaft. The authors discuss a theoretical approach to analyze the measurement problem taking into account the chief nonidealities related to the measurement setup, i.e., they have investigated the effects of both the shaft side vibrations and the irregular shape of the targets. On the basis of the theoretical results, the authors propose a measurement method that can reject the effects of these mentioned nonidealities, exploiting the measurements of two or more probes properly positioned around the shaft.

Versatile measurement system for the characterization of gas sensing materials

A measurement system designed for the development of novel conductometric gas sensors and of new gas sensing materials is described. The system allows to simultaneously characterize up to 8 sensors. Prototype sensors can be easily realized thanks to an ad hoc structure based on an alumina substrate equipped with electrodes, a heater and an accurate temperature sensor, on this structure the studied material can be deposited by screen printing, spin coating or dip coating. The system is designed to study the behavior of the sensors by accurately setting the operating conditions in terms of chemical environment composition, gas flow, humidity and temperature. The system is fully programmable and it individually controls the film temperatures or measures them with a resolution lower than 0.1 °C. Both chemical transients and thermal transients can be studied. These features make the system suitable for determining the principal performance indexes of a gas sensing device (e.g., sensitivity, stability, selectivity, response/recovery times, etc.) as functions of various combinations of measurement conditions (e.g., gas concentrations, temperature, humidity, flow). The proposed measurement system will find also useful applications in sensor model validation.

A multi-probe setup for the measurement of angular vibrations in a rotating shaft

In this paper we discuss a measurement method based on the zero-crossing demodulation method of FM signals to estimate the angular velocity vibrations of a rotating shaft. The demodulation algorithm is applied without any filtering to the direct output voltage of probes sensing the tooth passing of a geared wheel installed on a rotating shaft. The proposed method rejects the effects on the measurements due to the irregular cogwheel shape profile.

Pseudo-Chaotic Lossy Compressors for True Random Number Generation

This paper presents a compression method that exploits pseudo-chaotic systems, to be applied to True Random Bit Generators (TRBGs). The theoretical explanation of the proposed compression scheme required the projection of some results achieved within the Ergodic Theory for chaotic systems on the world of digital pseudo-chaos. To this aim, a weaker and more general interpretation of the Shadowing Theory has been proposed, focusing on probability measures, rather than on single chaotic trajectories. The design of the compression scheme has been theoretically discussed in order to assure the final entropy of the compressed TRBG to be arbitrarily close to the maximum limit of 1 bit/time-step. The proposed solution requires extremely low-complex hardware circuits for being implemented, assures a constant throughput and is based on theoretical results of general validity.

Digitized Chaos for Pseudo-random Number Generation in Cryptography

Random numbers play a key-role in cryptography, since they are used, e.g., to define enciphering keys or passwords [1]. Nowadays, the generation of random numbers is obtained referring to two types of devices, that are often properly combined together: True Random Number Generators (TRNGs), and Pseudo Random Number Generators (PRNGs). The former are devices that exploit truly stochastic physical phenomena [2, 3, 4, 5, 6], such as the electronic noise or the chaotic dynamics of certain nonlinear systems: for these devices the output sequences have an intrinsic degree of unpredictability, that is measured referring to the theoretical tools provided by Information Theory (e.g., in terms of the Shannon entropy) [7,4]. On the other hand, PRNGs are deterministic periodic finite state machines whose aim is to emulate, within the period, the random behavior of a truly random source of numbers. From a theoretical point of view, due to their deterministic nature, PRNGs are potentially predictable by observing their generated sequences [8, 9, 10, 1]. Nevertheless, in literature some families of PRNGs are classified to be ‘secure’, meaning that their algorithmic structure involves calculations that in average, referring to the prediction task, require an amount of computation time that is asymptotically unfeasible with the size of the problem, when referring to both the computational equipment at disposal and the known computing fastest algorithms [1,11]. It is worth noting that a given generator, even if belonging to an asymptotically secure family of PRNGs, can generate short periodic (and unsecure) sequences for several values of the initial seed. Therefore, apart from the cryptographic robustness of their algorithmic structure, a cryptographic PRNG must generate sequences that are acceptable from a statistical point of view, i.e., that pass a certain number of standard statistical tests [1, 12].

A Zero-Crossing Detection System Based on FPGA to Measure the Angular Vibrations of Rotating Shafts

In this paper, the efficient implementation of a reliable measurement device to measure the angular velocity vibrations of rotating shafts is discussed. The solution is particularly suitable to be fit in measurement embedded systems equipped with field-programmable gate arrays (FPGAs). The proposed measurement method is analyzed from a theoretical point of view, focusing the study on the frequency response of the technique. On the basis of the theoretical results, a reliable and low-complexity design of the measurement device has been proposed. In the adopted solution, the high clock rates of FPGAs are exploited to increase the accuracy of the zero-crossing times estimation, for a given A/D acquisition frequency, using an upsampling approach. The experimental results confirm the validity of the technique. The upsampling method allows an increase of the measurement accuracy and an improvement of about 10 dB for the output signal-to-noise ratio over a wide range of vibration frequencies.