Random number generators in digital information systems make use of physical entropy sources such as electronic and photonic noise to add unpredictability to deterministically generated pseudo-random sequences1,2. However, there is a large gap between the generation rates achieved with existing physical sources and the high data rates of many computation and communication systems; this is a fundamental weakness of these systems. Here we show that good quality random bit sequences can be generated at very fast bit rates using physical chaos in semiconductor lasers. Streams of bits that pass standard statistical tests for randomness have been generated at rates of up to 1.7 Gbps by sampling the fluctuating optical output of two chaotic lasers. This rate is an order of magnitude faster than that of previously reported devices for physical random bit generators with verified randomness. This means that the performance of random number generators can be greatly improved by using chaotic laser devices as physical entropy sources. Random-number generators are important in digital information systems. However, the speed at which current sources operate is much slower than the typical data rates used in communication and computing. Chaos in semiconductor lasers might help to bridge the gap.

Fast physical random bit generation with chaotic semiconductor lasers

Autonomic communications seek to improve the ability of network and services to cope with unpredicted change, including changes in topology, load, task, the physical and logical characteristics of the networks that can be accessed, and so forth. Broad-ranging autonomic solutions require designers to account for a range of end-to-end issues affecting programming models, network and contextual modeling and reasoning, decentralised algorithms, trust acquisition and maintenance---issues whose solutions may draw on approaches and results from a surprisingly broad range of disciplines. We survey the current state of autonomic communications research and identify significant emerging trends and techniques.

A survey of autonomic communications

Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of handling nonlinear functions. We review models and applications of MINLP, and survey the state of the art in methods for solving this challenging class of problems.Most solution methods for MINLP apply some form of tree search. We distinguish two broad classes of methods: single-tree and multitree methods. We discuss these two classes of methods first in the case where the underlying problem functions are convex. Classical single-tree methods include nonlinear branch-and-bound and branch-and-cut methods, while classical multitree methods include outer approximation and Benders decomposition. The most efficient class of methods for convex MINLP are hybrid methods that combine the strengths of both classes of classical techniques.Non-convex MINLPs pose additional challenges, because they contain non-convex functions in the objective function or the constraints; hence even when the integer variables are relaxed to be continuous, the feasible region is generally non-convex, resulting in many local minima. We discuss a range of approaches for tackling this challenging class of problems, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non-convex structures to obtain improved convex relaxations.We finish our survey with a brief discussion of three important aspects of MINLP. First, we review heuristic techniques that can obtain good feasible solution in situations where the search-tree has grown too large or we require real-time solutions. Second, we describe an emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP. Third, we survey the state of the art in software for MINLP.

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Mixed-integer nonlinear optimization

In this paper, a fast chaos-based image encryption system with stream cipher structure is proposed. In order to achieve a fast throughput and facilitate hardware realization, 32-bit precision representation with fixed point arithmetic is assumed. The major core of the encryption system is a pseudo-random keystream generator based on a cascade of chaotic maps, serving the purpose of sequence generation and random mixing. Unlike the other existing chaos-based pseudo-random number generators, the proposed keystream generator not only achieves a very fast throughput, but also passes the statistical tests of up-to-date test suite even under quantization. The overall design of the image encryption system is to be explained while detail cryptanalysis is given and compared with some existing schemes.

A fast image encryption system based on chaotic maps with finite precision representation

http://ieeexplore.ieee.org/iel5/5/31324/01456901.pdf

Microelectronic circuits

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.

Embeddable ADC-based true random number generator for cryptographic applications exploiting nonlinear signal processing and chaos

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.

Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications

This book deals with a number of fundamental issues related to the practical implementation of ultrasonic NDT techniques in an industrial environment. The book discusses advanced academic research results and their application to industrial procedures. The text covers the choice and generation of the signals energizing the system to probe position optimization, from quality assessment evaluation to tomographic inversion. With a focus to deepen a number of fundamental aspects involved in the specific objective of designing and developing an ultrasonic imaging system for nondestructive testing, aimed to automatically classify the entire production of an industrial production line, targeted to the field of precision mechanics. The contents of this book is the result of the common effort of six University Research Groups that focused their research activities for two years on this specific objective, working in direct conjunction with primary industrial firms, in a research project funded by the Italian government as a Strategic Research Project.

Sergio Callegari

Papers

Embeddable ADC-based true random number generator for cryptographic applications exploiting nonlinear signal processing and chaos

Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications

Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications

Ultrasonic Nondestructive Evaluation Systems: Industrial Application Issues

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS Editor-in-Chief