SLs are artificial crystals whose periods comprise two very wide layers of different semiconductors having similar lattice constants. Two Appendices provide details on the derivation of the model equations. Section 4 summarizes our findings and perspectives for fast random bit generators based on semiconductor superlattices.
, we explain how to obtain a high-speed true random bit generator by processing the chaotic current oscillations provided by the device. We also discuss the relation of our results to experiments and which features of the model need to be revised in order to optimize the chaotic oscillations. The noises also induce chaos in nearby voltage intervals where the deterministic system had periodic oscillations. In Section 3.1, numerical solutions of the model equations show that the thermal and shot noises existing in the SL enhance stable spontaneous chaos in voltage intervals where the corresponding deterministic model exhibits chaos. The model consists of a number of coupled stochastic differential equations together with algebraic boundary and voltage bias conditions. In Section 2, we discuss the mathematical model for a single SL under voltage bias. In this paper, we comment the possible use of spontaneously chaotic semiconductor superlattices (SLs) as true random number generators. If they show to be scalable, these devices could be vastly useful, as the performance and reliability of our digital networked society relies on the ability to generate fast and cheaply large quantities of random numbers. As of now, these two types of devices have been shown to reliably produce truly random sequences of numbers at fast rates in laboratory experiments.
While semiconductor lasers require a mixture of optical and electronic components, semiconductor superlattices are all electronic submicron devices that can be integrated in more complex circuits. This signal can be detected by using conventional electronics that is much faster than optical photon counting detectors. In both cases, quantum fluctuations are amplified by chaotic dynamics to a macroscopic fluctuating signal. Recently, fast generation of truly random numbers (tens or hundreds of Gb/s) has been achieved using chaotic semiconductor lasers and superlattices. More robust systems are based on quantum mechanical uncertainty, e.g., on whether a photon is detected, but they are limited to relatively low rates of number generation (tens of Mb/s). These physical processes yield a low analog signal and are easily affected by disturbances including temperature fluctuations. Other physical sources of entropy are too sensitive to external influences and lack robustness, for example, thermal noise or electrical noise in diodes and resistors. An obvious drawback of these mechanical methods is that they are too slow for practical use.
Similar analyses apply to the case of rolling dice, card shuffling or spinning a roulette wheel. For instance, the mechanics of coin tossing shows that small uncertainties in the initial condition ensure equal probability of heads and tails provided some parameter (e.g., initial velocity) is large enough. Deterministic processes that are difficult to predict have been used in gambling since antiquity. To get cryptographically secure PRNGs, it is convenient to have generated truly random numbers that may be obtained ideally from inherently random or unpredictable processes.
Then vulnerability in the pseudorandom number generator (PRNG) may follow, as it famously was the case for Microsoft Windows operating system secure encryption several years ago. However, the number sequences thus produced are only pseudorandom, as two identical programs that begin at the same state will produce the same sequence. This conventional approach is cheap and fast, as it is limited only by the processor speed. Such numerical strings yield the keys for secure storage and transmission of data. The generator is a function whose input is a short random seed, and whose output is a long stream which is indistinguishable from truly random bits. Usually, these generators are based on numerical algorithms that produce seemingly unpredictable number sequences. We also talk about random bit generators (RBGs) when emphasizing that binary numbers are produced. Online gambling, finance, computer telecommunications, online commerce and data encryption systems,, stochastic modeling, and Monte Carlo simulations among many others, rely on fast random number generators (RNGs). Generation of random numbers at high speed is at the core of many activities of economic importance.