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Register a new userA Mathematical Random Number Generator (MRNG)
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A novel Mathematical Random Number Generator (MRNG) is presented here. In this case, mathematical refers to the fact that to construct that generator it is not necessary to resort to a physical phenomenon, such as the thermal noise of an electronic device, but rather to a mathematical procedure. The MRNG generates binary strings - in principle, as long as desired - which may be considered genuinely random in the sense that they pass the statistical tests currently accepted to evaluate the randomness of those strings. From those strings, the MRNG also generates random numbers expressed in base 10. An MRNG has been installed as a facility on the following web page: http://www.appliedmathgroup.org. This generator may be used for applications in tasks in: a) computational simulation of probabilistic-type systems, and b) the random selection of samples of different populations. Users interested in applications in cryptography can build another MRNG, but they would have to withhold information - specified in section 5 - from people who are not authorized to decode messages encrypted using that resource.
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Currently, statistical tests for random number generators (RNGs) are widely used in practice, and some of them are even included in information security standards. But despite the popularity of RNGs, consistent tests are known only for stationary ergodic deviations of randomness (a test is consistent if it detects any deviations from a given class when the sample size goes to $ infty $). However, the model of a stationary ergodic source is too narrow for some RNGs, in particular, for generators based on physical effects. In this article, we propose computable consistent tests for some classes of deviations more general than stationary ergodic and describe some general properties of statistical tests. The proposed approach and the resulting test are based on the ideas and methods of information theory.
The heart of every Monte Carlo simulation is a source of high quality random numbers and the generator has to be picked carefully. Since the ``Ferrenberg affair it is known to a broad community that statistical tests alone do not suffice to determine the quality of a generator, but also application-based tests are needed. With the inclusion of an extensible random number library and the definition of a generic interface into the revised C++ standard it will be important to have access to an extensive C++ random number test suite. Most currently available test suites are limited to a subset of tests are written in Fortran or C and cannot easily be used with the C++ random number generator library.
The generation of random bits is of enormous importance in modern information science. Cryptographic security is based on random numbers which require a physical process for their generation. This is commonly performed by hardware random number generators. These exhibit often a number of problems, namely experimental bias, memory in the system, and other technical subtleties, which reduce the reliability in the entropy estimation. Further, the generated outcome has to be post-processed to iron out such spurious effects. Here, we present a purely optical randomness generator, based on the bi-stable output of an optical parametric oscillator. Detector noise plays no role and no further post-processing is required. Upon entering the bi-stable regime, initially the resulting output phase depends on vacuum fluctuations. Later, the phase is rigidly locked and can be well determined versus a pulse train, which is derived from the pump laser. This delivers an ambiguity-free output, which is reliably detected and associated with a binary outcome. The resulting random bit stream resembles a perfect coin toss and passes all relevant randomness measures. The random nature of the generated binary outcome is furthermore confirmed by an analysis of resulting conditional entropies.
Random number generators (RNGs) that are crucial for cryptographic applications have been the subject of adversarial attacks. These attacks exploit environmental information to predict generated random numbers that are supposed to be truly random and unpredictable. Though quantum random number generators (QRNGs) are based on the intrinsic indeterministic nature of quantum properties, the presence of classical noise in the measurement process compromises the integrity of a QRNG. In this paper, we develop a predictive machine learning (ML) analysis to investigate the impact of deterministic classical noise in different stages of an optical continuous variable QRNG. Our ML model successfully detects inherent correlations when the deterministic noise sources are prominent. After appropriate filtering and randomness extraction processes are introduced, our QRNG system, in turn, demonstrates its robustness against ML. We further demonstrate the robustness of our ML approach by applying it to uniformly distributed random numbers from the QRNG and a congruential RNG. Hence, our result shows that ML has potentials in benchmarking the quality of RNG devices.
Quantum random number generation exploits inherent randomness of quantum mechanical processes and measurements. Real-time generation rate of quantum random numbers is usually limited by electronic bandwidth and data processing rates. Here we use a multiplexing scheme to create a fast real-time quantum random number generator based on continuous variable vacuum fluctuations. Multiple sideband frequency modes of a quantum vacuum state within a homodyne detection bandwidth are concurrently extracted as the randomness source. Parallel post-processing of raw data from three sub-entropy sources is realized in one field-programmable gate array (FPGA) based on Toeplitz-hashing extractors. A cumulative generation rate of 8.25 Gbps in real-time is achieved. The system relies on optoelectronic components and circuits that could be integrated in a compact, economical package.
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