True random number generators are in high demand for secure cryptographic algorithms. Unlike algorithmically generated pseudo-random numbers, they are unclonable and non-deterministic. In this paper, we extract the white noise from stochastic Brownian Markov trajectories and use it to generate random numbers that qualify NIST standard tests of randomness. We trap colloidal particles in water using optical tweezers and record its confined Brownian motion in real-time. Next, in a two-step process, we use the initial section of incoming data to train and calibrate our iterative algorithm on the trap stiffness and viscosity of the solution based on the autocorrelation and power spectrum properties of the noise; then, we extract random arrays from the next section of the data. Interestingly, we get the best random number sequence for the best calibration. We test the random number sequence, which we have obtained, using standard randomness tests and observing the randomness to improve with increasing sampling frequencies.1 In the next steps, we extend this method to a wider class of processes, such as an optically trapped particle modulated by a square pulse or an external colored noise generated by an Ornstein Uhlenbeck process – we estimate the timescale of both the modulation and viscous effect using our algorithm.
True random number generators are in high demand for secure cryptographic algorithms. Unlike algorithmically generated pseudo-random numbers, they are unclonable and non-deterministic. In this paper, we extract the white noise from stochastic Brownian Markov trajectories and use it to generate random numbers that qualify NIST standard tests of randomness. We trap colloidal particles in water using optical tweezers and record its confined Brownian motion in real-time. Next, in a two-step process, we use the initial section of incoming data to train and calibrate our iterative algorithm on the trap stiffness and viscosity of the solution based on the autocorrelation and power spectrum properties of the noise; then, we extract random arrays from the next section of the data. Interestingly, we get the best random number sequence for the best calibration. We test the random number sequence, which we have obtained, using standard randomness tests and observing the randomness to improve with increasing sampling frequencies.1 In the next steps, we extend this method to a wider class of processes, such as an optically trapped particle modulated by a square pulse or an external colored noise generated by an Ornstein Uhlenbeck process – we estimate the timescale of both the modulation and viscous effect using our algorithm.
True random number generators are in high demand for secure cryptographic algorithms. Unlike algorithmically generated pseudo-random numbers they are unclonable and non-deterministic. A particle following Brownian dynamics as a result of the stochastic Ornstein-Uhlenbeck process is a source of true randomness because the collisions with the ambient molecules are probabilistic in nature. In this paper, we trap colloidal particles in water using optical tweezers and record its confined Brownian motion in real-time. Using a segment of the initial incoming data we train our learning algorithm to measure the values of the trap stiffness and diffusion coefficient and later use those parameters to extract the “white” noise term in the Langevin equation. The random noise is temporally delta correlated, with a flat spectrum. We use these properties in an inverse problem of trap-calibration to extract trap stiffnesses, compare it with standard equipartition of energy technique, and show it to scale linearly with the power of the trapping laser. Interestingly, we get the best random number sequence for the best calibration. We test the random number sequence, which we have obtained, using standard tests of randomness and observe the randomness to improve with increasing sampling frequencies. This method can be extended to the trap-calibration for colloidal particles confined in complex fluids, or active particles in simple or complex environments so as to provide a new and accurate analytical methodology for studying Brownian motion dynamics using the newly-emerged but robust machine learning platform.
True random numbers with high security originate from non-deterministic physical processes. Random laser with random feedback arising from multiple elastic scattering in a highly disordered structure is an ideal physical entropy source theoretically. In this work, a secure optical ultrafast random number generator based on random laser spectra was demonstrated. Unlike the usual method of recording laser intensity over time, the random laser spectrum under each pump pulse was recorded and converted into random numbers through post-processing. Approaches in three different dimensions—space, spectrum and time were used to increase the rate of random number generation. The randomness of resulting random bit streams was verified by the NIST statistics tests. Experimental results showed that an instantaneous bit rate of 810 terabits per second with off-line post-processing could be theoretically reached with an ideal experimental condition. This novel technique has big advantages in secure communications and promises to further increase the speed of random number generators to the lever of petabits per second or even higher.
A physical random number generator based on the intrinsic randomness of quantum mechanics is described. The random events are realized by the choice of single photons between the two outputs of a beamsplitter. We present a simple device, which minimizes the impact of the photon counters ’ noise, dead-time and after pulses. Random numbers are employed today as well for numerical simulations as for cryptography. Unfortunately computers are not able to generate true random numbers, as they are deterministic systems. Numerical pseudo-random generators rely on complexity [1]. Although such pseudo-random numbers can generally be employed for numerical computation, such as Monte-Carlo simulations, their use in cryptography, for example to generate keys, is more critical. The only way to get true random numbers, hence true security for crypto-systems, is to build a generator based on a random physical phenomenon [2,3,4]. As quantum theory is intrinsically random, a quantum process is an ideal base for a physical random number generator. The randomness of a sequence of numbers can be extensively tested, though not proven. It is thus of interest to thoroughly understand the behavior of the random process, so as to gain
Random Number Generators (RNGs) are crucial for applications ranging from cryptography to simulations. Depending on the source of randomness, RNGs are classified into Pseudo-Random Number Generators (PRNGs), True Random Number Generators (TRNGs), and Quantum Random Number Generators (QRNGs). This work presents the end-to-end development of a high-speed, high-efficiency, phase-noise-based QRNG system that taps into the quantum phase noise of a single-frequency laser, with randomness originating from spontaneous emission. Using a self-heterodyne measurement with a semiconductor laser (linewidth ≈ 5.23 GHz) operated near threshold and a $\sim$48 cm fiber delay line, a raw data generation rate of 2.0 Gbps is achieved. To ensure uniform randomness in the QRNG output, robust extraction techniques developed in-house, such as the Toeplitz Strong Extractor (TSE), are used. Randomness validation using the NIST and Diehard test suites confirms that all statistical tests pass at standard confidence levels. The developed system achieves a post-processed generation rate of 1.0 Gbps in operation and attains a Technology Readiness Level (TRL) of 7, approaching TRL 8, making it suitable for real-time secure applications such as cryptographic key generation and stochastic modeling.
In this work, we investigate colloidal particle patterns as a possible noise source for random number generation. We systematically analyze the minimum entropy of the noise source over different particle concentrations of {1, 3, 5, 7, 10, 12, 15} mg/ml according to the recommendations of the National Institute of Standards and Technology Special Publication 800-90B. The estimated minimum entropy of the non-independent and identically distributed particle pattern noise source is Hmin = 0.5896/1 bit at a particle amount of 5 mg/ml. For further entropy extraction on the noise source data, the secure hash algorithm is used to construct an entropy source. The randomness of the derived entropy source is verified according to the National Institute of Standards and Technology Special Publication 800-22 Rev. 1a and the accompanying statistical test suite. The entropy source passes all randomness tests of the statistical test suite and shows an estimated minimum entropy of Hmin = 0.9992/1 bit.
Random number generators (RNG) are fundamental to cryptographic systems, requiring high entropy, unpredictability, and resistance to cloning attacks. This work proposes RNG based on optical physical unclonable function (PUF) that uses random scattering of structured vortex beams through rough surface. The inherent disorder of the scattering medium with tunable beam parameters like vortex order, provides a rich source of physical randomness. The generated speckle patterns are processed using a post processing algorithm to produce random sequences at a rate of 1.42 Gbps. The statistical quality of the sequences is evaluated using the NIST SP 800-22, AIS-31, and Dieharder test suites, which meet the required randomness criteria. Further assessment using entropies and Kolmogorov complexity shows high entropy and algorithmic randomness. The physical unclonability and uniqueness are verified through inter-device hamming distances, Pearson correlation of sequences obtained from different spatial regions and vortex orders, revealing negligible correlations. To assess resilience against data based adversaries, machine learning modeling attacks are performed. The prediction accuracies remain close to random guessing, showing resistance to learning based cloning and response prediction attacks. These results establish the proposed optical PUF method as a high speed, physically unclonable, and machine learning resistant source of random numbers for secure cryptographic applications.