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arXiv:2501.06318 · Applied Physics Letters

High-speed tunable generation of random number distributions using actuated perpendicular magnetic tunnel junctions

Ahmed Sidi El Valli, Michael Tsao, J. Darby Smith, Shashank Misra, Andrew D. Kent

Published May 26, 2025• 6 citations

Abstract

Perpendicular magnetic tunnel junctions (pMTJs) actuated by nanosecond pulses are emerging as promising devices for true random number generation (TRNG) due to their intrinsic stochastic behavior and high throughput. In this work, we demonstrate the tunability and quality of random number distributions generated by pMTJs operating at a frequency of 104 MHz. First, changing the pulse amplitude is used to systematically vary the probability bias. The variance of the resulting bitstreams closely matches the expected binomial distribution, demonstrating consistency with an underlying sequence of Bernoulli trials. Second, the quality of uniform distributions of 8-bit random numbers generated with a probability bias of 0.5 is considered. A reduced chi-square analysis of these data shows that only two XOR operations are sufficient to achieve this distribution with p-values greater than 0.05. Finally, we show that there is a correlation between long-term probability bias variations and pMTJ resistance. These findings suggest that variations in the characteristics of the pMTJ underlie the observed variation of probability bias. Our results highlight the potential of stochastically actuated pMTJs for high-speed, tunable TRNG applications, showing the importance of the stability of pMTJ device characteristics in achieving reliable, long-term performance.

DOI: 10.1063/5.0259366

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Perpendicular magnetic tunnel junctions (pMTJs) actuated by nanosecond pulses are emerging as promising devices for true random number generation (TRNG) due to their intrinsic stochastic behavior and high throughput. In this work, we demonstrate the tunability and quality of random number distributions generated by pMTJs operating at a frequency of 104 MHz. First, changing the pulse amplitude is used to systematically vary the probability bias. The variance of the resulting bitstreams closely matches the expected binomial distribution, demonstrating consistency with an underlying sequence of Bernoulli trials. Second, the quality of uniform distributions of 8-bit random numbers generated with a probability bias of 0.5 is considered. A reduced chi-square analysis of these data shows that only two XOR operations are sufficient to achieve this distribution with p-values greater than 0.05. Finally, we show that there is a correlation between long-term probability bias variations and pMTJ resistance. These findings suggest that variations in the characteristics of the pMTJ underlie the observed variation of probability bias. Our results highlight the potential of stochastically actuated pMTJs for high-speed, tunable TRNG applications, showing the importance of the stability of pMTJ device characteristics in achieving reliable, long-term performance.

Large quantities of random numbers are crucial in a wide range of applications. We have recently demonstrated that perpendicular nanopillar magnetic tunnel junctions (pMTJs) can produce true random bits when actuated with short pulses. However, our implementation used high-end and expensive electronics, such as a high-bandwidth arbitrary waveform generator and analog-to-digital converter, and was limited to relatively low data rates. Here, we significantly increase the speed of true random-number generation of our stochastic actuated pMTJs (SMART-pMTJs) using field-programmable gate arrays (FPGAs), demonstrating the generation of over

{\text{10}}^{\text{12}}

bits at rates exceeding 10 Mb/s. The resulting bitstreams pass the NIST Statistical Test Suite for randomness with only onexoroperation. In addition to a hundred-fold reduction in the setup cost and a thousand-fold increase in bitrate, the advancement includes simplifying and optimizing random bit generation with a custom-designed analog daughterboard to interface an FPGA and SMART-pMTJ. The resulting setup further enables FPGA at-speed processing of MTJ data for stochastic modeling and cryptography.

Magnetic tunnel junction (MTJ)-based true random number generators (TRNG), which are promisingly utilized as hardware accelerators for probabilistic computing, may suffer intrinsic performance drifting and fluctuation in the probability space and performance variations in device arrays. In order to preventively avoid these concerns, it is necessary to develop strategies that can help MTJ-based TRNG to be self-stabilized and calibration-free. Here, we derived a simple and easily handleable strategy that only depends on the current sampled state of an MTJ device without any historical or statistic information or a pre-calibrated probabilistic switching property to dynamically tune its sampling probability for the next sampling operation. In this way, the long-term sampling probability of the MTJ can be proved to automatically converge into a desired probability with little fluctuation and drifting. We further experimentally demonstrate such a self-stabilized MTJ-based TRNG. Our results show that the TRNG can generate binary random numbers with any destined probability regardless of its initial state. Furthermore, the TRNG also displays the desired capability of excellently hedging against performance drifting and fluctuations. All these combined allow the self-stabilized TRNG without calibration to be more viable for high-quality entropy source applications.

We demonstrate a method to generate application-ready truly random bits from a magnetic tunnel junction driven by a Field-Programmable Gate Array (FPGA). We implement a real-time feedback loop that stabilizes the switching probability near 50% and apply an XOR operation, both on the FPGA, to suppress short-term correlations, together mitigating long-term drift and bias in the bitstream. This combined approach passes the NIST Statistical Test Suite for random bit generation at 5 Mb/s without post-processing, providing a practical hardware solution for fast and reliable true random number generation. Beyond cryptographic applications, these capabilities open opportunities for stochastic hardware accelerators, probabilistic computing, and large-scale modeling where real-time access to unbiased randomness is essential.

True random-number generators (TRNGs) are crucial in modern information technology, especially in cryptographic systems. TRNGs can be realized via stochastic physical processes, such as the thermally activated magnetization switching in a magnetic tunnel junction (MTJ). The fluctuations in MTJ-based TRNGs are still too slow for many practical purposes, though. This study proposes that the simple application of a small magnetic field can increase the generation rate of a MTJ-TRNG by several orders of magnitude, up to gigahertz frequencies. This approach could turn commercialized MTJ-MRAM devices into fast TRNGs with minimal modification.

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Generation of practical random numbers (RNs) by a spintronics-based, scalable truly RN generator called "spin dice" was demonstrated.The generator utilizes the stochastic nature of spin-torque switching in a magnetic tunnel junction (MTJ) to generate RNs.We fabricated eight perpendicularly magnetized MTJs on a single-board circuit and generated eight sequences of RNs simultaneously.The sequences of RNs of different MTJs were not correlated with each other, and performing an exclusive OR (XOR) operation among them improved the quality of the RNs.The RNs obtained by performing a nested XOR operation passed the statistical test of NIST SP-800 with the appropriate pass rate.