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Applied Physics Letters

Self-stabilized true random number generator based on spin–orbit torque magnetic tunnel junctions without calibration

Yingqian Xu, Xiaohan Li, Ran Zhang, Caihua Wan, Yizhan Wang, Shiqiang Liu, Xuming Luo, Guibin Lan, J. H. Xia, Guoqiang Yu, Xiufeng Han

Published Sep 23, 2024• 16 citations

Abstract

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.

DOI: 10.1063/5.0226007

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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.

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.

In recent years, true random number generators (TRNGs) based on magnetic tunnel junctions (MTJs) have become increasingly attractive. This is because MTJ-based TRNGs offer some advantages over traditional CMOS-based TRNGs, such as smaller area and simpler structure. However, there has been no work thus far that has quantified the quality of the raw output of a MTJ-based TRNG and performed suitable randomness extraction to produce provably secure random bits, unlike the case for CMOS-based TRNGs. In the work presented here, we implement a MTJ-based TRNG and characterize the entropy of the raw output. Using this information, we perform postprocessing to extract a set of random bits that are provably secure.

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.

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.

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.

True random number generation is a critical capability for fault-tolerant quantum computing at millikelvin temperatures. Yet existing Josephson-junction-based TRNGs all rest on a widely accepted but untested assumption: that reliable entropy extraction requires precisely controlled device parameters. Here we show that this assumption does not always hold. We demonstrate a counterintuitive finding: a single current-biased Josephson junction, regardless of its parameter quality, can serve as a cryptographic-grade true random number generator. To establish the universality of this conclusion, we deliberately selected the most extremely deviated devices from fabrication, with critical currents three orders of magnitude away from theoretical predictions and

I_cR

products an order of magnitude above conventional values, as the ultimate stress test. Even under these extreme conditions, the raw Shannon entropy reaches 0.9981~bit (99.8\% of the theoretical maximum), with a min-entropy of 0.9271~bit. Using a square-wave pulsed-bias scheme, we tune the switching probability to

P\approx0.5

. After SHA-256 post-processing, the bitstreams pass all 15 NIST SP 800-22 tests under a conservative

m=3

criterion that is more demanding than the standard recommendation, and this certification holds across the entire 100-700~mK operating window of a dilution refrigerator.