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arXiv:2404.14307 · IEEE Magnetics Letters

One Trillion True Random Bits Generated With a Field-Programmable Gate Array Actuated Magnetic Tunnel Junction

Andre Dubovskiy, Troy Criss, Ahmed Sidi El Valli, Laura Rehm, Andrew D. Kent, A. Haas

Published Jan 1, 2024• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/lmag.2024.3416091

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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 over1012{\text{10}}^{\text{12}}1012bits 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.
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.
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.
High-speed true random number generator is a building block in the modern information security system. We propose and demonstrate an efficient high-speed true random number generator based on multiple parallel self-timed rings (STRs). To improve the security, we evaluate the randomness of the entropy source by min-entropy and exploit the information-theoretically provable Toeplitz-hashing extractor. To minimize the consumption of hardware resources of a field programmable gate array at a predetermined high throughput and maximize the throughput with the limited hardware resources, we systematically derive and investigate the dependence of the data throughput and the total consumed resources of the random number generator on the system parameters. On this basis, we make a joint optimization for the degree of parallelism of the STRs and the extraction efficiency of the extractor. A 10-Gbps true random number generator is implemented efficiently, so that the output random bits can pass all the National Institute of Standards and Technology (NIST) and Dieharder test suites.
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.
Multi-junctional magnetic tunneling junction spin dice based on orthogonal spin-transfer devices, a new type of true random number (RN) generator (TRNG) is demonstrated in this paper. Orthogonal spin-transfer devices use a planar polarizer to push the free layer with perpendicular anisotropy to metastable state (high-energy state) when power is on. The stochastic precessional switching behavior in ferromagnetic free layer is utilized as the entropy source of the TRNG. Once the power is turned off, anisotropy field and demagnetization field relax the magnetization of free layer from metastable state to one of the two stable states, producing a random bit whose value is solely determined by the stochastic switching behavior. The generation and detection of random bits were summarized under the macrospin picture. RN sequences with high randomness can be produced steadily in the proposed TRNG with a wide operation range of temperature and applied current density. Furthermore, the RN sequences pass the statistical test of NIST SP-800 with an appropriate pass rate without any need of post-procession of data. Ease of design, ultrafast switching as well as high randomness of the bit sequences make the proposed TRNG a competitive device in information security field.