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Cited by 238Magnetic properties of thin filmsPhysical Unclonable Functions (PUFs) and Hardware SecurityQuantum Information and Cryptography

Spin dice: A scalable truly random number generator based on spintronics

Open access
Fukushima, Akio, Seki, Takayuki, Yakushiji, Kay, Kubota, Hitoshi, Imamura, Hiroshi, Yuasa, Shinji, Ando, Koji·2014·Applied Physics Express
DOI 10.7567/apex.7.083001
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Abstract

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.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper demonstrates a spintronics-based true random number generator, “spin dice,” using the stochastic spin-torque switching of perpendicular magnetic tunnel junctions (p-MTJs). Eight p-MTJs on a single-board circuit generated random bits simultaneously, and nested XOR operations improved the bit quality enough to pass NIST SP-800 statistical tests at practical pass rates.

Key findings

  • Eight perpendicularly magnetized MTJs were integrated on a single-board circuit and generated random bits simultaneously at 0.6 million bits/s.
  • Raw random bits were not ideal: normalized variance \(R\) was about 3–5, and raw bits had a NIST SP-800 pass rate of 0.000 for all MTJs.
  • XOR operations improved quality: after XOR, \(R\) decreased to about 1.04; after nested XOR\(_2\) and XOR\(_3\), \(R\) reached about 1.00, close to the binomial ideal.
  • NIST SP-800 pass rates increased after nested XOR: for example, MTJ1 gave 0.417 for XOR\(_2\) and 0.467 for XOR\(_3\), while MTJ5 gave 0.475 for XOR\(_2\); the authors conclude these are practical truly random numbers.

Methods

  • The p-MTJ stack included a 2-nm FeB free layer, 1-nm MgO barrier, and CoPt/Ru/CoPt reference layer, with a nominal 70 × 200 nm pillar and about 100% magnetoresistance ratio.
  • Random bits were generated by resetting the MTJ, applying a 200-ns excite pulse to set switching probability \(P_{\rm sw}=0.5\), then reading the resistance state as “0” or “1” via a comparator.
  • Statistical evaluation used 120 sequences of \(1 \times 10^9\) random bits from eight spin dice, totaling \(1.2 \times 10^{11}\) bits generated over about 2.5 days at \(35.7 \pm 0.4^\circ\)C, and tested with the NIST SP-800 suite (188 tests).

Limitations

  • The paper states that raw random bits were not perfect and required XOR treatment; raw NIST pass rates were zero, and the pass rate for a limited number of bits is lower than the infinite-bit estimate of 0.590.
  • The demonstration used eight p-MTJs on a single-board circuit rather than a high-density on-chip array, and the statistical tests were performed at a controlled temperature of \(35.7 \pm 0.4^\circ\)C.
  • The paper does not report long-term reliability, aging, or integration-level scalability data beyond the eight-device board demonstration.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.7567/apex.7.083001

Cites

Statistics

Nothing to recompute.

Claims the paper makes

0 of 15 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    The random numbers obtained by performing a nested XOR operation passed the NIST SP-800 statistical test with an appropriate pass rate.

    “The RNs obtained by performing a nested XOR operation passed the statistical test of NIST SP-800 with the appropriate pass rate.”
    Quote in the paperSubstantial claim
  • Findingown data

    Generation of practical random numbers by a spintronics-based scalable truly random number generator called spin dice was demonstrated.

    “Generation of practical random numbers (RNs) by a spintronics-based, scalable truly RN generator called “spin dice” was demonstrated.”
    Quote in the paperSubstantial claim
  • Findingown data

    The sequences of random numbers generated by different MTJs were not correlated with each other.

    “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.”
    Quote in the paperSubstantial claim
  • Findingown data

    Performing an exclusive OR operation among random number sequences from different MTJs improved the quality of the random numbers.

    “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.”
    Quote in the paperSubstantial claim
  • Findingown data

    The temperature dependence of Psw at I = 0.73 mA exhibits good linearity between 29 and 38 °C with a slope of 0.037 °C^-1.

    “One can see that P sw exhibits good linearity between 29 and 38 °C with a slope of 0.037 °C ¹1 .”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 7
  • May combine two claims. 30

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data

    The p-MTJ pillar had a nominal cross section of 70 × 200 nm and a magnetoresistance ratio of about 100%.

    “The nominal cross section of the pillar was 70 © 200 nm, and the magnetoresistance ratio was about 100%.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Psw gradually increases with increasing current from I = 0.7 to 0.8 mA, which enables precise control of Psw by altering the current.

    “As shown in Fig. 2(c), P sw gradually increases with increasing current from I = 0.7 to 0.8 mA, which enables us to precisely control P sw by altering the current.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The P to AP and AP to P switchings were observed at currents of 0.75 mA and -0.27 mA, corresponding to 160 mV and -110 mV, respectively.

    “As shown in Fig. 2(b), the P to AP (AP to P) switchings were observed at a current of 0.75 mA (¹0.27 mA), which corresponds to 160 mV (¹110 mV).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given

    The initially used CoFeB/MgO/CoFeB in-plane magnetized MTJs had only a narrow magnetic field range for bistable states and a high switching current density, causing practical difficulty in their development as spin dice.

    “At the beginning of this study, we used CoFeB/MgO/ CoFeB in-plane magnetized MTJs.However, those MTJs had only a narrow magnetic field range for bistable states and a high switching current density, which caused practical difficulty in their development as spin dice.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Eight perpendicularly magnetized MTJs were fabricated on a single-board circuit and generated eight sequences of random numbers simultaneously.

    “We fabricated eight perpendicularly magnetized MTJs on a single-board circuit and generated eight sequences of RNs simultaneously.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The resistances of the P and AP states were 212 and 411 Ω, respectively.

    “The resistances of the P and AP states were 212 and 411 ³, respectively.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The P to AP and AP to P switchings of the p-MTJ were observed at magnetic fields of 1260 Oe and -440 Oe, respectively, about ten times larger than those of in-plane magnetized MTJs.

    “As shown in Fig. 2(a), the P to AP (AP to P) switchings were observed at a magnetic field of 1260 Oe (¹440 Oe), which are about ten times larger than that of in-plane magntized MTJs.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    A single-board circuit was fabricated that can roll eight spin dice simultaneously at a rate of 0.6 million bits/s and generate XOR bits at the same rate.

    “We fabricated a single-board circuit that can roll eight spin dice simultaneously at a rate of 0.6 millionbits/s and could generate the XOR bits at the same rate.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The mean values of Psw and R were 0.513 and 3.52 for MTJ1 and 0.487 and 3.53 for MTJ2, respectively.

    “The mean values of P sw and R • were 0.513 and 3.52 for MTJ1 and 0.487 and 3.53 for MTJ2, respectively.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The autocorrelations of random bits generated by MTJ1 and MTJ2 are positive and decay very slowly with lag; their mean and standard deviation are ~3 × 10^-3 and ~5 × 10^-5, respectively.

    “They are positive and decay very slowly with lag.The mean and standard deviation of the autocorrelation are ³3 © 10 ¹3 and ³5 © 10 ¹5 , respectively.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given

    The switching probability fluctuates around the nominal value of Psw = 0.5 owing to environmental effects such as thermal and current fluctuations, and this lack of equiprobability causes deviation from the binomial distribution.

    “However, the switching probability fluctuates around the nominal value of P sw = 0.5 owing to environmental effects such as thermal and current fluctuations.This lack of equiprobability causes the deviation from the binomial distribution.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The raw random bits generated by MTJ1 and MTJ2 were independent, as shown by a circular scatter diagram of Psw and a correlation within ±1 × 10^-4, the same order as expected for the binomial distribution.

    “To confirm that the RBs generated by MTJ1 and MTJ2 were independent, we plotted the scatter diagram of P sw in Fig. 4(c), which shows a good circular shape, meaning that the raw RBs generated by MTJ1 and MTJ2 were independent.”
    • Also stated in: § R · plain
      “As shown in Fig. 4(d), the correlation between the two raw RBs was as small as within the range of «1 © 10 ¹4 , which was the same order as the expected values for the binomial distribution (³«3 standard deviations of the autocorrelation).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The mean and standard deviation of R for raw bits were ~3-5; after XOR, R decreased to ~1.04; XOR2 and XOR3 reduced R to the ideal value of 1.00.

    “R • of the raw RBs were ³3-5.After the XOR operation, R • decreased to ³1.04.Performing the XOR 2 and XOR 3 operations reduced R • to the ideal value of 1.00.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The histogram of Psw after the XOR operation is almost identical to the binomial distribution, and the autocorrelation is as small as within ±1 × 10^-4.

    “One can clearly see that the histogram of P sw after the XOR operation is performed is almost identical to the binomial distribution (solid line), and the autocorrelation is as small as within the range of «1 © 10 ¹4 .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    120 sequences of 1 × 10^9 random bits (total 1.2 × 10^11 bits) were generated by eight different spin dice on a single-board circuit; generation took about 2.5 days at a temperature kept at 35.7 ± 0.4 °C.

    “We generated 120 sequences of 1 © 10 9 RBs (from a total number of bits of 1.2 © 10 11 RBs) generated by eight different spin dice (p-MTJs) implemented on a single-board circuit.It took about 2.5 days, and during the generation of RBs the temperature was kept at 35.7 « 0.4 °C.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The p-MTJ has a larger magnetic field margin, and stable operation of the spin dice is possible practically at zero magnetic field.

    “This means that the p-MTJ has a larger magnetic field margin and stable operation of the spin dice can be possible practically at zero magnetic field.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    The switching current of a p-MTJ nano-pillar has a distribution as a result of thermal agitation, yielding the switching probability expressed by Eq. (1).

    “Similarly, the switching current of a p-MTJ nano-pillar also has a distribution as a result of thermal agitation, which yields the switching probability expressed as 21)”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [21] Suzuki Y., 2008, Nanomagnetism and Spintronics

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    To generate high-quality random numbers, equiprobability of each switching event is indispensable.

    “To generate high-quality RNs, equiprobability of each switching event is indispensable.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    Top-free-type perpendicularly magnetized MTJs with a synthetic antiferromagnetic bottom reference layer achieved a wide magnetic field range for bistable states around zero magnetic field and a lower switching current density, resulting in a very low writing voltage (<200 mV).

    “Recently, we have succeeded in developing top-free-type perpendicularly magnetized MTJs (p-MTJs) with a synthetic antiferromagnetic bottom reference layer, thereby achieving a wide magnetic field range for the bistable states around zero magnetic field as well as a lower switching current density, which resulted in a very low writing voltage (<200 mV).17)”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [17] Yakushiji K., 2013, Appl. Phys. Express source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    This type of p-MTJ is promising for both high integration and ultra-low-voltage operation of spin dice.

    “This type of p-MTJ is promising for both high integration and ultra-low-voltage operation of spin dice.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    Owing to the scalability of spin-torque switching, spin dice can operate as a scalable TRNG and can be integrated on a chip in high density.

    “Owing to the scalability of spin-torque switching, spin dice can operate as a scalable TRNG and can be integrated on a chip in high density.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    At the bifurcation point, thermal agitation induces a small random deviation of magnetization, and the magnetization relaxes to the AP or P state with the same probability of 50%.

    “At the bifurcation point, thermal agitation induces a small random deviation of magnetization.As a result, the magnetization will relax to the AP or P state with the same probability of 50%.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [22] source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Since 2007, the authors have been studying a spintronics-based TRNG called spin dice, in which binary random bits are generated using the stochastic nature of spin-transfer-torque switching in MTJs.

    “Since 2007, we have been studying a spintronics-based TRNG referred to as “spin dice”, [8][9][10] in which binary RNs or random bits (RBs) are generated by using the stochastic nature of spin-transfer-torque (STT) switching [11][12][13][14][15] in magnetic tunnel junctions (MTJs).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [8][9][10]

      Not checked in the free run.

    • cites [11][12][13][14][15]

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    The basic mechanism for generating a random bit in spin dice is the same as that for writing a data bit in STT-MRAM, except the switching probability is set to 0.5 for spin dice whereas it should be 1.0 for STT-MRAM.

    “The basic mechanism for generation of an RB is the same as that for writing a data bit in STT magnetic random access memory (STT-MRAM).16) The main difference is that the switching probability is set to be 0.5 for generation of an RB in the spin dice, whereas it should be 1.0 for STT-MRAM.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [16] source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    The scalability of spin-torque switching makes it possible to fabricate a large number of arrays of spin dice on a chip and will provide an unlimited supply of practical truly random numbers.

    “(iii) the scalability of spin-torque switching makes it possible to fabricate a large number of arrays of spin dice on a chip and will provide an unlimited supply of practical truly random numbers.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The binary random numbers are directly obtained from the results of spin-torque switching, and thus the equiprobability of the spin dice is ideal after a nested XOR operation is performed.

    “(i) The binary random numbers are directly obtained from the results of spin-torque switching, and thus the equiprobability of the spin dice is ideal after a nested XOR operation is performed;”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Interpretationreasoning

    Spin dice should prove to be a promising candidate for a scalable truly random number generator suitable for encrypting and would enable handling an enormous amount of data securely and confidentially.

    “We note that spin dice should prove to be a promising candidate for a scalable truly random number generator suitable for encrypting and would enable us to handle an enormous amount of data securely and confidentially.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisenone given

    For ideal random bits obeying the binomial distribution, the mean of the autocorrelation should be zero and the standard deviation should be 1/√n; for n = 1 × 10^9, the standard deviation is 3.2 × 10^-5, much smaller than that observed.

    “For ideal RBs obeying the binomial distribution, the mean of the autocorrelation should be zero and the standard deviation of the autocorrelation should be 1= ffiffiffi n p , where n is the number of bits.For n = 1 © 10 9 , the standard deviation of the autocorrelation is 3.2 © 10 ¹5 , which is much smaller than that for the results shown in Fig. 4(b).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    As pointed out by Yamaguchi et al., the pass rate for a limited number of random bits is smaller than the pass rate of 0.590 obtained for an infinite number of random bits.

    “However, as pointed out by Yamaguchi et al., 25) the pass rate for a limited number of RBs is smaller than the pass rate of 0.590 that is obtained for an infinite number of RBs.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [25] source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    The quality of the sequence of raw random bits generated by the spin dice is not perfect, and an extra treatment is necessary to obtain high-quality practical random bits.

    “The results shown in Figs.4(a) and 4(b) imply that the quality of the sequence of raw RBs generated by the spin dice is not perfect, and an extra treatment is necessary to obtain high-quality practical RBs.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    If Psw is exactly equal to 0.5 for all switching events, the statistical distribution of Psw of the generated random bits should be the same as the binomial distribution.

    “If P sw is exactly equal to 0.5 for all switching events, the statistical distribution of P sw of the generated RBs should be the same as the binomial distribution.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    The NIST SP-800 statistical test suite consists of 15 kinds of statistical tests (188 tests in all) and is a significance test with a certain pass rate.

    “This test suite consists of 15 kinds of statistical tests (and 188 tests in all).It should be noted that these statistical tests are not simple yes-no test but significance tests with a certain pass rate.24)”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [18]

      Not checked in the free run.

    • cites [24] Okutomi H., 2010, Denshi Joho Tsushin Gakkaishi A

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Yamaguchi et al. performed numerical experiments to obtain pass rates of 1 × 10^9 bits for 1000 sets of 1 million random bits generated by VSC128S, CatMap2D, SHA-1, and AES; obtained pass rates were 56%, 55%, 43%, and 41%, respectively.

    “They performed numerical experiments to obtain the pass rates of 1 © 10 9 bits for 1000 sets of 1 million RBs generated by using the following four types of PRNGs: VSC128S, 26) CatMap2D, 27) SHA-1, 28) and AES.29) The obtained pass rates were distributed from 41% to 56%: 56% for VSC128S, 55% for CatMap2D, 43% for SHA-1, and 41% for AES.”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [25] source

      Not checked in the free run.

    • cites [26]

      Not checked in the free run.

    • cites [27] Araki T., Proc. 55th NCTAM2006, 2006

      Not checked in the free run.

33 of 33

  • The paper relies on this without support.

    PRNGs are cryptographically insecure because they are deterministic and require seeds.

    “PRNGs are implemented in software and use deterministic algorithms to generate a sequence of RNs.They require seeds of RNs and will always generate the same sequence of RNs from the same seed.Thus, they are considered to be cryptographically insecure.”

  • The paper relies on this without support.

    All existing TRNGs based on nondeterministic physical events have a drawback in scalability.

    “However, all of these TRNGs have a drawback in scalability, which is important for a system expected to handle a growing amount of data securely.”
2 of 2

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • All prior true random number generators have suffered from drawbacks in scalability, circuit complexity, or reliance on post-processing such as a Von Neumann corrector to remove bias.

    “However, all prior TRNGs have suffered from drawbacks in scalability, circuit complexity, or relied on post-processing such as a “Von Neumann corrector” to remove bias from the generated bit sequences4–13.”

    From A novel true random number generator based on a stochastic diffusive memristor (2017) · cites this paper as [13]

The citation lists haven’t been fetched yet

References 26 · Cited by 238

Research works printed but not linked: 4

  1. Fukushima A., Japan Patent
  2. Fukushima A., Ext. Abstr. Solid State Devices and Materials, 2010, 1128
  3. Okutomi H., 2010, Denshi Joho Tsushin Gakkaishi A, J93-A, 11
  4. Araki T., Proc. 55th NCTAM2006, 2006, 185

Authors
Fukushima, A., Seki, T., Yakushiji, K., Kubota, H., Imamura, H., Yuasa, S., & Ando, K.
Affiliations
National Institute of Advanced Industrial Science and Technology (JP)
ORCID
Venue
Applied Physics Express
Publisher
IOP Publishing
Published
2014-07-25
Volume
7
Issue
8
Pages
083001
ISSN
  • 1882-0778 (ISSN-L)
  • 1882-0786
DOI
10.7567/apex.7.083001
OpenAlex
W1999802284
Semantic Scholar
ae670b247732f7633aed68e20bc11ab26e988682
Cited by
238
References
26
Citations by year
2026: 9 · 2025: 18 · 2024: 26 · 2023: 22 · 2022: 12 · 2021: 19 · 2020: 21 · 2019: 26 · 2018: 24 · 2017: 26 · 2016: 19 · 2015: 15 · 2012: 1
FWCI
9.91
Type
journal article
Language
en
Open access
Licence
Locations
Applied Physics Express (publishedVersion, cc-by)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Magnetic properties of thin films
  • Physical Sciences › Computer Science › Hardware and Architecture › Physical Unclonable Functions (PUFs) and Hardware Security
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
spintronics, spin-torque switching, magnetic tunnel junctions, perpendicular magnetic anisotropy, XOR operation, hardware random number generator

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