Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Graphene-based physically unclonable functions that are reconfigurable and resilient to machine learning attacks

Nature Electronics volume 4, pages 364–374 (2021)Cite this article

Subjects

Abstract

Graphene has a range of properties that makes it suitable for building devices for the Internet of Things. However, the deployment of such devices will also likely require the development of suitable graphene-based hardware security primitives. Here we report a physically unclonable function (PUF) that exploits disorders in the carrier transport of graphene field-effect transistors. The Dirac voltage, Dirac conductance and carrier mobility values of a large population of graphene field-effect transistors follow Gaussian random distributions, which allow the devices to be used as a PUF. The resulting PUF is resilient to machine learning attacks based on predictive regression models and generative adversarial neural networks. The PUF is also reconfigurable without any physical intervention and/or integration of additional hardware components due to the memristive properties of graphene. Furthermore, we show that the PUF can operate with ultralow power and is scalable, stable over time and reliable against variations in temperature and supply voltage.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Fabrication, characterization and models for GFETs.
Fig. 2: Construction and properties of GFET PUFs.
Fig. 3: Reconfiguration of GFET PUFs.
Fig. 4: ML attack on GFET PUFs using predictive regression model.
Fig. 5: ML attack on GFET PUF using a GAN.
Fig. 6: Reliability and energy efficiency of GFET PUFs.

Similar content being viewed by others

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author upon reasonable request.

Code availability

The codes used for plotting the data are available from the corresponding author upon reasonable request.

References

  1. Kruger, C. P. & Hancke, G. P. Benchmarking internet of things devices. In 2014 12th IEEE International Conference on Industrial Informatics (INDIN) 611–616 (IEEE, 2014).

  2. Atzori, L., Iera, A. & Morabito, G. The internet of things: a survey. Comput. Netw. 54, 2787–2805 (2010).

    Article  MATH  Google Scholar 

  3. Zhao, K. & Ge, L. A survey on the internet of things security. In 2013 9th International Conference on Computational Intelligence and Security (CIS) 663–667 (IEEE, 2014).

  4. Xia, F., Yang, L. T., Wang, L. & Vinel, A. Internet of things. Int. J. Commun. Syst. 25, 1101–1102 (2012).

    Article  Google Scholar 

  5. Suh, G. E. & Devadas, S. Physical unclonable functions for device authentication and secret key generation. In 2007 44th ACM/IEEE Design Automation Conference 9–14 (IEEE, 2007).

  6. Pappu, R., Recht, B., Taylor, J. & Gershenfeld, N. Physical one-way functions. Science 297, 2026–2030 (2002).

    Article  Google Scholar 

  7. Hwang, K.-M. et al. Nano-electromechanical switch based on a physical unclonable function for highly robust and stable performance in harsh environments. ACS Nano 11, 12547–12552 (2017).

    Article  Google Scholar 

  8. Hu, Z. et al. Physically unclonable cryptographic primitives using self-assembled carbon nanotubes. Nat. Nanotechnol. 11, 559–565 (2016).

    Article  Google Scholar 

  9. Kuribara, K. et al. Organic physically unclonable function on flexible substrate operable at 2 V for IoT/IoE security applications. Org. Electron. 51, 137–141 (2017).

    Article  Google Scholar 

  10. Qin, Z., Shintani, M., Kuribara, K., Ogasahara, Y. & Sato, T. OCM-PUF: organic current mirror PUF with enhanced resilience to device degradation. In 2019 IEEE International Conference on Flexible and Printable Sensors and Systems (FLEPS) 1–3 (IEEE, 2019).

  11. Rajendran, J., Rose, G. S., Karri, R. & Potkonjak, M. Nano-PPUF: a memristor-based security primitive. In 2012 IEEE Computer Society Annual Symposium on VLSI 84–87 (IEEE, 2012).

  12. Zhang, R. et al. Nanoscale diffusive memristor crossbars as physical unclonable functions. Nanoscale 10, 2721–2726 (2018).

    Article  Google Scholar 

  13. Chen, A. Utilizing the variability of resistive random access memory to implement reconfigurable physical unclonable functions. IEEE Electron Device Lett 36, 138–140 (2015).

    Article  Google Scholar 

  14. Gao, L., Chen, P., Liu, R. & Yu, S. Physical unclonable function exploiting sneak paths in resistive cross-point array. IEEE Trans. Electron Devices 63, 3109–3115 (2016).

    Article  Google Scholar 

  15. Gao, Y., Ranasinghe, D. C., Al-Sarawi, S. F., Kavehei, O. & Abbott, D. Emerging physical unclonable functions with nanotechnology. IEEE Access 4, 61–80 (2016).

    Article  Google Scholar 

  16. Dodda, A. et al. Biological one-way functions for secure key generation. Adv. Theor. Simul. 2, 1800154 (2019).

  17. Wali, A. et al. Biological physically unclonable function. Commun. Phys. 2, 39 (2019).

    Article  Google Scholar 

  18. Maes, R. & Verbauwhede, I. in Towards Hardware-Intrinsic Security (eds Sadeghi, A.-R. & Naccache, D.) 3–37 (Springer, 2010).

  19. Gassend, B., Clarke, D., Van Dijk, M. & Devadas, S. Silicon physical random functions. In Proceedings of the 9th ACM Conference on Computer and Communications Security 148–160 (ACM, 2002).

  20. Schrijen, G.-J. & Van Der Leest, V. Comparative analysis of SRAM memories used as PUF primitives. In 2012 Design, Automation & Test in Europe Conference & Exhibition (DATE) 1319–1324 (EDA Consortium, 2012).

  21. Katzenbeisser, S. et al. PUFs: myth, fact or busted? A security evaluation of physically unclonable functions (PUFs) cast in silicon. In International Workshop on Cryptographic Hardware and Embedded Systems 283–301 (Springer, 2012).

  22. Yu, M.-D. & Devadas, S. Secure and robust error correction for physical unclonable functions. IEEE Des. Test. Comput. 27, 48–65 (2010).

    Article  Google Scholar 

  23. Haensch, W. et al. Silicon CMOS devices beyond scaling. IBM J. Res. Dev. 50, 339–361 (2006).

    Article  Google Scholar 

  24. Jung, Y. H. et al. High-performance green flexible electronics based on biodegradable cellulose nanofibril paper. Nat. Commun. 6, 7170 (2015).

    Article  Google Scholar 

  25. Akinwande, D., Petrone, N. & Hone, J. Two-dimensional flexible nanoelectronics. Nat. Commun. 5, 5678 (2014).

    Article  Google Scholar 

  26. Kim, D. & Moon, J. Highly conductive ink jet printed films of nanosilver particles for printable electronics. Electrochem. Solid-State Lett. 8, J30–J33 (2005).

    Article  Google Scholar 

  27. Schwierz, F. Graphene transistors. Nat. Nanotechnol. 5, 487–496 (2010).

    Article  Google Scholar 

  28. Miao, X. et al. High efficiency graphene solar cells by chemical doping. Nano Lett. 12, 2745–2750 (2012).

    Article  Google Scholar 

  29. Xia, F., Mueller, T., Lin, Y.-M., Valdes-Garcia, A. & Avouris, P. Ultrafast graphene photodetector. Nat. Nanotechnol. 4, 839–843 (2009).

    Article  Google Scholar 

  30. Torrisi, F. et al. Inkjet-printed graphene electronics. ACS Nano 6, 2992–3006 (2012).

    Article  Google Scholar 

  31. Kim, J. T. & Choi, S.-Y. Graphene-based plasmonic waveguides for photonic integrated circuits. Opt. Express 19, 24557–24562 (2011).

    Article  Google Scholar 

  32. Wu, L., Chu, H., Koh, W. & Li, E. Highly sensitive graphene biosensors based on surface plasmon resonance. Opt. Express 18, 14395–14400 (2010).

    Article  Google Scholar 

  33. El-Kady, M. F., Strong, V., Dubin, S. & Kaner, R. B. Laser scribing of high-performance and flexible graphene-based electrochemical capacitors. Science 335, 1326–1330 (2012).

    Article  Google Scholar 

  34. Mannoor, M. S. et al. Graphene-based wireless bacteria detection on tooth enamel. Nat. Commun. 3, 763 (2012).

    Article  Google Scholar 

  35. Wang, Y. et al. Wearable and highly sensitive graphene strain sensors for human motion monitoring. Adv. Funct. Mater. 24, 4666–4670 (2014).

    Article  Google Scholar 

  36. Bae, S. et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat. Nanotechnol. 5, 574–578 (2010).

    Article  Google Scholar 

  37. Lee, Y. et al. Wafer-scale synthesis and transfer of graphene films. Nano Lett. 10, 490–493 (2010).

    Article  Google Scholar 

  38. Lin, Y.-M. et al. Wafer-scale graphene integrated circuit. Science 332, 1294–1297 (2011).

    Article  Google Scholar 

  39. Kim, K. S. et al. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 457, 706–710 (2009).

    Article  Google Scholar 

  40. Hallam, T., Berner, N. C., Yim, C. & Duesberg, G. S. Strain, bubbles, dirt, and folds: a study of graphene Polymer‐Assisted transfer. Adv. Mater. Interfaces 1, 1400115 (2014).

    Article  Google Scholar 

  41. Chen, J.-H. et al. Charged-impurity scattering in graphene. Nat. Phys. 4, 377–381 (2008).

    Article  Google Scholar 

  42. Zhang, Y., Brar, V. W., Girit, C., Zettl, A. & Crommie, M. F. Origin of spatial charge inhomogeneity in graphene. Nat. Phys. 5, 722–726 (2009).

    Article  Google Scholar 

  43. Giovannetti, G. et al. Doping graphene with metal contacts. Phys. Rev. Lett. 101, 026803 (2008).

    Article  MathSciNet  Google Scholar 

  44. Yazyev, O. V. & Louie, S. G. Electronic transport in polycrystalline graphene. Nat. Mater. 9, 806–809 (2010).

    Article  Google Scholar 

  45. Chen, H. J. et al. Defect scattering in graphene. Phys. Rev. Lett. 102, 236805 (2009).

    Article  Google Scholar 

  46. Yang, X., Peng, H., Xie, Q., Zhou, Y. & Liu, Z. Clean and efficent transfer of CVD-grown graphene by electrochemical etching of metal substrate. J. Electroanal. Chem. 688, 243–248 (2013).

    Article  Google Scholar 

  47. Suk, J. W. et al. Transfer of CVD-Grown monolayer graphene onto arbitrary substrates. ACS Nano 5, 6916–6924 (2011).

    Article  Google Scholar 

  48. Gehrer, S. & Sigl, G. Reconfigurable PUFs for FPGA-based SoCs. In 2014 International Symposium on Integrated Circuits (ISIC) 140–143 (IEEE, 2015).

  49. Lao, Y. & Parhi, K. K. Reconfigurable architectures for silicon physical unclonable functions. In 2011 IEEE International Conference on Electro/Information Technology 1–7 (IEEE, 2011).

  50. Kursawe, K., Sadeghi, A.-R., Schellekens, D., Skoric, B. & Tuyls, P. Reconfigurable physical unclonable functions—enabling technology for tamper-resistant storage. In 2009 IEEE International Workshop on Hardware-Oriented Security and Trust 22–29 (IEEE, 2009).

  51. Gao, Y., Al-Sarawi, S. F. & Abbott, D. Physical unclonable functions. Nat. Electron. 3, 81–91 (2020).

    Article  Google Scholar 

  52. Zhang, L., Fong, X., Chang, C.-H., Kong, Z. H. & Roy, K. Highly reliable spin-transfer torque magnetic RAM-based physical unclonable function with multi-response-bits per cell. IEEE Trans. Inf. Forensics Security 10, 1630–1642 (2015).

    Article  Google Scholar 

  53. Schranghamer, T. F., Oberoi, A. & Das, S. Graphene memristive synapses for high precision neuromorphic computing. Nat. Commun. 11, 5474 (2020).

    Article  Google Scholar 

  54. Rührmair, U. et al. PUF modeling attacks on simulated and silicon data. IEEE Trans. Inf. Forensics Security 8, 1876–1891 (2013).

    Article  Google Scholar 

  55. Rührmair, U. et al. Modeling attacks on physical unclonable functions. In Proceedings of the 17th ACM Conference on Computer and Communications Security 237–249 (ACM, 2010).

  56. Goodfellow, I. et al. Generative adversarial nets. In NIPS'14: Proceedings of the 27th International Conference on Neural Information Processing Systems 2, 2672–2680 (2014).

  57. Hitaj, B., Gasti, P., Ateniese, G. & Perez-Cruz, F. PassGAN: a deep learning approach for password guessing. In International Conference on Applied Cryptography and Network Security 217–237 (Springer, 2019).

  58. Yan, W., Tehranipoor, F. & Chandy, J. A. PUF-based fuzzy authentication without error correcting codes. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 36, 1445–1457 (2016).

    Article  Google Scholar 

  59. Byun, K.-E. et al. Graphene for true ohmic contact at metal–semiconductor junctions. Nano Lett. 13, 4001–4005 (2013).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA

    Akhil Dodda, Shiva Subbulakshmi Radhakrishnan, Thomas F. Schranghamer, Drew Buzzell & Saptarshi Das

  2. Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA

    Parijat Sengupta

  3. Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA, USA

    Saptarshi Das

  4. Materials Research Institute, Pennsylvania State University, University Park, PA, USA

    Saptarshi Das

Authors
  1. Akhil Dodda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shiva Subbulakshmi Radhakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas F. Schranghamer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Drew Buzzell
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Parijat Sengupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Saptarshi Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.D. conceived the idea, designed the experiments and wrote the paper. A.D., T.F.S. and D.B. performed the experiments. S.S.R. performed the machine learning attacks. P.S. developed the theoretical models. S.D. developed the empirical model. All the authors analysed the data, discussed the results, agreed on their implications and contributed to the preparation of the manuscript.

Corresponding author

Correspondence to Saptarshi Das.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Electronics thanks Derek Abbott and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–18, Discussions 1–24 and Tables 1 and 2.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dodda, A., Subbulakshmi Radhakrishnan, S., Schranghamer, T.F. et al. Graphene-based physically unclonable functions that are reconfigurable and resilient to machine learning attacks. Nat Electron 4, 364–374 (2021). https://doi.org/10.1038/s41928-021-00569-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41928-021-00569-x

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing