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Twin physically unclonable functions based on aligned carbon nanotube arrays


Physically unclonable functions (PUFs) are a promising technology for generating cryptographic primitives using random imperfections in a physical entity. However, the keys inside PUFs are still vulnerable as they must be written into non-volatile memories and shared with participants that do not hold the PUF before secure communication. Here we show that pairs of identical PUFs (twin PUFs) can be fabricated together on an aligned carbon nanotube array and used for secure communication without key pre-extraction and storage. Two rows of field-effect transistors are fabricated perpendicular to the carbon nanotube growth direction, randomly producing three types of transistor channel—based on metallic nanotubes, semiconducting nanotubes and no nanotubes—that can be used to extract ternary bits for use as a shared key. The twin PUFs exhibit high uniformity, uniqueness, randomness and reliability, as well as a consistency of approximately 95%. We show that separated twin PUFs can provide secure communication with a bit error rate of one bit per trillion via a fault-tolerant design.

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Fig. 1: Twin PUFs based on aligned CNT arrays and usage in secure communication.
Fig. 2: Structure and performance of CNT twin PUFs and PUF-generated ternary bits.
Fig. 3: Characteristics of CNT-PUF-generated secret keys.
Fig. 4: Consistency of CNT twin PUFs and their application in secure communication.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.


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This work was supported by the National Key Research & Development Program (grant no. 2021YFA1202904); the Beijing Municipal Science and Technology Commission (grant no. Z191100007019001-3); the Basic and Applied Basic Research Major Programme of Guangdong Province, China (grant no. 2021B0301030003); and Jihua Laboratory (project no. X210141TL210).

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Authors and Affiliations



Z.Z. and L.-M.P. proposed and supervised the project. D.Z., Z.Z. and L.-M.P. conceived the idea of twin PUFs and designed the experiment. D.Z. fabricated the devices. D.Z., J.L., Y.X., H.S. and C.Z. performed the electrical measurements. D.Z. performed the modelling and simulations. M.X. grew and characterized the aligned CNT arrays. J.L., L.J. and L.D. performed the NIST statistical randomness test. D.Z., Z.Z. and L.-M.P. analysed the data and co-wrote the manuscript. All the authors discussed the results and commented on the manuscript.

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Correspondence to Lian-Mao Peng or Zhiyong Zhang.

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Nature Electronics thanks Miguel Garcia-Bosque, Jin-Woo Han and Satish Kumar for their contribution to the peer review of this work.

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Supplementary Figs. 1–21 and Table 1.

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Zhong, D., Liu, J., Xiao, M. et al. Twin physically unclonable functions based on aligned carbon nanotube arrays. Nat Electron 5, 424–432 (2022).

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