Physically unclonable functions in analog integrated circuits

Objectives. The paper provides a comprehensive overview of analog and passive physical unclonable functions (PUFs), analyzing their vulnerabilities to machine-learning (ML) attacks, and assessing their practical deployment in modern integrated circuits and Internet of Things (IoT) devices.

Methods. Quantitative metrics were used to compare PUF implementations and their formal properties, such as computability, uniqueness, implementability, difficulty of cloning, and protection against unauthorized access.

Results. Analog PUFs were shown to belong to the class of “strong” PUFs. However, special measures are required to counteract environmental and ageing effects. Examples are cited to demonstrate their near-ideal uniqueness (inter-Hamming distance ≈ 50%), high stability (intra-Hamming distance < 1%), and excellent energy performance (from units to tens of femtojoules per bit). While characterized by high stability, passive PUFs are classified as “weak” PUFs. A consideration of ML-based modeling attacks confirmed that convolutional neural networks and multilayer perceptrons outperform classical approaches. By limiting the amount of data available to an attacker, protocol-level protection prevents the PUF architecture from being modified.

Conclusions. Analog and passive PUFs expand the range of tools available for hardware authentication and anticounterfeiting, particularly in low-power, resource-constrained IoT nodes. The most promising directions include architectures with on-chip self-calibration and minimal area/power overhead, as well as passive schemes for onetime identification and tamper evidence. However, open challenges remain in terms of standardizing readout and digitization procedures, increasing robustness to environmental variation and diverse attacks, and integrating error correction and post-processing on the chip. The practical adoption and selection of architectures requires conservative threat modeling and defense-in-depth strategies that account for current attack capabilities and likely future advances in ML.

1. Pevtsov E.Ph., Demenkova T.A., Korotaev Yu.A., Sigov A.S. Physically unclonable functions in digital integrated circuits. Russian Technological Journal. 2026;14(2):80–102. https://doi.org/10.32362/2500-316X-2026-14-2-80-102

2. Lofstrom K., Daasch R., Taylor D. IC identification circuit using device mismatch. In: Proceedings of the IEEE International Solid-State Circuits Conference (ISSCC 2000). February 7–9, 2000. San Francisco, CA, USA. Piscataway, NJ: IEEE; 2000. Р. 372–373. https://doi.org/10.1109/ISSCC.2000.839821

3. Venkatesh A., Sanyal A. A machine learning resistant strong PUF using subthreshold voltage divider array in 65nm CMOS. In: Proceedings of the 2019 IEEE International Symposium on Circuits and Systems (ISCAS 2019). May 26–29, 2019. Sapporo, Japan. Piscataway, NJ: IEEE; 2019. P. 1–5. https://doi.org/10.1109/ISCAS.2019.8702525

4. Mitchell-Moreno J.H., Espinosa Flores-Verdad G. A low bit instability CMOS PUF based on current mirrors and WTA cells. J. Electron. Test. 2023;39:611–620. https://doi.org/10.1007/s10836-023-06085-4

5. Jadhav V.D., Kalloor R., Poola L., Prabhakar T.V. Diode-PUF for intelligent electronic devices. In: Proceedings of the 16th International Conference on Communication Systems & Networks (COMSNETS 2024). January 2–6, 2024. Bengaluru, India. Piscataway, NJ: IEEE; 2024. P. 330–332. https://doi.org/10.1109/COMSNETS59351.2024.10427169

6. Kim N., Jeon S.-B., Jang B. Hardware-intrinsic physical unclonable functions by harnessing nonlinear conductance variation in oxide semiconductor-based diode. Nanomaterials (Basel). 2023;13(4):675. https://doi.org/10.3390/nano13040675

7. Takahashi Y., Koyasu H., Kumar S.D., et al. Quasi-adiabatic SRAM based silicon physical unclonable function. SN Comput. Sci. 2020;1:237. https://doi.org/10.1007/s42979-020-00253-5

8. Liu J., Takahashi Y. Design of low-power 6T adiabatic PUF circuit. In: Proceedings of the 2024 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS 2024). October 27–30, 2024. Taipei, Taiwan. Piscataway, NJ: IEEE; 2024. P. 599–603. https://doi.org/10.1109/APCCAS62602.2024.10808318

9. Nagata S., Takahashi Y. A design of PUF circuit using adiabatic logic. In: Proceedings of the 2024 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS 2024). October 27–30, 2024. Taipei, Taiwan. Piscataway, NJ: IEEE; 2024. P. 595–598. https://doi.org/10.1109/APCCAS62602.2024.10808900

10. Helinski R., Acharyya D., Plusquellic J. A physical unclonable function defined using power distribution system equivalent resistance variations. In: Proceedings of the 46th ACM/IEEE Design Automation Conference (DAC 2009). July 26–31, 2009. San Francisco, CA, USA. New York: ACM; 2009. P. 676–681. https://doi.org/10.1145/1629911.1630089

11. Jeon D., Baek J.H., Kim Y.-D., Lee J., Kim D.K., Choi B.-D. A physical unclonable function with bit error rate <2.3 × 10−8 based on contact formation probability without error correction code. IEEE J. Solid-State Circuits. 2020;55(3):805–816. https://doi.org/10.1109/JSSC.2019.2951415

12. Csaba G., Ju X., Chen Q., Porod W., Schmidhuber J., Schlichtmann U., Lugli P., Rührmair U. On-chip electric waves: an analog circuit approach to physical uncloneable functions [preprint]. IACR Cryptology ePrint Archive. 2009;2009/246.

13. Tuyls P., Schrijen G-J., Škorić B., van Geloven J., Verhaegh N., Wolters R. Read-proof hardware from protective coatings. In: Goubin L., Matsui M. (Eds.). Cryptographic Hardware and Embedded Systems. CHES 2006, Yokohama, Japan, October 10–13, 2006. Book Series: Lecture Notes in Computer Science. Berlin: Springer; 2006. V. 4249. P. 369–383. https://doi.org/10.1007/11894063_29

14. Skoric B., Maubach S., Kevenaar T., Tuyls P. Information-theoretic analysis of coating PUFs [preprint]. IACR Cryptology ePrint Archive. 2006;2006/101.

15. Aysu A., Farhady Ghalaty N., Franklin Z., Yali M., Schaumont P. Digital fingerprints for low-cost platforms using MEMS sensors. In: Proceedings of the Workshop on Embedded Systems Security (WESS ’13). September 29, 2013. Montreal, QC, Canada. New York: ACM; 2013. Article 2. P. 1–6. https://doi.org/10.1145/2527317.2527319

16. Yu M.D., M’Raihi D., Sowell R., Devadas S. Lightweight and secure PUF key storage using limits of machine learning. In: Preneel B., Takagi T. (Eds.). Cryptographic Hardware and Embedded Systems. CHES 2011. Book Series: Lecture Notes in Computer Science. Berlin Heidelberg: Springer; 2011. V. 6917. P. 358–373. https://doi.org/10.1007/978-3-642-23951-9_24

17. Saadvikaa N., Saketi K.J., Gopishetti A., et al. PUF modeling attacks using deep learning and machine learning algorithms. Eng. Proceedings. 2023;56(1):187. https://doi.org/10.3390/ASEC2023-15948

18. Dubrova E., Näslund O., Degen B., et al. CRC-PUF: A machine learning attack resistant lightweight PUF construction. In: 2019 IEEE European symposium on security and privacy workshops (EuroS&PW). IEEE; 2019. P. 264–271. https://doi.org/10.1109/EuroSPW.2019.00036

19. Tripathy S., Rai V.K., Mathew J. MARPUF: physical unclonable function with improved machine learning attack resistance. IET Circuits, Devices & Systems. 2021;15(5):465–474. https://doi.org/10.1049/cds2.12042

20. Ebrahimabadi M., Lalouani W., Younis M., et al. Countering PUF modeling attacks through adversarial machine learning. In: 2021 IEEE Computer Society Annual Symposium on VLSI (ISVLSI). IEEE. 2021. P. 356–361. https://doi.org/10.1109/ISVLSI51109.2021.00071

21. Khalfaoui S., Leneutre J., Villard A., et al. Security analysis of machine learning-based PUF enrollment protocols: A review. Sensors. 2021;21(24):8415. https://doi.org/10.3390/s21248415

22. Strieder E., Frisch C., Pehl M. Machine learning of physical unclonable functions using helper data: Revealing a pitfall in the fuzzy commitment scheme. IACR Transactions on Cryptographic Hardware and Embedded Systems. 2021;2:1–36. https://doi.org/10.46586/tches.v2021.i2.1-36

23. Ali-Pour A., Afghah F., Hely D., et al. Secure PUF-based authentication and key exchange protocol using machine learning. In: 2022 IEEE Computer Society Annual Symposium on VLSI (ISVLSI). IEEE. 2022. P. 386–389. https://doi.org/10.1109/ISVLSI54635.2022.00086

24. Yadav A., Kumar S., Singh J. A review of physical unclonable functions (PUFs) and its applications in IoT environment. In: Hu Y.C., Tiwari S., Trivedi M.C., Mishra K.K. (Eds.). Ambient Communications and Computer Systems. Book Series: Lecture Notes in Networks and Systems. Singapore: Springer; 2022. V. 356. P. 1–3. https://doi.org/10.1007/978-981-16-7952-0_1

25. Gao Y., Al-Sarawi S.F., Abbott D. Physical unclonable functions. Nat. Electron. 2020;3(2):81–91. https://doi.org/10.1038/s41928-020-0372-5

26. Wisiol N., Mühl C., Pirnay N., et al. Splitting the interpose PUF: A novel modeling attack strategy. IACR Transactions on Cryptographic Hardware and Embedded Systems. 2020;3:97–120. https://doi.org/10.13154/tches.v2020.i3.97-120

27. Arapinis M., Delavar M., Doosti M., et al. Quantum physical unclonable functions: Possibilities and impossibilities. Quantum. 2021;5:475. https://doi.org/10.22331/q-2021-06-15-475

28. Kayaci N., Ozdemir R., Kalay M., et al. Organic light‐emitting physically unclonable functions. Adv. Funct. Mater. 2022;32(14):2108675. https://doi.org/10.1002/adfm.202108675

29. Awano H., Iizuka T., Ikeda M. PUFNet: A deep neural network based modeling attack for physically unclonable function. In: 2019 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE. 2019. P. 1–4. https://doi.org/10.1109/ISCAS.2019.8702431

30. Idriss T.A., Idriss H.A., Bayoumi M.A. A lightweight PUF-based authentication protocol using secret pattern recognition for constrained IoT devices. IEEE Access. 2021;9:80546–80558. https://doi.org/10.1109/ACCESS.2021.3084903

31. Shah A., Pandya H., Soni M., Karimov A., Maaliw R.R., Keshta I. PUF-based lightweight authentication protocol for IoT devices. In: Balas V.E., Semwal V.B., Khandare A. (Eds.). Intelligent Computing and Networking. IC-ICN 2023. Book Series: Lecture Notes in Networks and Systems. Singapore: Springer; 2023. V. 699. P. 401–412. https://doi.org/10.1007/978-981-99-3177-4_29

32. Alladi T., Deo M., Chamola V., Sikdar B., Chao H.C. SecAuthUAV: a novel authentication scheme for UAV-ground station and UAV-UAV communication. IEEE Trans. Veh. Technol. 2020;69(12):15068–15077. https://doi.org/10.1109/TVT.2020.3033060

33. Bansal G., Sikdar B. S-MAPS: scalable mutual authentication protocol for dynamic UAV swarms. IEEE Trans. Veh. Technol. 2021;70(11):12088–12100. https://doi.org/10.1109/TVT.2021.3116163

34. Yanambaka V.P., Mohanty S.P., Kougianos E., Puthal D. PMsec: physical unclonable function-based robust and lightweight authentication in the Internet of Medical Things. IEEE Trans. Consum. Electron. 2019;65(3):388–397. https://doi.org/10.1109/TCE.2019.2926192

35. Jiang Q., Zhang X., Zhang N., et al. Three-factor authentication protocol using physical unclonable function for IoV. Comput. Commun. 2021;173:45–55. https://doi.org/10.1016/j.comcom.2021.03.022

36. Mershad K., Cheikhrouhou O., Ismail L. Proof of accumulated trust: a new consensus protocol for the security of the IoV. Veh. Commun. 2021;32:100392. https://doi.org/10.1016/j.vehcom.2021.100392

37. Kaveh M., Aghapour S., Martín D., Mosavi M.R. A secure lightweight signcryption scheme for smart grid communications using reliable physically unclonable function. In: 2020 IEEE International Conference on Environment and Electrical Engineering & 2020 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe). June 9–12, 2020. Madrid, Spain. Piscataway. NJ: IEEE; 2020. P. 1–6. https://doi.org/10.1109/EEEIC/ICPSEurope49358.2020.9160596

38. Cao Y.-N., Wang Y., Ding Y., Zheng H., Guan Z., Wang H. A PUF-based lightweight authenticated metering data collection scheme with privacy protection in smart grid. In: 2021 IEEE International Conference on Parallel & Distributed Processing with Applications, Big Data & Cloud Computing, Sustainable Computing & Communications, Social Computing & Networking (ISPA/BDCloud/SocialCom/SustainCom). August 30 – September 3, 2021. New York, USA. Piscataway, NJ: IEEE; 2021. P. 876–883. https://doi.org/10.1109/ISPA-BDCloud-SocialCom-SustainCom52081.2021.00124

39. Maqsooq B., Qadri S., Shamshad S., Ayub M.F., Mahmood K., Kumar N. An identity-based authentication protocol for smart grid environment using physical unclonable function. IEEE Trans. Smart Grid. 2021;12(5):4426–4434. https://doi.org/10.1109/TSG.2021.3072244

40. Zerrouki F., Ouchani S., Bouarfa H. PUF-based mutual authentication and session key establishment protocol for IoT devices. J. Ambient Intell. Human. Comput. 2023;14:12575–12593. https://doi.org/10.1007/s12652-022-04321-x

41. Müelich S., Bossert M. A New Error Correction Scheme for Physical unclonable Functions. arXiv. arXiv:1611.01960 [cs.CR]. 2016. https://doi.org/10.48550/arXiv.1611.01960

42. Shamsoshoara A., Korenda A.R., Afghah F., Zeadally S. A Survey on Hardware-Based Security Mechanisms for Internet of Things. arXiv. arXiv:1907.12525 [cs.CR]. 2019. https://doi.org/10.48550/arXiv.1907.12525

43. Maes R., Verbauwhede I. Physically Unclonable Functions: A Study on the State of the Art and Future Research Directions. In: Sadeghi A.-R., Naccache D. Towards Hardware-Intrinsic Security: Foundations and Practice. Book series: Information Security and Cryptography. Berlin: Springer; 2010. P. 3–37. https://doi.org/10.1007/978-3-642-14452-3_1

44. Dodis Y., Ostrovsky R., Reyzin L., Smith A. Fuzzy extractors: how to generate strong keys from biometrics and other noisy data. SIAM J. Comput. 2008;38(1):97–139. https://doi.org/10.1137/060651380

45. Muthammal R., Sindhuja N. VLSI architecture of turbo codes for dedicated short-range communication. Int. J. Eng. Res. Online. 2015;3(5):412–416. URL: https://www.researchgate.net/publication/321669464_VLSI_Architecture_of_Turbo_Codes-IP_Secure_With_PUF_for_DSRC_systems. Accessed July 19, 2025.

46. Wong C.-W., Wu M. Counterfeit detection using paper PUF and mobile cameras. In: Proceedings of the IEEE International Workshop on Information Forensics and Security (WIFS 2015). November 16–19, 2015. Rome, Italy. Piscataway, NJ: IEEE; 2015. P. 1–6. https://doi.org/10.1109/WIFS.2015.7368579

47. Zheng J., Potkonjak M. A digital PUF-based IP protection architecture for network embedded systems. In: Proceedings of the Tenth ACM/IEEE Symposium on Architectures for Networking and Communications Systems (ANCS’14). 2014. P. 255–256. https://doi.org/10.1145/2658260.2661776

48. Zhang J., Lin Y., Lyu Y., Qu G. A PUF-FSM binding scheme for FPGA IP protection and pay-per-device licensing. IEEE Trans. Inf. Forensics Secur. 2015;10(6):1137–1150. https://doi.org/10.1109/TIFS.2015.2400413

49. Guo Q., Gong Y., Hu Y., Li X.-W. PUF-based pay-per-device scheme for IP protection of CNN model. In: 2018 IEEE Asian Test Symposium (ATS 2018). December 10–13, 2018. Hefei, China. Piscataway, NJ: IEEE; 2018. P. 115–120. https://doi.org/10.1109/ATS.2018.00032

50. Kalanadhabhatta S., Kumar D., Anumandla K.K., Reddy A., Acharyya A. PUF-based secure chaotic random number generator design methodology. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 2020;28(9):1994–2004. https://doi.org/10.1109/TVLSI.2020.2979269

51. Kaya T. A true random number generator based on a Chua and RO-PUF: design, implementation and statistical analysis. Analog Integr. Circ. Sig. Process. 2020;102:577–588. https://doi.org/10.1007/s10470-019-01474-2

52. Calhoun J., Minwalla C., Helmich C., Saqib F., Che W., Plusquellic J. Physical Unclonable Function (PUF)-based e-cash transaction protocol (PUF-Cash). Cryptography. 2019;3(3):18. https://doi.org/10.3390/CRYPTOGRAPHY3030018

53. ZhangY., QinY., FengD., YangB., WangW. An efficient Trustzone-based in-application isolation schema for mobile authenticators. In: Lin X., Ghorbani A., Ren K., Zhu S., Zhang A. (Eds.). Security and Privacy in Communication Networks. SecureComm 2017. Book Series: Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering. Cham: Springer; 2018. V. 238. P. 585–605. https://doi.org/10.1007/978-3-319-78813-5_30

54. Kish L.B., Entesari K., Granqvist C.G., Kwan C. Unconditionally secure credit/debit card chip scheme and physical unclonable function. Fluctuation Noise Lett. 2017;16(1):1750002. https://doi.org/10.1142/S021947751750002X

55. Suh G.E., O’Donnell C., Devadas S. Aegis: a single-chip secure processor. IEEE Des. Test Comput. 2007;24(6):570–580. https://doi.org/10.1109/MDT.2007.179

56. Suresh V., Manimegalai R. SPIC-SRAM PUF integrated chip based software licensing model. In: Thampi S., Madria S., Wang G., Rawat D., Alcaraz Calero J. (Eds.). Security in Computing and Communications. SSCC 2018. Communications in Computer and Information Science. Springer; 2018. V. 969. P. 377–388. https://doi.org/10.1007/978-981-13-5826-5_29

57. Kohnhäuser F., Schaller A., Katzenbeisser S. PUF-based software protection for low-end embedded devices. In: Conti M., Schunter M., Askoxylakis I. (Eds.). Trust and Trustworthy Computing. Trust 2015. Book Series: Lecture Notes in Computer Science. Cham: Springer; 2015. V. 9229. P. 3–21. https://doi.org/10.1007/978-3-319-22846-4_1

58. Zheng Y., Liu W., Gu C., Chang C-H. PUF-based Mutual Authentication and Key-Exchange Protocol for Peer-to-Peer IoT Applications [preprint]. TechRxiv; 2021.

59. Mahmood K., Shamshad S., Rana M., et al. PUF-enabled lightweight key-exchange and mutual authentication protocol for multi-server-based D2D communication. J. Inf. Secur. Appl. 2021;61:102900. https://doi.org/10.1016/j.jisa.2021.102900

60. Bathalapalli V.K.V.V., Mohanty S.P., Pan C., Kougianos E. QPUF: quantum physical unclonable functions for security-by-design of industrial Internet-of-Things. In: 2023 IEEE International Symposium on Smart Electronic Systems (iSES 2023). December 18–20, 2023. Hyderabad, India. Piscataway, NJ: IEEE; 2023. P. 296–301. https://doi.org/10.1109/iSES58672.2023.00067