ditionally the randomness of the design is enhanced because it depends on the

# Ditionally the randomness of the design is enhanced

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ditionally, the randomness of the design is enhanced because it depends on the delay of the gates and also on the threshold voltage of current mirror transistors. The block diagram of the proposed model is shown in Figure 5. Fig. 5. Proposed PUF model 16 corrected outputs from 32-bit input current mirror PUFs act as input challenges to the 16-bit Arbiter PUF. The time sequence diagram of the two stage PUF is shown in Figure 6. Obviously, the overall numbers of zeros and ones are very close, while the inputs from 16 PUFs vary a lot. IV. E VALUATION Monte Carlo (MC) analysis is applied on PUFs to model property changes in transistors caused by the fabrication processes. The uniqueness and uniformity of the PUFs are evaluated in this section. Temperature and supply voltage variations are also modelled in the simulation to determine the reliability of the PUFs. Fig. 6. Outputs from 16 CM PUFs to Arb-PUF A. Uniqueness and Uniformity For the CM PUF, the uniqueness is 48.92% from 64 instances with 2000 responses. The uniformity is 51.0% from 1 instance with 12000 responses. For the 16-bit arbiter PUF, the uniformity is 40.8%, calculated from 4000 CRPs. The uniqueness of 16-bit arbiter PUF from 48 PUF instances is 48.31%. The uniformity of the two stage PUF is 39.06% based on 3200 CRPs, and the uniqueness is 47.76% based on 32 instances. The uniformity and uniqueness of the series combined PUF is mainly determined by the last stage of the PUF, which is the 16-bit arbiter PUF. B. Reliability When operating at a changed temperature or supply voltage, the change of the output responses determines the reliability of the device. The simulated temperature for devices varied from 20 C to 105 C. The current mirror PUF alone has an average reliability value of 97.63% with temperature. Supply voltage variation has a higher influence on the current mirror PUF, giving 92.38% and 95.89% at 1.0 Volt and 1.4 Volt, respectively. For the 16-bit arbiter PUF, the temperature relia- bility is 98.03% on average and the supply voltage reliability is 96.76% on average. The influence on the reliability of serial PUF is shown in the Table I. Three other PUFs were also compared in the table and detailed information can be found in the referenced papers, [5], [10], [11]. TABLE I C HARACTERISTIC C OMPARISON PUFs Uniformity % Uniqueness % Reliability % NLCMPUF [5] 47 49 98 IOPUF [10] 49.95 NA 93.79 TCO [11] 63.04 50.23 91.58 32-bit CM-PUF 51 48.92 92.82 16-bit Arb-PUF 40.80 48.31 97.40 Proposed PUF 39.06 47.76 70.50 The figure of the reliability of the proposed PUF is 70.5%, caused by inefficient error correction in the CM PUF, which 54 3rd International Verification and Security Workshop (IVSW)
Fig. 7. ML on CM-PUF (blue) and Arb-PUF (orange) using 3000 CRPs TABLE II C OMPARISON OF P REDICTION A CCURACY . Type Prediction Accuracy [%] 64-bit Arbiter-PUF Permutation [4] 69.04 32-bit Arbiter-PUF Substitution [4] 66.40 32-bit TCO-PUF Substitution [4] 62.50 4-XOR 64-bit Arbiter-PUF [8] 99 4-XOR 64-bit Lightweight-PUF [8] 99 Implemented Arbiter PUF 100 Implemented CM PUF 96.9 Proposed PUF 59.85 can be easily affected by external condition changes. Another problem is the structure of the two stage PUF which accumu- lates response errors from all 16 current mirror PUFs. Table I

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