Comment in the 110 Faraday Discussion on Chemical Reaction Theory. General

Based on the statistical analysis results, the performance comparisons of the MUX-based PUFs are summarized in Table 3.4.

Table 3.4: Theoretical Performance Indicators Comparison

Indicator Expression Relation

Reliability 1− Pintra original MUX > MFFO > MFFS > MFFC

Uniqueness 1− |2Pinter− 1| MFFC > MFFS > MFFO > original MUX > MUX/DeMUX Randomness 1− |2P (R = 1) − 1| MFFC > MFFS > MFFO > original MUX > MUX/DeMUX

These analysis results enable deeper understandings of the MUX-based PUFs, which could be exploited to improve the performance during PUF design. A number of claims are listed below:

(a) In a MUX PUF, if we increase the number of stages, uniqueness and randomness will improve while reliability will be degraded.

(b) Smaller skew of the arbiter will lead to higher uniqueness and randomness.

(c) The stage variation probability will increase with the number of previous feed-forward paths in a feed-feed-forward structure, as the error in previous path would propagate to later stages.

(d) When designing the feed-forward PUF, an appropriate tradeoff point should be achieved based on the particular application and the performance requirement.

Designer should be careful in selecting the type, the number, and the locations of feed-forward paths.

(e) The number and the locations of the paths in the MUX/DeMUX PUF also provide a tradeoff between reliability and uniqueness.

3.7 Experiments

3.7.1 Experimental Setup

Experiments were carried out by SPICE simulations on a 65-nm technology pro-cess. We use the Monte-Carlo method to simulate the effect of process variations and environmental variations. In our simulation, we set up the transistor parameters and process variations based on a major industrial standard model, according to the findings in the area of statistical static timing analysis [11, 34]. All of the simulated MUX-based PUFs have 100 MUX stages. We placed 10 feed-forward paths regularly on the MUX stages for each PUF structure with feed-forward paths and 10 DeMUXs regularly for MUX/DeMUX PUFs. We generated 100-bit responses for measurement in our experi-ments. All the structures were tested by at least 1000 Monte-Carlo runs.

The inter-chip variations and the intra-chip variations are computed according to the Hamming distances obtained for different chips and the same chip under different readouts, respectively. Part of these results have already been presented in [31, 32].

The randomness values are calculated based on the total numbers of 0’s and 1’s for each MUX-based PUF structure.

3.7.2 Results

Table 3.5 presents the results of inter-chip variations, intra-chip variations, and the percentage of 1’s in the response., while Table 3.6 presents the results of the three per-formance indicators: reliability, uniqueness, and randomness. First, it can be observed

66 that the minimum inter-chip variation is larger than the maximum intra-chip variation for all of the simulated structures. Thus, we can conclude that the variations caused by the randomness in manufacturing process are more significant than the variations under different environmental conditions. Therefore, these PUFs can be used as reliable secret keys with some error correcting techniques. Second, it can also be observed that by adding feed-forward arbiters into the MUX PUF circuit, the inter-chip variations and intra-chip variations are both increased, since the noise influences the select sig-nals of some of the intermediate stages. Furthermore, it can be seen that the modified feed-forward structures lead to better reliability than the standard feed-forward MUX PUFs. Compared to the original MUX PUF, the intra-chip variation of the standard feed-forward MUX PUF is increased by 68% on average. But the intra-chip variation of the modified feed-forward MUX PUF is only increased by 17% on average, which is only

14 of the standard feed-forward PUFs. Therefore, we can conclude that the reliability is improved by adopting the proposed modified feed-forward path. Finally, it can also be observed that the randomness is improved by introducing feed-forward paths into the original MUX PUF.

Table 3.5: Results of Inter-Chip and Intra-Chip Variations for 100-Stage PUFs Structures Inter-Chip Variation Intra-Chip Variation

P (R = 1)

Max Min Max Avg

Original MUX 59% 22% 13% 5.8% 32.8%

Feed-forward Overlap 66% 27% 15% 8.7% 38.8%

Feed-forward Cascade 64% 25% 20% 10.7% 42.1%

Feed-forward Separate 65% 26% 17% 9.9% 40.3%

Modified Feed-forward Overlap 61% 25% 14% 6.6% 37.3%

Modified Feed-forward Cascade 64% 25% 15% 7.0% 39.9%

Modified Feed-forward Separate 61% 27% 15% 6.9% 38.4%

MUX/DeMUX 57% 23% 16% 7.1% 29.9%

Table 3.6: Results of Performance Indicators for 100-Stage PUFs Structures Reliability Uniqueness Randomness

Original MUX 94.2% 88.2% 65.6%

Feed-forward Overlap 91.3% 95.0% 77.6%

Feed-forward Cascade 89.3% 97.5% 84.2%

Feed-forward Separate 90.1% 96.2% 80.6%

Modified Feed-forward Overlap 93.4% 93.5% 74.6%

Modified Feed-forward Cascade 93.0% 95.9% 79.8%

Modified Feed-forward Separate 93.1% 94.6% 76.8%

MUX/DeMUX 92.9% 83.8% 59.8%

3.7.3 Discussion

By comparing the experimental results presented in Table 3.5 and Table 3.6, it can be concluded that the relations between the performances of different types of MUX-based PUFs are consistent with the theoretical results shown in Table 3.4. Note that the value of P (R = 1) which is more close to 0.5 indicates better randomness. It can also be observed from Table 3.5 and Table 3.6 that the feed-forward separate structure is the most reliable structure while the feed-forward cascade is the least reliable one among the three feed-forward structures. Moreover, the MUX/DeMUX PUF has relatively low inter-chip variations; as a result, the uniqueness of this structure is decreased.

These experimental results validate the correctness of our statistical analysis. Over-all, all the MUX-based PUF structures can be used as reliable secret keys for authen-tication and identification within certain error tolerance, as the PUFs exhibit sufficient gaps between the minimum of the inter-chip variations and the maximum of intra-chip variations.

3.8 Conclusion

We have presented a systematic statistical approach to quantitatively evaluate var-ious types of MUX-based PUFs. We defined three performance indicators - reliability, uniqueness, and randomness - to compare the performances of these MUX-based PUFs.

68 These indicators are also validated by the corresponding simulation results. The exper-imental results show that the proposed statistical analysis approach effectively reflects the characteristics of various PUF designs. We have also proposed a novel modified forward MUX PUF structure, which has better reliability than the standard feed-forward MUX PUF.

Chapter 4

Lightweight, Secure, and Reliable