# A PUF- and Biometric-Based Lightweight Hardware Solution to Increase Security at Sensor Nodes
## 6 Experimental Results and Discussion
### Trusted Sensor Nodes Based on SRAM PUFs
Applying Equation (3) with \(n=8\), \(t=3\), and \(p\) estimated as 0.0063 (the average fractional Hdist of the genuine responses measured experimentally as commented above), the probability of failure in reconstructing a bit of the secret \(K\) is 1.08 \(\times\) 10\({}^{-7}\) (Equation (3) is evaluated as 1-binocdf(3, 8, 0.0063) in Matlab). Therefore, the  
Figure 7: Fractional Hamming Distances obtained from SRAM PUFs. probability to find some error in a 128-bit secret is 1.38 \(\times\) 10\({}^{-5}\) (1-binocdf (0, 128, 1.08 \(\times\) 10\({}^{-7}\))). If lower bit error rate is required, the codeword length of the repetition ECC can be increased. For example, considering a 16-bit ECC, the probability of failure in reconstructing a bit of the secret \(K\) is 3.05 \(\times\) 10\({}^{-14}\) (1-binocdf (7, 16, 0.0063)) and the probability to find some error in a 128-bit secret is 3.91 \(\times\) 10\({}^{-12}\) (1-binocdf (0, 128, 3.05 \(\times\) 10\({}^{-14}\))). The above commented results correspond to nominal operation conditions and to the model based on Equations (1)-(3) described in Section 3.2. However, the reliability of a PUF is usually evaluated under different environmental conditions. Bit flipping in SRAM PUFs is mostly affected by changes in ramp-up time (i.e., the time to reach power supply voltage value after power-up) and temperature [8; 9]. Supposing that the ramp-up time cannot be modified (because the on-chip voltage regulator cannot be tampered), the robustness of the key reconstruction stage using an 8-bit repetition ECC against changes in operation temperature was evaluated. A specific firmware was developed to carry out the key reconstruction stage and five CC2541 chips were evaluated more exhaustively at 5 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 75 \({}^{\circ}\)C with 100 measurements for each temperature and 4096 secret bits reconstructed for each chip by using the 8-bit repetition ECC. In total, for the three temperatures and the 100 measurements, 6,144,000 bits were reconstructed for the 5 chips. For all the measurements, only 20 bits were not reconstructed correctly (corresponding to 4 bits for 5 measurements at 75 \({}^{\circ}\)C). That means a failure rate of 20/6,144,000 = 3.26 \(\times\) 10\({}^{-6}\). This can be acceptable since an error rate of 10\({}^{-6}\) is considered by many authors as a conservative value that fulfils the requirements of most of typical security applications [11; 21]. Therefore, secret keys of 128 bits (that is, for example, the key length for the standard cipher AES) can be recovered by the 1024-bit ID responses of the genuine sensor node with high probability. Hence, the QFM-based features employed at registration can also be recovered. The distribution of fractional Hamming distances (Hdist) obtained from the comparisons of \(\left\{\overline{ID}_{i}^{A}\right\}\) and \(\left\{ID_{j}^{B}\right\}\), for any pair of chips (\(A\
eq B\), \(\forall\,i,j\)) or any pair of responses (\(i\
eq j\), \(\forall\,A,B\)), which corresponds to the impostor population of ID responses is illustrated at the right of Figure 7. The average fractional Hdist, calculated as in (1), is 0.5004. Hence, the bit flipping probability of impostor responses can be approximated by 50.04%, as described in Section 3.2. The probability of having the same bit value in two different ID responses was like tossing a coin. No correlation was found among the start-up values of different ID responses (they were independent), from the same or different SRAMs. Hence, no correlation is found between Helper Data \(\left\{ID_{x}^{D}\oplus\ Koded_{x}\right\}\) stored in the same sensor node as well as between Helper Data in different sensor nodes. A secret key obfuscated by one ID response cannot be recovered by a different ID response. The minimum entropy of the impostor responses, calculated as in (5), is 91.92%. This means that in a 1024-bit response, there are 941.26 independent bits and the secret is almost fully obfuscated because the response is almost fully random.