Fig. 3: Physical unclonability.

Entropy, normalized Hamming Distance (n-HD), and correlation coefficient (CC) of the first PUF, i.e., PUF₁, at a the initial state and b the final state. The final state means that all the individual transistors are configured to the final low conductance states. See Supplementary Fig. 11 for the entropy, n-HD, and CC in five other randomly configured states, where the individual transistors are randomly configured in each of the states. Entropy ~1, n-HD ~ 0.5, and CC ~ 0 in all the tests prove an ideal physical unclonability of the PUFs, i.e., ideal randomness, uniqueness, and irrelevance characteristics of the PUFs. c PUF-to-PUF n-HD matrix across the PUF chip at the initial state, with n-HD ~ 0.48 proving all the individual PUFs are unique from one another across the PUF chip. The insert shows the PMF of the n-HD. d Entropy, n-HD, and CC of PUF₁ in consecutive configuration operations, with entropy ~0.7 to ~0.95, n-HD ~ 0.5, CC ~ 0.2 to 0 proving an ideal physical unclonability. See Supplementary Table 2 for the detailed physical unclonability metric values.