Fig. 5: Brute force cracking.

a Authentication with PUFs – PUF generates and stores primitives in the central server; the edge user with PUF sends a validation request to the server, and is then feedback with the specific configuration and challenge to generate a primitive to be sent back to the server; if the primitive agrees with the stored one, the edge user is authorized as right user. b Key generation with the PUFs, with enrolment and key generation stages—enrolment engages the random number with the entropy of the PUFs; key generation generates the key via two approaches, with the simpler approach generating the key directly through Hash function, while the other complex approach further engaging the entropy of the PUFs before key generation through Hash function. c Brute force cracking of the PUFs, with the primitives challenged by one bit at a time until successful. The averaged cracking time is estimated by the total time divided by the number of cracking attempts. d Plot of the cracking time versus the bit length of the primitives, and e plot of the cracking probability versus the number of attempts, showing the primitives of a 108-bit length take an estimated 10¹⁶ years to crack. f Quantitative comparison and g the radar plot in some key performance metrics of our PUFs with state-of-the-art reports. See Supplementary Table 1 for a detailed quantitative comparison.