Algorithm 1 Computation of Output Transition Probability N 1000 Require a

# Algorithm 1 computation of output transition

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Algorithm 1 Computation of Output Transition Probability, N = 1000 . Require: a) Generate N random challenges, c . b) Generate N challenges, ˆc from c with HD=1 for every challenge bit index. c) Simulate k -bit Arbiter-PUF using a TSMC 65-nm technology node. d) Collect CRPs for r PUF ( c ) and ˆr PUF ( ˆc ) Ensure: Value of output transition probability 1: count 0 2: for index = 1 to k do 3: for i = 1 to N do 4: if r = ˆr then 5: count count + 1 6: end if 7: end for 8: probability[index] count/N 9: count 0 10: end for Figure 1 shows the computed output transition probability for k = { 16 , 32 , 64 } . A challenge bit index in the x-axis is referring to a bit position of the challenge which was ﬂipped. As can be seen from Figure 1, for all Arbiter-PUFs, they produce a generic pattern where the output transition probability increases as the challenge bit index arising from 1 to k . It can be observed that the probability values for the first index is significantly poor, very close to zero. Based on this observation, given a set of CRPs, one can simply generate another set of CRPs by merely ﬂipping the first-bit position of all the challenges where the corresponding responses remain the same. It can be concluded that an Arbiter-PUF does not fulfills SAC, resulted in CRPs mapping can be predicted easily using ML technique. Next, the impact of challenge permutation on output transition probability and the correlation with ML- attack prediction accuracy will be discussed. 2) Challenge Permutation Technique: For a given size of Arbiter-PUF, the challenge permutation space is extremely huge. As a starting point, we analyze the permutation as shown in Figure 2 and investigate the impact on the output transition probability. k is the bit-length of the challenge and n is the length of the bit challenge that gets combined. The value of n is a power of two. Afterwards, this permutation scheme is known as an n -block permutation. 1 n A B 2 n B A n + 1 k - n k ( k - n ) + 1 n bit challenge position permutation ( k - 2 n ) + 1 Fig. 2. n -block permutation scheme. We applied the n -block permutation on generated CRPs used to compute the output transition probability in Figure 1. Next, the output transition probability based on n -block permutation is computed using Algorithm 1 and the values are illustrated in Figure 3 1 for 32-bit Arbiter-PUF. As can be seen from Figure 3, the probability for n = k 2 is essentially the probability in Figure 1 in which the corresponding probability value of index 1 to k 2 and index ( k 2 +1) to k has been swapped over. It similarly applies to the rest of n values. A similar pattern has been observed for k = { 16 , 64 } , hence, they are not shown for brevity. Next, an n -block permutation is applied on 32000 ran- domly generated challenges. Subsequently, the permutated challenges are applied on Arbiter-PUF to generate correspond- ing responses as described in Section III-A. The ML-attack is performed on the CRPs and the prediction accuracy is listed in Table II. For each Arbiter-PUF configuration, as n reduces, the predictability of the response reduces. For small

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