As a result the learning algorithm has some probability of failure that scales

As a result the learning algorithm has some

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parameter space. As a result, the learning algorithm has some probability of failure that scales inversely with the size of the training set (the number of observed CRPs). If the algorithm fails, it must be restarted again with differ- ent parameters. It was identified that an arbiter PUF with a 512-bit challenge and eight output xor s would defeat the machine learning approaches used by Ru ¨hrmair et al. in 2010. The postprocessing scheme used in ‘‘lightweight secure’’ PUFs proved to have the same exponential dependence with a similar complexity requirement. A newer set of attacks leveraging both machine learn- ing and side-channel information has recently emerged [19], [36]. It has been shown that by coordinated Fig. 3. Code distance distribution for 256-bit PUF responses. Herder et al. : Physical Unclonable Functions and Applications: A Tutorial 1132 Proceedings of the IEEE | Vol. 102, No. 8, August 2014
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application of timing or power side-channel analysis and adapted machine learning techniques, very efficient attacks can be performed, i.e., attacks that use linearly many CRPs and low degree polynomial computation times. The practical viability of the combined attacks has been demonstrated by machine learning experiments on numerically simulated CRPs. This work has shown that xor arbiter PUF and lightweight PUFs have to be im- plemented in such a manner that power side channels are protected, else PUFs can be easily cloned. One key consideration in studying the complexity of PUFs is stability (described as ‘‘intra-PUF variation’’ in the RFID IC example). This will be discussed further in Section IV-E. However, it should be noted that although output xor ’ing has an exponential effect on modeling complexity, it also has an exponential effect on decreasing stability. In doing so, it decreases the effectiveness of a PUF in an actual authentication environment and simul- taneously decreases the accuracy requirement of an attack model, as the greater intrinsic PUF error must be tolerated by the authentication protocol. The task of identifying an approach to exponentially increase model complexity while only having a polynomial effect decreasing PUF stability is an area of active research. E. Error Correction Versus Tolerance In the RFID IC example, random noise contributes to the PUF stability being roughly 90%, i.e., the intra-PUF variation is ² 10%. In addition, this stability worsens when the temperature changes. In perhaps the earliest reference to error correction in silicon PUFs, Gassend mentioned the use of 2-D Hamming codes [6]. Suh suggested the use of Bose–Chaudhury– Hochquenghen (BCH) codes V more specifically the BCH (255,63, t ¼ 30) code [38]. In this case, the PUF generates 255 bits, but the code exposes 192 syndrome bits publicly, so the actual security of the system is at most 63 bits. This error corrects at most 30 errors out of 255 bits. This corresponds to a PUF with ² 88% stability.
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