C PUF Descriptions and Models 1 Arbiter PUFs Arbiter PUFs Arb PUFs were fi rst

C puf descriptions and models 1 arbiter pufs arbiter

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C. PUF Descriptions and Models 1) Arbiter PUFs: Arbiter PUFs (Arb-PUFs) were fi rst intro- duced in [17], [23], [46]. It has become standard to describe the functionality of Arb-PUFs via an additive linear delay model [24], [27], [26]. The overall delays of the signals are modeled as the sum of the delays in the stages. In this model, one can express the fi nal delay difference between the upper and the lower path in a -bit Arb-PUF as , where and are of dimension . The parameter vector encodes the delays for the subcomponents in the Arb-PUF stages, whereas the fea- ture vector is solely a function of the applied bit challenge [24], [27], [26]. The output of an Arb-PUF is then determined by the sign of the fi nal delay difference . We make the technical convention of saying that when the Arb-PUF output is actually 0, and when the Arb-PUF output is 1: (3) Equation (3) shows that the vector via determines a separating hyperplane in the space of all feature vectors . Any challenges that have their feature vector located on the one side of that plane give response , those with feature vec- tors on the other side . Determination of this hyperplane allows prediction of the PUF. 2) XOR Arbiter PUFs: One possibility to strengthen the re- silience of arbiter architectures against machine learning, which has been suggested in [46], is to employ individual Arb-PUFs in parallel, each with stages (i.e., each with bitlength ). The same challenge is applied to all of them, and their individual outputs are XORed in order to produce a global response . We denote such an architecture as -XOR Arb-PUF (with the 1-XOR Arbiter PUF being identical to the standard Arbiter PUF). A formal model for XOR Arb-PUFs can be derived as fol- lows. Making the convention as done earlier, it holds that . This leads with equation (3) to a parametric model of an -XOR Arb-PUF, where and de- note the parameter and feature vector, respectively, for the -th Arb PUF: (4) (5) While (4) gives a nonlinear decision boundary with pa- rameters, (5) de fi nes a linear decision boundary by a separating hyperplane which is of dimension .
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1880 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 8, NO. 11, NOVEMBER 2013 3) Lightweight Secure PUFs: Another type of PUF, which we term Lightweight Secure PUF or Lightweight PUF for short, has been introduced in [27]. At its heart are individual stan- dard Arb-PUFs arranged in parallel, each with stages (i.e., with bitlength ), which produce individual outputs . These individual outputs are XORed to produce a multibit re- sponse of the Lightweight PUF. Another difference to the XOR Arb-PUFs lies in the inputs which are applied to the individual Arb-PUFs. Contrary to XOR Arb-PUFs, it does not hold that , but a more complicated input mapping that derives the individual inputs from the global input is applied. We refer the reader to [27] for further details.
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