Successful application of our techniques to a Controlled PUF only becomes

Successful application of our techniques to a

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security of the applied one-way hash function. Successful application of our techniques to a Controlled PUF only becomes possible if Eve can probe the internal, digital re- sponse signals of the underlying Strong PUF on their way to the control logic. Even though this is a signi fi cant assumption, probing digital signals is still easier than measuring continuous analog parameters within the underlying Strong PUF, for ex- ample determining its delay values. Note again that physical ac- cess to the PUF is part of the natural attack model on PUFs, as mentioned above. If a Controlled PUF has been modeled, the same effects for protocols resting on their unpredictability and physical unclonability apply that have been described in the last Section I-B1. 3) Weak PUFs: Weak PUFs (or POKs) are PUFs with few, fi xed challenges, in the extreme case with just one challenge [41], [38]. It is usually assumed that their response(s) remain inside the PUF-carrying hardware, for example for the deriva- tion of a secret key, and are not easily accessible for external parties. Weak PUFs are the PUF class that is the least suscep- tible to the presented modeling attacks. We stress that our attacks only apply to them under relatively rare and special circumstances: namely if a Strong PUF, em- bedded in some hardware system and with a not publicly acces- sible CRP interface, is used to implement the Weak PUF. This method has been suggested in [14], [46]. Thereby only a few (of the very many possible) challenges of the Strong PUF are used for internal key derivation. Our attacks make sense in this context only in the special case that the Strong PUF challenges that are used in the key derivation process are not yet fi xed in the hardware at the time of fabrication, but are selected later on. For one reason or another, the adversary may learn about these challenges at a point in time that lies after his point of physical access to the PUF. In this case, machine learning and modeling of the Strong PUF can help the adversary to derive the key, even though the points in time where he has access to
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1878 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 8, NO. 11, NOVEMBER 2013 the PUF and where he learns the challenges strictly differ. In order to make our ML methods applicable in this case, one must assume that the adversary was able to collect many CRPs of the Strong PUF, for example by physically probing the internal digital response signals of the Strong PUF to randomly injected challenges, or by malware that abuses internal access to the un- derlying Strong PUF’s interface. We comment that the latter scenarios obviously represent very strong attack models. Under comparable circumstances also many standard Weak PUFs and other secret key based architectures break down. In any other cases than the above, our modeling attacks will not be relevant for Weak PUFs. This means that they are not applicable to the majority of current Weak PUF implementa- tions, including the Coating PUF [47], SRAM PUF [18], But- ter fl y PUF [22], and similar architectures.
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