For the first kind of countermeasures typical designs use hash functions XOR

For the first kind of countermeasures typical designs

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For the first kind of countermeasures, typical designs use hash functions, XOR gates, and random bits to hide the original responses. The controlled PUF [5] and the reverse fuzzy extractor PUF [11] use hash functions. The original response of the arbiter PUF is input to a hash function, and then output to the outside. In this way, attackers cannot directly obtain the original responses. However, in [15], the unreliability of responses is utilized to successfully attack such PUFs. This is based on the observation that, if a response is very unreliable, the delays of two paths are very likely to be similar. The XOR PUF [6] and the lightweight PUF [7] adopt multiple arbiter PUFs. A challenge is input directly or through certain conversion to these arbiter PUFs, and then their original responses are XORed to produce the output response. Attackers can only obtain the XORed results without knowing the original responses. Such PUFs can still be attacked by Eq.1 with some modifications to mathmatically express the XOR gates. But with more arbiter PUFs adopted in one XOR PUF or lightweight PUF, much longer time is needed for achieving high prediction accuracy. However, the work in [16] shows that, by also utilizing the unreliability of responses, such PUFs are still easy to be broken. In [14], the correlation among multiple response bits of lightweight PUF is further explored to simplify the attack. The slender PUF [12] uses random bits. If the original m -bit response of arbiter PUF is [ r 1 , r 2 , ..., r m ], then the output response is [ t 1 , ..., t k , r 0 , r 1 , ..., r m , t k +1 , ..., t m ], where k , t 1 ~ t m are random values. In this way, when attackers obtain 2× m response bits, they do not know which bits are the original response bits. However, the work in [17] uses the evolution strategy to successfully break the slender PUF. Therefore, above countermeasures are still insufficient to resist modeling attacks. For the second kind of countermeasures, to replace the delay, the current and the voltage are used in current mirror PUF [8] and voltage transfer PUF [9], respectively. Due to the non-linear characteristic of current mirror and voltage transfer, Eq.1 cannot be used anymore. However, we proposed a compound heuristic algorithm of evolution strategy, simulated annealing, and ant colony to successfully break them [20]. 3. RPUF 3.1 Design As shown in Fig.1, the basic arbiter PUF has only 1-bit response, but in practical application, multi-bit response is needed. To realize it, there are mainly two ways [6][7]. One way is to implement multiple arbiter PUFs to produce multiple response bits respectively. Obviously, this requires large hardware cost. The other way is to use a Linear Feedback Shift Register (LFSR) or similar modules to extend a challenge to multiple sub-challenges, and the sub-challenges are input to the arbiter PUF one by one, so each sub-challenge produces one response bit, and the multi-bit response is composed. This paper adopts LFSR, which requires small hardware cost.
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