The proposed RPUF with n bit challenge C and m bit response R is shown in Fig2

The proposed rpuf with n bit challenge c and m bit

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The proposed RPUF with n -bit challenge C and m -bit response R is shown in Fig.2. The challenge C is input to a proposed challenge randomization module. Then the randomized challenge C R is input to the LFSR, and the LFSR produces m sub-challenges C R - SUB [1~ m ] . Each sub- challenge produces one response bit through the strong PUF to compose the m -bit response R . The strong PUF can be arbiter PUF, current mirror PUF, voltage transfer PUF, and so on, so the proposed RPUF structure is a common structure for existing strong PUFs to resist modeling attacks. In the paper, we use the arbiter PUF as illustration. The challenge randomization module is proposed to randomize the input challenge so that attackers do not know what sub-challenges are really input to the arbiter PUF to produce the observed responses. The circuits of challenge randomization module with different randomization levels are shown in Fig.2. The RNG is adopted in the challenge randomization module. The RNG is a commonly used module. There are already many previous works working on the design of RNG. Since the objective of this paper is to design PUF for resisting modeling attacks, we will not further discuss the design of RNG, and we assume a qualified RNG is used in RPUF, which can generate effectively random bits. Fig.2 RPUF
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Fig.3 Challenge Randomization Module For randomization level 1, the RNG is adopted to generate a 1-bit random number t . According to t , C R can be the same as C , or C R =~ C . In other words, for one challenge C , at different time, different C R may be input to the LFSR, and to produce different responses R . Therefore, in the proposed RPUF, one challenge has more than one response. For randomization level 1, each challenge has two different responses. For randomization level 2, the RNG generates 2 bits t 0 and t 1 , so C R has four possibilities: C , [ c 1 , c 2 , ..., c n /2 , ~ c n /2+1 , ~ c n /2+2 , ..., ~ c n ], [~ c 1 , ~ c 2 , ..., ~ c n /2 , c n /2+1 , c n /2+2 , ..., c n ], ~ C . Hence, each challenge has four different responses. Similarly, for randomization level l , each challenge has 2 l different responses. But notice that, a large l could lead to large storage space requirement of enrolled CRP data, so this paper sets l =1, 2. More specific analysis will be given later. From the aspect of attackers, who try to use the non- invasive modeling attacks to break the RPUF, the problem they confront is that, when a response is observed, they do not know what challenge, C or ~C , produces the response. Hence, obtaining an effective training set for machine learning becomes a problem. Random guess of the challenge for each response is obviously not a good way. In the experimental section, we will further evaluate the capability of RPUF for resisting modeling attack in detail. 3.2 Application In RPUF, every challenge has multiple responses, so the PUF based applications need some modifications to adapt RPUF. Taking the PUF based authentication as an example, a server authenticates a token through the PUF [22]. It normally contains two phases: the enrollment phase and the deployment phase. In the enrollment phase, the
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