The results are displayed in Table II B Scalability Figs 3 and 4 display the

The results are displayed in table ii b scalability

This preview shows page 8 - 10 out of 16 pages.

. The results are displayed in Table II. B. Scalability Figs. 3 and 4 display the results of our scaling experiments with LR. Again, the smallest number of CRPs in the training set needed to achieve predictions with a misclassi fi ca- tion rate scales linearly with the number of parameters of the problem (the product of the number of stages and the number of XORed Arb-PUFs ): (10) But, in contrast to standard Arb-PUFs, optimizing the nonlinear decision boundary (4) on the training set now is a nonconvex problem, so that the LR algorithm is not guaranteed to fi nd (an attractor of) the global optimum in its fi rst trial. It needs to be Fig. 3. Double logarithmic plot of misclassi fi cation rate on the ratio of training CRPs and problem size . Fig. 4. Average rate of success of the LR algorithm plotted in dependence of the ratio [see (11)] to . iteratively restarted times. thereby can be expected to not only depend on and , but also on the size of the employed training set. As is argued in greater detail in [45], the success rate of fi nding (an attractor of) the global optimum is de- termined by the ratio of dimensions of gradient information ( as the gradient is a linear combination of the feature vector) and the dimension in which the problem is linear separable. The dimension is the number of independent di- mensions of . As the tensor product of several vectors consists of all pos- sible products between their vector components, the indepen- dent dimensions are given by the number of different products of the form for (where we say that for all ). For XOR Arb-PUFs, we furthermore know that the same challenge is ap- plied to all internal Arbiter PUFs, which tells us that for all and . Since a repetition of one component does not affect the product regardless of its value (recall that ), the number of the above products can be obtained by counting the unrepeated components. The number of different products of the above form is therefore given as the number of -tuples without repetition, plus the number of -tuples without repetition (corresponding to all -tuples with 1 repetition), plus
Image of page 8
1884 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 8, NO. 11, NOVEMBER 2013 TABLE III LR ON L IGHTWEIGHT PUF S FOR N OISE -F REE , S IMULATED CRP S . P REDICTION R ATE R EFERS TO S INGLE O UTPUT B ITS . T RAINING T IMES W ERE A VERAGED O VER D IFFERENT PUF I NSTANCES the number of -tuples without repetition (corresponding to all -tuples with 2 repetitions), etc. Writing this down more formally, is given by (11) The approximation applies when is considerably larger than , which holds for the considered PUFs for stability reasons. Fol- lowing [45], this seems to lead to an expected number of restarts to obtain a valid decision boundary on the training set (that is, a parameter set that separates the training set), of (12) Furthermore, each trial has the complexity (13) V. L IGHTWEIGHT S ECURE PUF S This section investigates the ML-resilience of LW PUFs on simulated, noise-free CRPs.
Image of page 9
Image of page 10

You've reached the end of your free preview.

Want to read all 16 pages?

  • Summer '15

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors