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Title of the paper: Theoretical Limits of Helperless Stabilizers for Physically Unclonable Constants

(extended version of Helper-less physically unclonable functions and chip authentication)

Available at: https://ieeexplore.ieee.org/abstract/document/6998080

ABSTRACT Physically unclonable constants (PUCs) have recently been proposed for private ID generation. Because in most of the proposed PUC schemes the generated value is not stable (i.e., it can change at different turn-ons), a postprocessing with a stabilizer is usually required. Most of the proposed stabilizer schemes use auxiliary data (helper data) to overcome the inherent randomness of the generation process. However, this complicates the structure of the scheme and poses additional security problems (e.g., helper data can be vectors for attacks), so that there is some interest in stabilizers that do not use helpers (helperless stabilizers). In this paper, we begin the study of the theoretical limits of helperless stabilizers. We show three main results: 1) perfect stability is unachievable; 2) we can make as small as desired the probability that a PUC has low stability; and 3) we can reliably recognize the bad devices at production time and discard them. The proofs of the latter two results are constructive.

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The only helperless stabilizer we are aware of is a brute-force exhaustive search for the error pattern proposed in [28].

OUR CONTRIBUTION

This paper has three main results.

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Although Algorithm 1 can be used in practice, no claim is done about its optimality. Actually, the problem of constructing the optimal helper-less stabilizer for a given RPUC is still open.

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Note that if the distribution of Q changes because of aging or environmental variations, the right hand side of (23) will be likely to change too. If (23) is going to be used in a real design, a possible approach is to consider the worst case and take for K the maximum of (23), taken over all the environment
conditions.

Note that the right hand side of (23) is likely to be a ``pessimistic'' bound, since it is derived from Chebyshev's inequality. A less pessimistic bound can be derived by approximating mq (mean of q) with a Gaussian variable.

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