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2015 | OriginalPaper | Chapter

Secure Key Generation from Biased PUFs

Authors : Roel Maes, Vincent van der Leest, Erik van der Sluis, Frans Willems

Published in: Cryptographic Hardware and Embedded Systems -- CHES 2015

Publisher: Springer Berlin Heidelberg

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Abstract

PUF-based key generators have been widely considered as a root-of-trust in digital systems. They typically require an error-correcting mechanism (e.g. based on the code-offset method) for dealing with bit errors between the enrollment and reconstruction of keys. When the used PUF does not have full entropy, entropy leakage between the helper data and the device-unique key material can occur. If the entropy level of the PUF becomes too low, the PUF-derived key can be attacked through the publicly available helper data. In this work we provide several solutions for preventing this entropy leakage for PUFs suffering from i.i.d. biased bits. The methods proposed in this work pose no limit on the amount of bias that can be tolerated, which solves an important open problem for PUF-based key generation. Additionally, the solutions are all evaluated based on reliability, efficiency, leakage and reusability showing that depending on requirements for the key generator different solutions are preferable.

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previous chapter Leakage Assessment Methodology

next chapter The Gap Between Promise and Reality: On the Insecurity of XOR Arbiter PUFs

In this work, unpredictability of random variables is expressed by Shannon entropy, as is done in many earlier work on this subject, e.g. [7]. Note that Shannon entropy serves as a lower bound for average guesswork [19]. For a stronger (less practical) provable security notion, the more pessimistic min-entropy measure should be used.

Note that \(H(X|W) = H(S|W)\), see [16]. This shows the equivalence in security (in terms of entropy) for a key generated from S or X.

E.g., a variant thereof appeared before in an early version of [21].

This has led to some confusion and occasional misinterpretations, i.e. under- or overestimations of the leakage. A discussion on this is e.g. found in [3].

Note that in particular for a too high bias this entropy bound even becomes negative, making it absolutely clear that this is a pessimistic lower bound.

See [16] for the derivation of this formula and similar for min-entropy in [3].

Only \(p \le 0.5\) is shown; entropy-vs-bias graphs are symmetrical around \(p=0.5\).

Efficient in terms of PUF size, while following the design of Fig. 1 and using only a single enrollment measurement per derived key.

The key generator from [10] is based on an SRAM PUF, but in this work we make abstraction of the actual PUF used. Our analysis and solutions apply to all PUF types with i.i.d. response bits suffering from bias.

[10] aims for a seed of 171 bits, but this is rounded up to 180 for practicality. The need for having 171-bit seeds originated in [5], but the reasoning is not fully clear.

Since bits of X are assumed i.i.d., which particular bits from X are considered for the entropy calculation is of no importance.

\(X_{1:n_1}\mathbf {H_{rep}}^\mathbf {\top }\) and \(X_{1:n_2}\mathbf {H_2}^\mathbf {\top }\) are not necessarily independent.

Note that this does not directly imply that the key becomes predictable, just that it is potentially less unpredictable than it should be according to its length.

Note that we cannot increase beyond \(r=31\), without increasing the length of the repetition code, otherwise the failure rate gets too large.

Von Neumann extractors have a small effect on bit error rate, shown in Sect. 4.1.

This is just one possible exemplary representation of (W, D).

Failure rates differ slightly from the results in Table 1 which were extrapolated from [10]. For objective comparison, the results of Table 2 are based on a new simulations, with the Hackett Golay decoder from [10] implemented in Matlab. The single Golay decoding failure rate \(p_{{\text {Golay-fail}}}\) is estimated as the \(95\,\%\)-confidence upper bound from the simulations; the actual values for \(p_{{\text {Golay-fail}}}\) are hence likely smaller. The total reconstruction failure rate is computed as \(1-(1-p_{{\text {Golay-fail}}})^{r}\).

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Title: Secure Key Generation from Biased PUFs
Authors: Roel Maes
Vincent van der Leest
Erik van der Sluis
Frans Willems
Publisher: Springer Berlin Heidelberg
Book: Cryptographic Hardware and Embedded Systems -- CHES 2015
Print ISBN: 978-3-662-48323-7

Electronic ISBN: 978-3-662-48324-4

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-662-48324-4_26

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