A Multilevel Coding Scheme for Multi-Valued Physical Unclonable Functions

Müelich, Sven; Mandry, Holger; Ortmanns, Maurits; Fischer, Robert F. H.

doi:10.1109/tifs.2021.3089883

Cited by 6 publications

(17 citation statements)

References 38 publications

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“…We consider PUF architectures, where access to an analog, i.e., real-valued, physical quantity is possible. A particular example are ring oscillator PUFs (ROPUFs), introduced in [35], and also studied in [36], [5]. First, the basic principle is briefly reviewed and the error model is established.…”

Section: Multi-valued Physical Unclonable Functionsmentioning

confidence: 99%

“…As described in [5], at the Institute of Microelectronics at Ulm University, a set of ROPUFs has been implemented and an exhaustive measurement campaign has been conducted. Detailed information about the structure of the underlying hardware can be found in [36].…”

Section: A Data and Error Model Of Ring Oscillator Pufsmentioning

confidence: 99%

“…Various studies revealed that for some PUF constructions this assumption is too pessimistic, and more suited channel models have been adopted [11], [12]. The binary PUFs in [5] directly employ the analog PUF readouts as input to a soft-decision decoding algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…To that end, we interpret the readout process in PUFs as digital transmission schemes (cf. [5,Fig. 6]) and, based on that interpretation, coded modulation/signal shaping are applied.…”

Section: Introductionmentioning

confidence: 99%

“…Based on this, the capacities of the bit levels for the Gaussian distributed reference PUF readout in additive Gaussian noise are calculated and the sum capacity, which is the ultimate limit for the information rate which can be extracted, are derived. Thereby, the differences to conventional digital transmission (as used in [5]) are enlightened and the design of the coded modulation scheme can be matched to the present situation. This also includes the derivation of the metric for optimum soft-decision decoding.…”

Section: Introductionmentioning

confidence: 99%

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Coded Modulation and Shaping for Multivalued Physical Unclonable Functions

Fischer

Müelich

2022

IEEE Access

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In this paper, a coded modulation scheme employing signal shaping is proposed and designed for use in multi-valued physical unclonable functions (PUFs). In the literature, usually binary PUFs are considered, where less than one bit of entropy is extracted from each fundamental building block (PUF node). This randomness in the hardware may then used for the derivation of cryptographic keys. Meanwhile, PUFs over higher-order alphabets, so-called multi-valued PUFs (MVPUFs) have been presented. Typically, symbols from a higher-order alphabet are extracted by suited quantization. In contrast, in this paper we propose a coded modulation scheme which directly works on the analog values provided by the PUF nodes. We establish an interpretation as digital transmission with randomness at the transmitter, and thereon calculate the respective capacities of bit levels for the Gaussian distributed reference PUF readout in additive Gaussian noise. In addition, the metric for optimum soft-decision decoding is derived. Thereby, the coded modulation scheme can be designed for the present situation. A helper data scheme adapted to the given situation is proposed and analyzed. Moreover, on top of the multilevel coding scheme, we employ signal shaping for the first time in the context of PUFs. In particular, trellis shaping is applied. By this, the coded modulation scheme can be perfectly matched to the PUF statistics. This is reflected by the results of conducted numerical simulations. High coding rates can be used, i.e., a large entropy per PUF node can be extracted, with very high reliabilities.

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Section: Multi-valued Physical Unclonable Functionsmentioning

confidence: 99%

Section: A Data and Error Model Of Ring Oscillator Pufsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…To that end, we interpret the readout process in PUFs as digital transmission schemes (cf. [5,Fig. 6]) and, based on that interpretation, coded modulation/signal shaping are applied.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coded Modulation and Shaping for Multivalued Physical Unclonable Functions

Fischer

Müelich

2022

IEEE Access

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A New Helper Data Scheme for Soft-Decision Decoding of Binary Physical Unclonable Functions

Fischer

Müelich

2022

IEEE Access

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Physical unclonable functions (PUFs) exploit randomness in the hardware for the derivation of cryptographic keys. In the literature, usually the readout is two-level quantized and hard-decision channel decoding is used to stabilize the extracted key. In this paper, we assess soft-decision decoding of binary PUFs. It is well known in the literature on channel coding that soft-decision decoding provides significant gains over hard-decision decoding since reliability information about the symbols is utilized. The PUF readout process is interpreted as digital transmission over a noisy channel, the respective capacity is calculated, and the optimum decoding metric is derived. In addition, we propose an augmented helper data scheme which is suited for soft-decision decoding. This scheme utilizes the fact that operations on the analog readout values are possible, opposed to operations on hard-decided binary symbols in classical PUFs. The security of the new scheme is proven and a possible realization is discussed. The performance is covered by numerical simulations and by applying the scheme to measurement data from FPGA implementations of ring oscillator PUFs.INDEX TERMS Physical unclonable functions, helper data scheme, channel capacity.

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