A well-known problem when using Physical Unclonable Functions for secret key generation and storage, is the instability of PUF responses due to environmental conditions like temperature variations. Using Ring Oscillator PUFs (RO-PUFs), a response bit is usually derived based on the comparison of a RO frequency with either a threshold or another RO frequency. Especially for multi-valued PUFs it is of importance to decrease RO frequency errors before digitization. Otherwise, these errors can result in a huge amount of bit-flips. To counteract environmental influence in the reproduction phase, we propose to map a frequency, which might be remeasured under a temperature condition different from initialization, closer to the initial frequency by using a method based on polynomial interpolation. This paper presents how such an approach can decrease errors in multi-valued responses and evaluates the error based on the used polynomial order and thus complexity.

Physical unclonable functions (PUFs) produce responses by exploiting randomness that intrinsically occurs in integrated circuits due to uncontrollable variations in the manufacturing process of physical items. It is common practice that PUFs generate binary responses. Recently, it has been proposed to extract symbols from a higher-order alphabet in order to increase the length of the final response. In this paper, coding for this concept of multi-valued PUFs (MV-PUFs) is derived from the analogy to pulse-amplitude modulation in digital communications. To that end, based on ROPUF measurement data, we replace the classical binary symmetric channel model by a suited additive white Gaussian noise model. Consequently, the hard-input binary channel coding scheme is replaced by methods from coded modulation, utilizing the soft output. In addition, the functionality of helper data, which are required to stabilize noisy PUF responses, is transferred to the multi-valued case. By applying the designed methods to the available measurement data we eventually show that imagining the analog PUF output as$M$-ary amplitude-shift keying symbols observed over an AWGN channel, both the extracted entropy per response symbol and the reliability of the final key can be increased.

Physical Unclonable Functions (PUFs) offer the possibility to produce unique fingerprints for integrated circuits. As raw PUF responses are affected by noise, some post-processing steps are necessary. We present a coding chain test framework for PUFs on Field Programmable Gate Arrays. The framework allows easy exchange, evaluation and comparison of different PUF implementations, coding algorithms and other chain modules. For a testing framework, the execution time of the evaluated algorithm is a bottleneck, since a huge amount of runs are supposed to be done. Hence, we additionally present a new type of Reed-Muller decoder hardware architecture using parallel modules to speed up the decoding process. The decoding time could be decreased by 95% in comparison to existing implementations at the cost of 41 times higher slice count.

Gabidulin codes, originally defined over finite fields, are an important class of rank metric codes with various applications. Recently, their definition was generalized to certain fields of characteristic zero and a Welch-Berlekamp like algorithm with complexity O(n3) was given. We propose a new application of Gabidulin codes over infinite fields: low-rank matrix recovery. Also, an alternative decoding approach is presented based on a Gao type key equation, reducing the complexity to at least O(n2). This method immediately connects the decoding problem to well-studied problems, which have been investigated in terms of coefficient growth and numerical stability.