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.

中文翻译：

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多值物理不可克隆函数的多级编码方案

物理不可克隆功能 (PUF) 通过利用由于物理项目制造过程中的不可控变化而在集成电路中固有地发生的随机性来产生响应。PUF 生成二进制响应是常见的做法。最近，有人提出从高阶字母表中提取符号以增加最终响应的长度。在本文中，多值 PUF (MV-PUF) 概念的编码源自与数字通信中的脉冲幅度调制的类比。为此，基于 ROPUF 测量数据，我们用合适的加性高斯白噪声模型替换了经典的二进制对称信道模型。因此，硬输入二进制信道编码方案被编码调制方法取代，利用软输出。此外，辅助数据的功能（稳定嘈杂的 PUF 响应所需）被转移到多值情况。通过将设计的方法应用于可用的测量数据，我们最终表明将模拟 PUF 输出想象为 百万美元 AWGN 信道上观察到的 -ary 幅移键控符号，每个响应符号的提取熵和最终密钥的可靠性都可以增加。