Physical Unclonable Functions (PUFs) are widely used in key generation, with each PUF cell typically producing one bit of data. To enable the extraction of longer keys, a new non-binary response generation scheme based on the one-probability of PUF bits is proposed. Instead of using PUF bits directly as keys, non-binary responses are first derived by comparing the one-frequency of PUF bits with thresholds that evenly divide the area under the probability density function of the one-probability distribution and then converted to binary keys. To simplify the calculation of these thresholds, a re-scaling process is proposed and the beta distribution is used to model the one-probability distribution. Our FPGA implementation results demonstrate a significant increase in effective key length as opposed to previous works. Finally, we estimate the error rates and biases of the generated keys, and confirm the feasibility of the proposed key generation scheme.

翻译：物理不可克隆函数（PUF）被广泛用于密钥生成，每个PUF单元通常产生一位数据。为了提取更长的密钥，本文提出了一种基于PUF位"1"概率的非二进制响应生成新方案。该方案不直接将PUF位用作密钥，而是首先通过比较PUF位的"1"频率与阈值来推导非二进制响应——这些阈值将"1"概率分布的概率密度函数曲线下面积均匀划分——随后将其转换为二进制密钥。为简化阈值计算，本文提出了重缩放处理过程，并采用Beta分布对"1"概率分布进行建模。我们的FPGA实现结果表明，相较于先前工作，有效密钥长度显著增加。最后，我们评估了生成密钥的误码率与偏差，并验证了所提密钥生成方案的可行性。