A Lightweight and High-Reliability Challenge Generation Strategy for APUF
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摘要: 仲裁物理不可克隆函数(APUF)作为轻量级安全原语，已广泛应用于身份认证和密钥生成等安全场景，但其响应一致性易受温度、电压等环境因素干扰，导致同一激励在不同条件下产生不一致响应，严重降低应用的可靠性。针对现有基于硬件改进和激励筛选的APUF可靠性提升方案普遍存在资源开销大、效率低的问题，该文提出一种基于延迟差异约束的激励生成策略(DCGS)，旨在提升资源受限场景下APUF的可靠性。该策略首先利用逻辑回归模型建模APUF的路径延迟特性，构建延迟权重向量；随后通过前缀比特初始化与逐位扩展机制构造激励，实时控制生成激励的延迟差介于设定阈值区间，最终直接生成具有高可靠性和高随机性的激励序列，无需额外候选激励筛选环节。仿真结果表明：DCGS生成的激励在实际应用面临的最大噪声强度下，可靠性仍保持100%，响应均匀性达50.02%，唯一性达50.46%，且生成1万条高可靠激励仅需0.017秒，在可靠性提升效果、分布均匀性、唯一性和生成效率四方面均优于基准方案。该策略无需增加硬件开销，能显著增强APUF在复杂环境中的适用性，适用于物联网节点、嵌入式设备等多类资源受限设备的双向认证和密钥生成场景。Abstract:
Objective The Arbiter Physical Unclonable Function (APUF) is a lightweight security primitive that has been widely adopted in identity authentication and key generation for resource-constrained devices. However, its response consistency is highly sensitive to environmental perturbations, leading to inconsistent responses for the same challenge under different conditions, severely undermining the reliability of APUF-based security systems. Existing reliability improvement schemes for APUF, which mainly rely on hardware modification or challenge screening, generally suffer from high resource overhead and low efficiency. To address the limitations of these existing solutions, a Delay-Constrained Challenge Generation Strategy (DCGS) is proposed to enhance APUF reliability without extra hardware overhead or screening-related inefficiencies. Methods The core of DCGS lies in modeling APUF path delay properties and constructing challenges with constrained delay differences to ensure response stability. First, a logistic regression (LR) model is established to characterize the relationship between APUF challenge bits and path delays. From the trained LR model, a delay weight vector is derived to quantify the contribution of each challenge bit to the overall path delay. Second, a two-stage challenge generation mechanism is designed to integrate delay constraint control: The first stage is prefix bit initialization, which generates distinct prefix sequences to establish a stable delay baseline for subsequent bit extension. The second stage is bit-wise extension, where each remaining challenge bit is dynamically determined based on the delay weight vector. During this extension process, the cumulative delay difference of the challenge is monitored in real time, ensuring it stays within a preset threshold range. Unlike traditional screening methods that post-process candidate challenges, DCGS directly generates stable challenges by design, eliminating the need for candidate pools and improving generation efficiency. Results and Discussions Performance evaluations of DCGS are conducted under varying noise intensities. At a noise intensity of 0.3 (maximum practical level), the reliability of DCGS-generated challenges remains at 100% ( Fig.2 ). In terms of generation efficiency, DCGS consumes only 0.017 seconds to generate 10,000 challenges (Table 4 ). For response uniformity, DCGS achieves a value of 50.02% (Table 4 ). For uniqueness, it reaches 50.46% (Table 4 ). These two key metrics are both close to the ideal theoretical value of 50%. Security analysis shows that the average bit entropy of DCGS-generated challenges is0.9807 (Fig.3 ), and the conditional entropy is0.9878 —only0.0023 lower than that of random challenges (0.9901 ).Conclusions This paper proposes a delay-constrained challenge generation strategy for APUF, aiming to address the problems of inconsistent responses, low generation efficiency, and high hardware resource consumption of traditional schemes in high-noise environments. By modeling the path delay characteristics of APUF using LR and integrating a prefix initialization mechanism with a bit-wise extension mechanism, the strategy ensures that the generated challenges meet the preset delay difference threshold range. Through this method, the DCGS achieves high reliability, high efficiency, and good response uniformity without increasing hardware overhead. Experimental results show that DCGS can effectively enhance the reliability of APUF in complex environments, providing strong technical support for secure applications in resource-constrained devices. -
1 算法1 基于延迟差约束的激励生成算法
输入 生成激励数量$ N $，激励位数$ n $，延迟权重向量$ \boldsymbol{w} $，阈值
$ T $，前缀长度$ P $，温度参数$ \tau $输出 激励集$ \boldsymbol{C}\in {\left\{0,1\right\}}^{N\times n} $ (1) 设定阈值区间$ {I}_{+}=[T,1.2T] $; ${I}_{-}=[-1.2T,-T] $;
${C\leftarrow 全零矩阵(N,n)} $(2) for $ i=1 $ to $ N $ do (3) $ (\mathrm{low}[i],\mathrm{high}[i]) \leftarrow (i是奇数？{\mathrm{I}}_{+}\colon {\mathrm{I}}_{-}) $ (4) $ 净延迟差S[i]\leftarrow 0;累积符号\text{tail}[i]\leftarrow +1 $ (5) end for (6) 生成$ N $个互异前缀，写入$ \boldsymbol{C} $的后$ P $位 # 计算前缀净延迟差 (8) for $ i=1 $ to $ N $ do (9) for $ j=n-1 $ to $ n-p $ do (10) if $ \boldsymbol{C}[i,j]=1 $ then $ \text{sign}\leftarrow -1 $ (11) else $ \text{sign}\leftarrow 1 $ (12) end if (13) $ \text{tail}\leftarrow \textit{tail}[\mathrm{i}]\cdot \text{sign;}S[i]\leftarrow S[i]\text{+tail}[i]\cdot \boldsymbol{w}[j] $ (14) end for (15) end for # 逐比特生成剩余激励位 (16) for $ j=n-p-1 $ to 0 do (17) for $ i=1 $ to $ N $ do (18) $ {S}_{0}\leftarrow S[i]+\mathrm{tail}[i]\cdot \boldsymbol{w}[j] $; ${S}_{1}\leftarrow S[i]-\mathrm{ta}i\mathrm{l}[\mathrm{i}]\cdot \boldsymbol{w}[j] $; ${e}_{0}\leftarrow dist({S}_{0},(low[i],high[i]) ) $; ${e}_{1}\leftarrow dist({S}_{1},(low[i],high[i]) ) $ # 根据输入的固定参数$ \tau $，选择采样方式 (19) if $ \tau =0 $ then (20) $ \mathrm{bit}\leftarrow ({e}_{0}\leq {e}_{1}) ?0\colon 1 $ (21) else (22) ${a}_{0}\leftarrow \exp (-{e}_{0}/\tau ) $; ${a}_{1}\leftarrow \exp (-{e}_{1}/\tau ) $; ${p}_{0}\leftarrow {a}_{0}/ $$({a}_{0}+{a}_{1}) $; $ \mu \leftarrow \left[0,1\right) $; $\mathrm{bit}\leftarrow (\mu \lt {p}_{0}) ?0\colon 1 $ (23) end if (24) if $ \mathrm{bit}=0 $ then (25) $ \boldsymbol{C}[i,j]\leftarrow 0;S[i]\leftarrow {S}_{0} $ (26) else $ \boldsymbol{C}[i,j]\leftarrow 1;S[i]\leftarrow {S}_{1};\mathrm{tail}[i]\leftarrow -\mathrm{ta}i\mathrm{l}[\mathrm{i}] $ (27) end if (28) end for (29) end for # 混淆N个激励的排列顺序，不改变激励本身的比特组合 (30) $ \boldsymbol{C}\leftarrow \mathrm{Shuffle}(\boldsymbol{C}) $ (31) return $ \boldsymbol{C} $ 
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表 2 不同噪声下的可靠性
$ \lambda $ 可靠性(%) 0.00 100 0.05 90.87 0.10 82.74 0.20 64.29 0.30 50.08 0.60 17.92 0.80 8.72 1.00 3.93
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表 3 不同参数配置对性能的影响
目标翻转概率 阈值(T) 温度($ \tau $) 可靠性(%) 熵 10–1 14.11 0 70.29 0.7252 10–3 20.74 0 99.54 0.7527 10–6 28.10 0 100.00 0.7675 10–6 28.10 1 100.00 0.9172 10–6 28.10 2 99.99 0.9807 10–6 28.10 3 96.09 0.9898
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