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，无须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 s，在可靠性提升效果、分布均匀性、唯一性和生成效率4方面均优于基准方案。该策略无须增加硬件开销，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。
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关键词:
- 仲裁物理不可克隆函数 /
- 可靠性提升 /
- 机器学习 /
- 生成策略
Abstract:Objective The Arbiter Physical Unclonable Function (APUF) is a lightweight security primitive widely used for identity authentication and key generation in resource-constrained devices. However, its response consistency is highly sensitive to environmental perturbations. The same challenge may therefore produce inconsistent responses under different conditions, which reduces the reliability of APUF-based security systems. Existing reliability improvement schemes mainly rely on hardware modification or challenge screening. These schemes often require high resource overhead and have low efficiency. To address these limitations, a Delay-constrained Challenge Generation Strategy (DCGS) is proposed to improve APUF reliability without additional hardware overhead or inefficient candidate screening. Methods DCGS models APUF path-delay characteristics and constructs challenges with constrained delay differences to ensure response stability. First, a Logistic Regression (LR) model is established to characterize the relationship between challenge bits and path delays. A delay-weight vector is then derived from the trained LR model to quantify the contribution of each challenge bit to the overall path delay. Second, a two-stage challenge generation mechanism is designed for delay-constraint control. In the first stage, prefix-bit initialization generates different prefix sequences to establish a delay baseline for subsequent bitwise extension. In the second stage, bitwise extension dynamically determines each remaining challenge bit according to the delay-weight vector. During this process, the cumulative delay difference of each challenge is monitored in real time and maintained within a preset delay-difference threshold range. Unlike conventional screening methods that post-process candidate challenges, DCGS directly generates stable challenges by design. This design removes the need for candidate challenge pools and improves generation efficiency. Results and Discussions DCGS is evaluated under different noise intensities. At a noise intensity of 0.3, which represents the maximum practical noise level, the reliability of DCGS-generated challenges remains 100% ( Fig. 2 ). For generation efficiency, DCGS requires only 0.017 s to generate 10,000 challenges (Table 4 ). The response uniformity reaches 50.02% (Table 4 ), and the uniqueness reaches 50.46% (Table 4 ). Both metrics are close to the ideal theoretical value of 50%. The security analysis shows that the average bit entropy of DCGS-generated challenges is 0.980 7 (Fig. 3 ). The conditional entropy is 0.987 8, only 0.002 3 lower than that of random challenges (0.990 1).Conclusions This paper proposes DCGS for APUF to address inconsistent responses, low generation efficiency, and high hardware resource consumption in traditional schemes under high-noise conditions. By modeling path-delay characteristics with LR and combining prefix-bit initialization with bitwise extension, the proposed strategy ensures that the generated challenges satisfy the preset delay-difference threshold range. DCGS achieves high reliability, high efficiency, and good response uniformity without increasing hardware overhead. Experimental results show that DCGS improves APUF reliability in complex environments and supports secure applications in resource-constrained devices. -
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] $;
${\boldsymbol{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 {\bf{tail}}[\mathrm{i}]\cdot \text{sign;}\boldsymbol{S}[i]\leftarrow \boldsymbol{S}[i]+\bf{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 \boldsymbol{S}[i]+\bf{tail}[i]\cdot \boldsymbol{w}[j] $; ${S}_{1}\leftarrow \boldsymbol{S}[i]-\bf{tai}\bf{l}[\mathrm{i}]\cdot \boldsymbol{w}[j] $; ${e}_{0}\leftarrow \text{dist}({S}_{0},(\bf{low}[i],\bf{high}[i]) ) $; ${e}_{1}\leftarrow \text{dist}({S}_{1},(\bf{low}[i],\bf{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;\boldsymbol{S}[i]\leftarrow {S}_{0} $ (26) else $ \boldsymbol{C}[i,j]\leftarrow 1;\boldsymbol{S}[i]\leftarrow {S}_{1};\bf{tail}[i]\leftarrow -\bf{tai}\bf{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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