Controlled Physical Unclonable Function Research Based on Sensitivity Confusion Mechanism
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The Information Engineering University, Zhengzhou 450001, China
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摘要: 為了克服物理不可克隆函數(shù)(PUF)面對(duì)建模攻擊的脆弱性，該文提出一種基于敏感度混淆機(jī)制的控制型PUF架構(gòu)。根據(jù)PUF的布爾函數(shù)定義及Walsh譜理論，推導(dǎo)出各個(gè)激勵(lì)位具有不同敏感度，分析并歸納了與混淆值位寬奇偶性有關(guān)的位置選取規(guī)則。利用該規(guī)則指導(dǎo)了多位寬混淆算法(MWCA)的設(shè)計(jì)，構(gòu)建了具有高安全性的控制型PUF架構(gòu)。將基礎(chǔ)PUF結(jié)構(gòu)作為控制型PUF的防護(hù)對(duì)象進(jìn)行實(shí)驗(yàn)評(píng)估，發(fā)現(xiàn)基于敏感度混淆機(jī)制的控制型PUF所產(chǎn)生的響應(yīng)具有較好的隨機(jī)性。采用邏輯回歸算法對(duì)不同PUF結(jié)構(gòu)進(jìn)行建模攻擊，實(shí)驗(yàn)結(jié)果表明，相比基本ROPUF、仲裁器PUF以及基于隨機(jī)混淆機(jī)制的OB-PUF，基于敏感度混淆機(jī)制的控制型PUF能夠顯著提高PUF的抗建模攻擊能力。
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關(guān)鍵詞:
- 信息安全 /
- 機(jī)器學(xué)習(xí) /
- 布爾函數(shù) /
- 敏感度
Abstract: In order to overcome the vulnerability of Physical Unclonable Function (PUF) to modeling attacks, a controlled PUF architecture based on sensitivity confusion mechanism is proposed. According to the Boolean function definition of PUF and Walsh spectrum theory, it is derived that each excitation bit has different sensitivity, and the position selection rules related to the parity of the confound value bit width are analyzed and summarized. This rule guides the design of the Multi-bit Wide Confusion Algorithm (MWCA) and constructs a controlled PUF architecture with high security. The basic PUF structure is evaluated as a protective object of the controlled PUF. It is found that the response generated by the controlled PUF based on the sensitivity confusion mechanism has better randomness. Logistic regression algorithm is used to model different PUF attack. The experimental results show that compared with the basic ROPUF, the arbiter PUF and the OB-PUF based on the random confusion mechanism, the controlled PUF based on the sensitivity confusion mechanism can significantly improve the PUF resistance capabilities for modeling attack.-
Key words:
- Information security /
- Machine learning /
- Boolean function /
- Sensitivity information
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圖 3
${N_{{\rm{OB}}}} = {\rm{2}}$ 時(shí)概率期望${E_{\Pr }}\left( {\rm{{Aa,Ta,Sa}}} \right)$ 的分布圖
圖 4
${N_{{\rm{OB}}}} = {\rm{3}}$ 時(shí)概率期望${E_{\Pr }}\left( {\rm{{Aa,Ta,Sa}}} \right)$ 的分布圖表 1
${N_{{\rm{OB}}}} = {\rm{1}},2,{\rm{3}},{\rm{4}}$ 時(shí)混淆值位置選擇所有組合情況NOB (Aa,Ta,Sa) 1 (1,0,0);(0,1,0);(0,0,1) 2 (1,1,0);(1,0,1);(0,1,1);(2,0,0);(0,2,0);(0,0,2) 3 (1,1,1);(2,1,0);(2,0,1);(1,2,0);(0,2,1);(1,0,2);(0,1,2);
(3,0,0);(0,3,0);(0,0,3)4 (2,1,1);(1,2,1);(1,1,2);(2,2,0);(2,0,2);(0,2,2);(3,1,0);(3,0,1);
(1,3,0);(0,3,1);(1,0,3);(0,1,3);(4,0,0);(0,4,0);(0,0,4)
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表 2 MWCA的具體算法
輸入：混淆激勵(lì)集合${C_{\rm OB}} = \left\{ {c_{\rm OB}^k|k \in \left\{ {1,2, ·\!·\!· ,\sum\nolimits_{i = 1}^t {{2^{N - i}}} } \right\}} \right\}; $ 混淆值集合$Y = \left\{ {{y_k}|k \in \left\{ {1,2, ·\!·\!· ,\sum\nolimits_{i = 1}^t {{2^{N - i}}} } \right\}} \right\} $ 過(guò)程： $(1)\;{\rm for}\;\forall k \in \left\{ {1,2, ·\!·\!· ,\sum\nolimits_{i = 1}^t {{2^{N - i}}} } \right\}{\rm do} $ $(2)\;{\text{輸入混淆激勵(lì)集合}}c_{\rm OB}^k = \left\{ {{c_1},{c_2}, ·\!·\!· ,{c_t}} \right\}\text{、}\ {\text{混淆值}}{y_k}{\text{和標(biāo)識(shí)值}}{a_k} ; $ $(3)\;{\rm if}\;{a_k} = 1\;{\rm then} $ $(4)\;{\text{調(diào)用位置選擇策略}}{P_k} ;{\text{產(chǎn)生完整激勵(lì)}}{C_k}{\rm{ = }}{P_k}(c_{{\rm{OB}}}^k,{y_k}) ;{\rm return} $ $(5)\;{\rm else} $ $(6)\;{\text{計(jì)算}}{{ r = ({N} - t) }}\% 2 ; $ $(7)\;\rm end\;if$ $(8)\;{\rm if}\;r = 0\;{\rm then}$ $(9)\;{\text{調(diào)用偶數(shù)規(guī)則}}{\rm{Rule}}\_{\rm E},{\text{生成位置選擇策略}}{P_k},{a_k} = 1;$ $(10)\;\rm else $ $(11)\;{\text{調(diào)用奇數(shù)規(guī)則}}{\rm{Rule}}\_{\rm O},{\text{生成位置選擇策略}}{P_k},{a_k} = 1;$ $(12)\;\rm end\;if $ $(13)\;{\text{存儲(chǔ)標(biāo)識(shí)值}}{a_k}{\text{和策略}}{P_k} ,{\text{用于之后激勵(lì)混淆步驟的判斷依據(jù)}} ;$ (14) 按照策略將混淆值插入混淆激勵(lì)$c_{{\rm{OB}}}^k,$產(chǎn)生完整激勵(lì) ${C_k}{\rm{ = }}{P_k}(c_{{\rm{OB}}}^k,{y_k}) ;\rm return$ $ (15) \;\rm end\;for$ 輸出：完整激勵(lì)集合${C_f} = {\rm{\{ }}{C_k}|k \in {\rm{\{ }}1,2, ·\!·\!· ,\sum\nolimits_{i = 1}^t {{2^{N - i}}} {\rm{\} \} }}。$
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表 4 NIST隨機(jī)數(shù)測(cè)試結(jié)果
測(cè)試項(xiàng)目 基本ROPUF[10] 本文 P_value 結(jié)果 P_value 結(jié)果 頻率檢驗(yàn) 0.000003 失敗 0.829896 通過(guò) 塊內(nèi)頻數(shù)檢驗(yàn) 0.050764 通過(guò) 0.580358 通過(guò) 向前累加和檢驗(yàn) 0.000000 失敗 0.502594 通過(guò) 向后累加和檢驗(yàn) 0.000000 失敗 0.347179 通過(guò) 游程檢驗(yàn) 0.302788 通過(guò) 0.329404 通過(guò) 塊內(nèi)最長(zhǎng)游程檢驗(yàn) 0.000062 失敗 0.024892 通過(guò) 近似熵檢驗(yàn) 0.000001 失敗 0.693147 通過(guò) 向前序列檢驗(yàn) 0.070160 通過(guò) 0.024892 通過(guò) 向后序列檢驗(yàn) 0.192277 通過(guò) 0.756264 通過(guò)
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表 5 不同PUF結(jié)構(gòu)的攻擊結(jié)果對(duì)比
PUF類型 訓(xùn)練集數(shù)量 攻擊時(shí)間(s) 預(yù)測(cè)成功率(%) OB-PUF(1) 4400 26 87.6 OB-PUF(2) 5200 30 84.4 OB-PUF(3) 6000 62 73.1 OB-PUF(4) 8000 128 69.8 基本ROPUF 5200 8 99.5 控制型ROPUF 7200 262 53.4 仲裁器PUF 4800 15 93.9 控制型APUF 6500 187 67.2
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