一種基于動態(tài)環(huán)形振蕩器物理不可克隆函數(shù)統(tǒng)計模型的頻率排序算法
doi: 10.11999/JEIT180405
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解放軍信息工程大學 ??鄭州 ??450001
Frequency Sorting Algorithm Based on Dynamic Ring Oscillator Physical Unclonable Function Statistical Model
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The PLA Information Engineering University, Zhengzhou 450001, China
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摘要:
針對現(xiàn)有環(huán)形振蕩器物理不可克隆函數(shù)(ROPUF)設計存在的可靠性和唯一性不高，導致在應用時安全性較差的問題，該文提出面向ROPUF的統(tǒng)計模型，定量分析了可靠性和唯一性的影響因素，發(fā)現(xiàn)增大延遲差能夠提高可靠性，減小環(huán)形振蕩器(RO)單元間的工藝差異可以提高唯一性。根據(jù)該模型結論，設計了基于mesh拓撲結構的動態(tài)RO單元，結合RO陣列頻率分布特性，設計了一種新的頻率排序算法，以增大延遲差和減小RO單元的工藝差異，從而提高ROPUF的可靠性和唯一性。結果表明，與其他改進設計的ROPUF相比，所提設計的可靠性和唯一性具有顯著優(yōu)勢，可達到99.642%和49.1%，且受溫度變化的影響最小。安全性分析證明，該文的設計具有很強的抗建模攻擊能力。
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關鍵詞:
- 信息安全 /
- 物理不可克隆函數(shù) /
- 統(tǒng)計模型 /
- 頻率排序
Abstract:The existing Ring Oscillator (RO) Physical Unclonable Function (ROPUF) design has low reliability and uniqueness, resulting in poor application security. A statistical model for ROPUF is proposed, the factors of reliability and uniqueness are quantitatively analyzed, it is found that the larger delay difference can improve the reliability, and the lower process difference between RO units can improve the uniqueness. According to the conclusion of the model, a dynamic RO unit is designed based on the mesh topological structure. In combination with the frequency distribution characteristics of the RO array, a new frequency sorting algorithm is designed to increase the delay difference and reduce the process variation of the RO unit, thereby improving the reliability and uniqueness of ROPUF. The results show that compared with other improved ROPUF designs, the reliability and uniqueness of the proposed design has significant advantages, which can reach 99.642% and 49.1%, and temperature changes affect minimally them. It is verified by security analysis that the proposed design has strong anti-modeling attack capabilities.
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表 2 頻率比較結果的概率分布
RO級數(shù) 3 5 7 9 概率 3 0/1 1 1 1 ${\rho _{\rm{A}}}$ 5 0 0/1 1 1 ${\rho _{\rm{B}}}$ 7 0 0 0/1 1 ${\rho _{\rm{C}}}$ 9 0 0 0 0/1 ${\rho _{\rm{D}}}$ 概率 ${\rho _{\rm{A}}}$ ${\rho _{\rm{B}}}$ ${\rho _{\rm{C}}}$ ${\rho _{\rm{D}}}$ 100% 
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表 3 頻率排序算法偽代碼
算法 1 頻率排序算法(FSA) (1) for C determining CLB-X do (2) $F = \{ f(x,1),f(x,2), ·\!·\!· ,f(x,N)\} $; (3) for i=1 to N do (4) ${Z_i} = {\rm COUNTER}(f(x,i))$; (5) end for (6) $\bar Z = {{\left( {{Z_1} + {Z_2} + ·\!·\!· + {Z_N}} \right)} / N}$; (7) for i=1 to N do (8) ${d_i} = \left| {{Z_i} - \bar Z} \right|$; (9) end for (10) if (x>y) then (11) gt(x, y)=1 (12) else (13) gt(x, y)=0 (14) end if (15) for k=1 to N–1 do (16) for j=1 to k do (17) S1=0 (18) ${L_k} = {S_j} + gt\left( {{d_{k + 1}},{d_j}} \right)$; (19) end for (20) end for (21) $R = {\rm Gray}\left( {{L_1}} \right){\rm{|}}|{\rm Gray}\left( {{L_2}} \right){\rm{|}}| ·\!·\!· |{\rm{|}}{\rm Gray}\left( {{L_{N - 1}}} \right)$; (22) end for (23) return (R)
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表 5 RO單元資源利用效率對比
指標 傳統(tǒng)的ROPUF 可配置ROPUF D-ROPUF 本文的ROPUF CLB數(shù)量 2 1 1 2 Slice數(shù)量 5 3 4 4 LUT數(shù)量 6 6 8 15 RO單元可產生頻率數(shù) 1 8 4 18 抗建模攻擊能力 傳統(tǒng)的ROPUF<D-ROPUF<可配置ROPUF<本文的ROPUF
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表 6 破解不同規(guī)格PUF所需攻擊次數(shù)的比較
t N Q 2 8 1.04×1011 18 8 1.35×1075 36 8 2.47×10176 18 16 1.99×10258 36 16 3.85×10502
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