Frequency Sorting Algorithm Based on Dynamic Ring Oscillator Physical Unclonable Function Statistical Model
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摘要:
针对现有环形振荡器物理不可克隆函数(ROPUF)设计存在的可靠性和唯一性不高，导致在应用时安全性较差的问题，该文提出面向ROPUF的统计模型，定量分析了可靠性和唯一性的影响因素，发现增大延迟差能够提高可靠性，减小环形振荡器(RO)单元间的工艺差异可以提高唯一性。根据该模型结论，设计了基于mesh拓扑结构的动态RO单元，结合RO阵列频率分布特性，设计了一种新的频率排序算法，以增大延迟差和减小RO单元的工艺差异，从而提高ROPUF的可靠性和唯一性。结果表明，与其他改进设计的ROPUF相比，所提设计的可靠性和唯一性具有显著优势，可达到99.642%和49.1%，且受温度变化的影响最小。安全性分析证明，该文的设计具有很强的抗建模攻击能力。
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 频率比较结果的概率分布
RO级数 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 频率排序算法伪代码
算法 1 频率排序算法(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单元资源利用效率对比
指标 传统的ROPUF 可配置ROPUF D-ROPUF 本文的ROPUF CLB数量 2 1 1 2 Slice数量 5 3 4 4 LUT数量 6 6 8 15 RO单元可产生频率数 1 8 4 18 抗建模攻击能力 传统的ROPUF<D-ROPUF<可配置ROPUF<本文的ROPUF
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表 6 破解不同规格PUF所需攻击次数的比较
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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