基于非正交离散变换的物理不可克隆函数可靠性提升算法

doi:10.11772/j.issn.1001-9081.2023070936

《计算机应用》唯一官方网站 ›› 2024, Vol. 44 ›› Issue (7): 2116-2122.DOI: 10.11772/j.issn.1001-9081.2023070936

基于非正交离散变换的物理不可克隆函数可靠性提升算法

李诗扬, 倪少杰, 邓丁(), 陈雷, 林红磊

国防科技大学电子科学学院，长沙 410073

收稿日期:2023-07-14 修回日期:2023-09-12 接受日期:2023-09-20 发布日期:2023-10-26 出版日期:2024-07-10
通讯作者: 邓丁
作者简介:李诗扬（1998—），男，辽宁丹东人，硕士研究生，主要研究方向：硬件安全；
倪少杰（1978—），男，山东莱阳人，研究员，博士，主要研究方向：卫星导航、卫星载荷与导航终端设计；
陈雷（1987—），男，福建福州人，副研究员，博士，主要研究方向：导航时空系统设计、芯片安全；
林红磊（1989—），男，河南长垣人，副研究员，博士，主要研究方向：星基导航与定位。
第一联系人：邓丁（1993—），男，四川遂宁人，讲师，博士，主要研究方向：硬件安全、芯片设计；
基金资助:
国家自然科学基金资助项目(U20A0193);湖南省科技创新计划项目(2021RC3073)

Reliability enhancement algorithm for physical unclonable function based on non-orthogonal discrete transform

Shiyang LI, Shaojie NI, Ding DENG(), Lei CHEN, Honglei LIN

College of Electronic Science and Technology，National University of Defense Technology，Changsha Hunan 410073，China

Received:2023-07-14 Revised:2023-09-12 Accepted:2023-09-20 Online:2023-10-26 Published:2024-07-10
Contact: Ding DENG
About author:LI Shiyang， born in 1998， M. S. candidate. His research interests include hardware security.
NI Shaojie， born in 1978， Ph. D.， research fellow. His research interests include satellite navigation， satellite payload and navigation terminal design.
CHEN Lei， born in 1987， Ph. D.， associate research fellow. His research interests include navigation spatiotemporal system design， IC security.
LIN Honglei， born in 1989， Ph. D.， associate research fellow. His research interests include satellite based navigation and positioning.
First author contact:DENG Ding， born in 1993， Ph. D.， lecturer. His research interests include hardware security， IC design.
Supported by:
National Natural Science Foundation of China(U20A0193);Science and Technology Innovation Program of Hunan Province(2021RC3073)

摘要/Abstract

摘要：

为了解决物理不可克隆函数（PUF）受外部环境和自身老化因素影响存在响应不稳定的问题，提出基于非正交离散（NOD）变换的PUF可靠性提升算法。首先，设计了一种重排序混淆器，将随机种子向量及PUF响应经重排序混淆器迭代处理后得到非正交混淆矩阵与混淆响应矩阵的内积，据此建立NOD谱，有效缓解了因PUF本身均匀性不足而产生偏向性密钥的问题；随后，通过分区编解码策略，赋予NOD谱一定的波动容错能力，将不稳定响应的影响限制在有限的范围，从而显著提高最终响应的可靠性。所提算法相较于传统基于纠错码的方法，需要的帮助数据更少。基于SRAM-XMC数据集进行实验，所提算法在对2 949 120组64位响应进行101次重复实验过程中平均可靠性达到99.97%，唯一性达到49.92%，均匀性达到50.61%。实验结果表明，所提算法能够在保证PUF响应均匀性与唯一性的同时有效提高可靠性。

关键词: 非正交离散变换, 物理不可克隆函数, 可靠性, 分区编解码, 唯一性, 布尔函数

Abstract:

A reliability enhancement algorithm for Physical Unclonable Function （PUF） was proposed to address the instability of PUF’s response caused by external and internal factors. The proposed algorithm is based on the Non-Orthogonal Discrete （NOD） transform. Firstly， a reorder mixer was designed to iteratively process the random seed vector and PUF response， resulting in the inner product of the non-orthogonal confusion matrix and the response confusion matrix， upon which the NOD spectrum was established. The algorithm effectively solved the bias of key caused by insufficient uniformity of PUF. Then， the partition encoding and decoding strategy enabled the NOD spectrum to have the ability to tolerate certain errors， significantly improving the reliability of the final response by limiting the impact of unstable responses to a limited range. Compared to traditional error correcting code-based methods， the proposed algorithm requires fewer auxiliary data. Experimental results on SRAM-XMC dataset show that， during 101 repeated experiments with 2 949 120 sets of 64-bit responses， the average reliability of the proposed algorithm reaches 99.97%， the uniqueness achieves 49.92%， and the uniformity reaches 50.61%. The experimental results demonstrate that the proposed algorithm can effectively improve reliability while ensuring uniformity and uniqueness of PUF responses.

Key words: Non-Orthogonal Discrete (NOD) transform, Physical Unclonable Function (PUF), reliability, partition encoding and decoding, uniqueness, Boolean function

中图分类号:

TP302.8

李诗扬, 倪少杰, 邓丁, 陈雷, 林红磊. 基于非正交离散变换的物理不可克隆函数可靠性提升算法[J]. 计算机应用, 2024, 44(7): 2116-2122.

Shiyang LI, Shaojie NI, Ding DENG, Lei CHEN, Honglei LIN. Reliability enhancement algorithm for physical unclonable function based on non-orthogonal discrete transform[J]. Journal of Computer Applications, 2024, 44(7): 2116-2122.

图/表 11

图1 出厂测试阶段流程

Fig. 1 Flowchart of factory testing phase

图2 分类编码示意图

Fig. 2 Schematic diagram of classification coding

图3 用户使用阶段流程

Fig. 3 Flowchart of user usage phase

图4 分类解码示意图

Fig. 4 Schematic diagram of classification decoding

表1 预筛选后不稳定位概率分布

Tab. 1 Probability distribution of unstable bits after pre-screening

不稳定位个数	0	1	2	3
概率/%	56.35	34.25	8.37	1.03

图5 阈值分区示意图

Fig. 5 Schematic diagram of partitioning through thresholds

图6 可靠性提升效果

Fig. 6 Reliability improvement effects

图7 均匀性实验结果

Fig. 7 Experimental results of uniformity

图8 新生成响应单比特熵值实验结果

Fig. 8 Experimental results of entropy of each bit for new response

图9 唯一性实验结果

Fig. 9 Experimental results of uniqueness

表2 本文算法与其他可靠性提升方案比较

Tab. 2 Comparison of proposed algorithm with other reliability improvement schemes

对比算法	原生可靠性/%	处理后平均可靠性/%	可靠性提升方案	掩码掩蔽率/%	通用性	唯一性/%
本文算法	96.07	99.97	掩码、分类编解码	13.00	所有PUF	49.92
JSSC 23^［21］	96.80	100.00	掩码、新型PUF结构、检测与恢复算法	33.00	创新结构	49.95
Electronics 22^［22］	90.00	100.00	卷积滤波	—	SRAM PUF	50.50
ISSCC 20^［15］	91.38	99.91	掩码、空间多数表决、纠错码	25.00	创新结构	49.78
JSSC 22^［23］	97.30	100.00	掩码、时间多数表决	3.64	创新结构	49.63

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基于非正交离散变换的物理不可克隆函数可靠性提升算法

Reliability enhancement algorithm for physical unclonable function based on non-orthogonal discrete transform

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