针对静态随机存取存储器物理不可克隆功能密钥提取的优化方法研究

姜冬梅; 唐旭升; 李冰; 张清宇; 何卫国

doi:10.11999/JEIT250551

针对静态随机存取存储器物理不可克隆功能密钥提取的优化方法研究

doi: 10.11999/JEIT250551 cstr: 32379.14.JEIT250551

姜冬梅^{1, 3, ,},
唐旭升¹,
李冰¹,
张清宇²,
何卫国³

1.
东南大学网络空间安全学院南京 210000
2.
电子科技大学成都 610000
3.
三零嘉微电子有限公司成都 610000

详细信息

作者简介:
姜冬梅：女，高级工程师，研究方向为高性能安全芯片、高速接口技术等

唐旭升：男，研究生导师，研究方向为无线信息网络安全，芯片功能安全，电磁空间态势感知，无线信号处理，集成电路系统设计等

李冰：男，教授，博士生导师，研究方向为数模混合集成电路设计、信息安全和云计算等

张清宇：男，博士生，研究方向为数字电路设计、高性能计算、剩余数系统以及密码算法的硬件加速

何卫国：男，研究员，博士生导师，研究方向为高性能安全芯片、集成电路等

通讯作者:
姜冬梅　jiangdm20014007@163.com

中图分类号: TN918.91; TP309
计量
- 文章访问数: 29
- HTML全文浏览量: 12
- PDF下载量: 7
- 被引次数: 0
出版历程
- 收稿日期: 2025-06-16
- 修回日期: 2025-09-16
- 网络出版日期: 2025-09-19

Research on Optimization Methods for Static Random-Access Memory–Physical Unclonable Function Key Extraction

1.
School of Cyberspace Security, Southeast University, Nanjing 210000, China
2.
University of Electronic Science and Technology, Chengdu 610000, China
3.
Sanlingjia Microelectronics Co.Ltd, Chengdu 610000, China

摘要

摘要: 该文提出一种适应于比特筛选的静态随机存取存储器物理不可克隆功能(SRAM PUF)密钥提取新方案，使用SRAM的噪声单元生成密钥，使用SRAM的稳定单元重建PUF。该方案利用噪声单元的高熵特性，提高密钥熵值；基于稳定单元的低误码率优势，构建轻量级编解码体系，该方案的运算复杂度比方案2减少40%，比方案3减少98.9%，比方案4减少99.12%；通过实验数据统计出PUF单元变化率，并推导出PUF单元变化率与密钥重构成功率的关系，该方案密钥重构失败概率极低(1.4876E-9)，比方案2和方案3降低4个数量级，比方案5降低1个数量级。最后，实验数据表明1 024字节的 SRAM 空间可提取128位满熵值密钥。
- 物理不可克隆函数 /
- 稳定单元选择 /
- 密钥提取 /
- 高熵值
Abstract: Objective Non-Volatile Memory (NVM) storage keys are exposed to physical attacks, and most lightweight Internet-of-Things (IoT) devices cannot deploy costly protection. A Physical Unclonable Function (PUF) offers a practical defense. However, Static Random-Access Memory PUFs (SRAM-PUFs) used as key generators exhibit environmental sensitivity that degrades stability. Therefore, optimization methods for SRAM-PUF–based key extraction fall into three main categories: (1) circuit-level enhancements that modify the SRAM cell to strengthen its inherent 0/1 bias; (2) cell selection methods that identify and retain only stable cells through dedicated algorithms; and (3) fuzzy-extractor schemes tailored to SRAM-PUFs that correct residual noise to yield reproducible cryptographic keys. Methods The selection of SRAM cells can markedly enhance bit stability. However, although reducing the complexity of Error-Correcting Code (ECC) encoding and decoding, this approach requires consuming a large number of stable cells to satisfy key entropy requirements, which in turn increases ECC code length. To address this contradiction, this paper proposes a new key extraction scheme (Figure 2). In the proposed method, SRAM bits are divided into stable and noisy categories. The high entropy of noisy bits is leveraged for key generation: noisy bits are hashed to produce entropy-rich values, whereas stable bits with a low bit error rate are used to generate PUF responses. In the registration stage, the synthesized key is rearranged to form m vectors (R₁,R₂,…,Rm)according to m different rules. These m vectors are then combined into a new vector R . A repetition code of length 2t+1 (able to correct t errors) is applied to R to generate a codeword C . The codeword C is XORed with the PUF response to obtain helper data w, which is stored in NVM. In the reconstruction stage, w is XORed with a new PUF response to obtain C ′. Due to the repetition coding applied during registration, decoding is performed using a majority decision rule with a threshold of t+1. The decoding result R ' is reshaped into a matrix D with m rows and x columns, followed by reverse interleaving based on the rules used in registration. A majority decision is then executed independently for each column, with a decision threshold of m/2+1. The recovered key is output as the final result. Results and Discussions SRAM. Tests at −40 °C, 25 °C, and 85 °C show that the proposed bit-selection algorithm reduces the bit-change rate of SRAM-PUFs, with the number of screenings inversely proportional to the average change rate. The bit-change rate is highest at elevated temperatures. After 20 screenings, the average change rate at 85 °C decreases from 0.14 to 0.07, and after 80 screenings, it further decreases to 0.06. A quantitative analysis of error-correction capability is also performed. Based on the measured bit-change rates at high temperatures, the probability of key reconstruction failure is derived as low as 1.487 6E-9. In addition, 1 024 bytes of SRAM cells are shown to yield entropy keys of 128 bits. Conclusions This paper proposes a novel SRAM-PUF key extraction scheme that resolves the trade-off between stability requirements and high entropy demands by employing a bit-selection algorithm. The scheme simplifies error-correction encoding and decoding while enhancing the entropy of the generated keys. Compared with existing approaches, the computational complexity is reduced by 40% relative toScheme 2, by 98.9% relative to Scheme 3, and by 99.12% relative to Scheme 4. Furthermore, the method provides an integrated solution for screening stable SRAM cells, highlighting its practical application potential. Based on the bit error rate of 28 nm SRAM-PUFs, the key reconstruction success rate is calculated as (1-1.4876E-9). In tests conducted at –40 °C, 25 °C, and 85 °C, with 200 key reconstruction attempts per condition, all 11 chips achieved successful reconstruction. Considering variations across different fabrication processes, the number of screening cycles as well as parameters m and t can be adjusted to accommodate other process nodes.
- Physical Unclonable Function (PUF) /
- Stable node selection /
- Key extraction /
- High entropy value

HTML全文

图 1 SRAM PUF 密钥提取器

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图 2 比特筛选SRAM PUF 密钥提取方案

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图 3 SRAM PUF 筛选电路

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图 4 筛选次数与不同温度下的平均比特变化率关系

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图 5 稳定单元(经过常温筛选)在不同温度下的变化概率

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表 1 不同方法SRAM PUF稳定性对比

类型	研究思路	方法	PUF 重建成功率
第1类	扩大交叉耦合反相器之间的失配	文献[5]	0.992 2
第1类	扩大交叉耦合反相器之间的失配	文献[6]	1-1.28E-5
第2类	筛选稳定的SRAM单元构成PUF响应	文献[7]	0.061 1
		文献[8]	1-2.43E-6
		文献[10]	0.996 8
第3类	采用纠错码纠正响应错误比特	文献[13]方法1	1-5E-5
第3类	采用纠错码纠正响应错误比特	文献[13]方法2	1-3E-5

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1 译码成功概率评估算法

(1)初始化PMF，其中p为各次试验成功概率向量。
n=length(p);
pmf = zeros(1, n+1);
pmf(1) = 1;% 0次成功的概率为1
(2)逐步更新PMF。
for i = 1:n
%递归更新：前i-1次成功k-1次且第i次成功或者前i-1次成功k次且第i次失败
Pmf=[pmf(1)·(1–p(i)),pmf(2:end)·(1–p(i))+pmf(1:end–1)· 　　p(i)];
End
(3)k次成功的概率为pmf(k+1)，Puf 重建成功概率计算过程如下。
For j=1: x
For i=1:m
pmf₁=PMF_func(e(((i-1)·x+(j-1))·(2t+1)+1:((i-1)·x+j)·(2t+1)))
${p}{\text{(i,j)}} = 1 - \displaystyle\sum\limits_{k = t + 2}^{2t + 2} {{\text{pm}}{{\text{f}}_{\boldsymbol{1}}}} (k)$
end
end
(4)根据解交织规律，重排p, 得到p′。
p3 = 1;
for j=1:x
pmf₂ = PMF_func(p'(:,j))
${\boldsymbol{\gamma }}{\text{(j) = }}\displaystyle\sum\limits_{k = m/2 + 2}^{m + 1} {{\text{pm}}{{\text{f}}_2}(k)} $
p3=p3·γ(j)
end

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表 5 高温下PUF重建成功概率

编号	x=128, t=2, m=5	x=128, t=2, m=7	x=128, t=2, m=9
1	1-6.0390E-8	1-2.9159E-11	1- 6.2172E-15
2	1-4.3533E-7	1-1.5952E-10	1- 1.7542E-14
3	1-1.2722E-8	1-1.7840E-10	1- 4.7740E-15
4	1-3.7780E-8	1-2.8923E-11	1- 1.0769E-14
5	1-2.2309E-7	1-9.7857E-12	1- 1.2212E-15
6	1-4.4398E-6	1-7.5267E-10	1- 1.5432E-14
7	1-7.5811E-8	1-3.5191E-12	1-3.7748E-15
8	1-1.0748E-7	1-8.4819E-10	1- 1.4299E-12
9	1-8.8959E-7	1-1.4876E-9	1- 9.7844E-13
10	1-5.4529E-6	1-3.0186E-10	1- 3.6240E-12
11	1-5.8480E-8	1-3.0397E-9	1- 7.1021E-13

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表 3 运算量和密钥重建失败概率对比

方案	内码	外码	长度	失败概率	运算量
1	C_REP(5,1,2)	C_our(896,128,384)	4 480	1.4876E-9	5 376次加法、1 024次比较和56次置换
1	4 480次加法、896次比较	56次置位、896次加法、128次比较	4 480	1.4876E-9	5 376次加法、1 024次比较和56次置换
2	C_REP(3,1,1)	RM(2,7) = C_RM(128,29,15)	5 376	3E-5	8 764次小数加法、5 124次小数比较和 3 332次除2运算
2	5 376次小数加法、1 792次比较	3 332次小数比较、3 332次除2、 3 388次小数加法。	5 376	3E-5	8 764次小数加法、5 124次小数比较和 3 332次除2运算
3	C_REP(7,1,3)	BCH(1 754,742,105)	12 278	5E-5	480 368次加法和574 560 次乘法
3	12 278次加法、1 754次比较	468 090次加法、574 560次乘法	12 278	5E-5	480 368次加法和574 560 次乘法
4	无	BCH(2 236,1 024,106)	2 236	无	604 836次加法和733 520次乘法
4		604 836次加法、733 520次乘法	2 236	无	604 836次加法和733 520次乘法
5	无	C_REP(5,1,2)	640	6.07E-8	640次加法和128次比较
5		640次加法、128次比较	640	6.07E-8	640次加法和128次比较

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表 4 3温度下200次上电密钥成功重建次数

编号	重建成功次数
	-45°C	25°C	85°C
1	200	200	200
2	200	200	200
3	200	200	200
4	200	200	200
5	200	200	200
6	200	200	200
7	200	200	200
8	200	200	200
9	200	200	200
10	200	200	200
11	200	200	200

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表 5 1 664个噪声单元在常温下的熵值

编号	熵值
1	465.02
2	448.95
3	462.32
4	440.70
5	467.76
6	472.85
7	479.55
8	416.86
9	425.08
10	430.57
11	416.96

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表 6 6 528个PUF单元在常温下的熵值

编号	熵值
1	58.89
2	60.22
3	59.70
4	58.77
5	59.99
6	59.68
7	27.76
8	43.40
9	43.26
10	46.27
11	48.30

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