WSN中基于乱序多项式对偶密钥的攻击方案

doi:10.11959/j.issn.1000-436x.2015116

通信学报 ›› 2015, Vol. 36 ›› Issue (8): 110-117.doi: 10.11959/j.issn.1000-436x.2015116

WSN中基于乱序多项式对偶密钥的攻击方案

王爱文^1,²,温涛^1,³,张永³,朱奉梅⁴,吴镝¹

¹ 东北大学软件中心，辽宁沈阳 110819
² 沈阳化工大学计算机科学与技术学院，辽宁沈阳 110142
³ 大连东软信息学院计算机科学与技术系，辽宁大连 116023
⁴ 辽宁金融职业学院信息技术系，辽宁沈阳 110122

出版日期:2015-08-25 发布日期:2015-08-25
基金资助:
国家自然科学基金资助项目;国家自然科学基金资助项目;辽宁省教育厅科学技术基金资助项目;大连市科技计划基金资助项目

Attacking scheme against the permutation-based multi-polynomial scheme for pair-wise key establishment in wireless sensor networks

Ai-wen WANG^1,²,Tao WEN^1,³,Yong ZHANG³,Feng-mei ZHU⁴,Di WU¹

¹ Software Center,Northeastern University,Shenyang 110819,China
² College of Computer Science and Technology,Shenyang University Chemical Technology,Shenyang 110142,China
³ Department of Computer Science and Technology,Dalian Neusoft University of Information,Dalian 116023,China100081,China
⁴ Department of Information Technology,Liaoning Finance Vocational College,Shenyang 110122,China

Online:2015-08-25 Published:2015-08-25
Supported by:
The National Natural Science Foundation of China;The National Natural Science Foundation of China;The Science Foundation of Liaoning Education Ministry;The Foundation of Dalian Scientific and Technical Planning Project

摘要/Abstract

摘要：

针对Guo等的WSN中基于乱序对称多项式的对偶密钥方案提出一种攻击方案。通过构造黑盒的方式，对多项式进行攻击，通过整体求解多项式集合，而不是求解单个多项式的方式，使多项式的排列顺序在多项式的破解中失去作用，从而实现乱序多项式的破解。定理证明和实例分析表明Guo等的方案不能抵御大规模节点俘获攻击，未能突破多项式的容忍门限，是一种不安全的方案。

关键词: 无线传感器网络, 对偶密钥, 多项式, 攻击, 黑盒

Abstract:

An attacking scheme was proposed against the permutation-based multi-polynomial scheme proposed by Guo,et al for pair-wise key establishment in wireless sensor networks.Attacks on polynomials were carried out by constructing a black-box to integrally solve the set of polynomials rather than a single polynomial.The results show that this scheme can break the symmetric polynomials and make the permutation of polynomials lose its function.The proven theorems and instance analysis indicate that the scheme proposed by Guo,et al can’t frustrate the large-scale node capture attack and can’t break the tolerance threshold of polynomials.Therefore,the scheme is insecure.

Key words: WSN, pair-wise key establishment, polynomial, attack, black-box

王爱文,温涛,张永,朱奉梅,吴镝. WSN中基于乱序多项式对偶密钥的攻击方案[J]. 通信学报, 2015, 36(8): 110-117.

Ai-wen WANG,Tao WEN,Yong ZHANG,Feng-mei ZHU,Di WU. Attacking scheme against the permutation-based multi-polynomial scheme for pair-wise key establishment in wireless sensor networks[J]. Journal on Communications, 2015, 36(8): 110-117.

图/表 2

表1

表2

符号定义"

Y = [y^{m} (- 1) y^{m - 1} y^{m - 2} \dots {(- 1)}^{m} y^{0}]

参数	参数含义	参数取值
m	节点部署多项式个数
t	多项式阶数
p	素数
n	节点个数
GF(p)	特征为 p的有限域
ID	节点标识	ID∈[1,p?1]
N	节点ID集合	{ID₁,ID₂,…,ID_n?1,ID_n}
F	被俘获节点ID集合	${I D_{c_{1}}, I D_{c_{2}}, \dots, I D_{c_{m t}}, I D_{c_{m t + 1}}} (c_{i} \in [1, n], 1 \leq i \leq m t + 1)$
E	(m+1)×(mt+1)矩阵	$E (i, j) = e_{i - 1, j - 1}$
X	关于变量x的向量	$X = {[x^{0} x^{1} x^{2} \dots x^{m t - 1} x^{m t}]}^{'}$
Y	关于变量y的向量
UP(ID_i)	ID_i上m个一元t阶多项式系数矩阵	size(UP(ID_i))=[m t+1]
CUP	由mt+1个UP(ID_i)矩阵组成的三维矩阵	$C P U = [U P (I D_{c_{1}}) U P (I D_{c_{2}}) \dots U P (I D_{c_{m t + 1}})]$

表2

参考文献 20

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m	t=2	t=3	t=4	t=5	t=6	t=7	t=8
2	4	8	16	32	64	128	256
3	36	216	1 296	7 776	46 656	279 936	1.7 ×10⁶
4	576	13 824	331 776	8.0×10⁶	1.9×10⁸	4.6×10⁹	1.1×10¹¹
5	14 400	1.7 ×10⁶	2.1×10⁸	2.5×10¹⁰	3.0×10¹²	3.6×10¹⁴	4.3×10¹⁶
6	518 400	3.7 ×10⁸	2.7 ×10¹¹	1.9×10¹⁴	1.4×10¹⁷	1.0×10²⁰	7.2×10²²
7	2.5×10⁷	1.3×10¹¹	6.5×10¹⁴	3.3×10¹⁸	1.6×10²²	8.3×10²⁵	4.2×10²⁹
8	1.6×10⁹	6.6×10¹³	2.6×10¹⁸	1.1×10²³	4.3×10²⁷	1.7×10³²	7.0×10³⁶

WSN中基于乱序多项式对偶密钥的攻击方案

Attacking scheme against the permutation-based multi-polynomial scheme for pair-wise key establishment in wireless sensor networks

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