基于对称矩阵分解的无线传感网密钥恢复攻击
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摘要
密钥协议是保障无线传感网络(WSN, wireless sensor network)安全性的关键技术之一。Parakh等基于矩阵分解提出一种传感网密钥协议,然而研究表明该协议存在安全隐患。利用对称矩阵和置换矩阵性质,提出针对该协议的密钥恢复攻击方法。在截获节点行、列向量信息基础上,进行初等变换,构造线性代数攻击算法,求解出等价密钥,计算复杂度为O(N6)。实验结果表明,在多项式计算复杂度内,该方法可恢复出上述协议的等价密钥,内存开销在可接受范围内。此外,为了抵抗线性代数攻击,通过引入随机扰动矩阵,给出一种密钥协商修正方案,并进行了正确性与安全性分析。
The key protocol is one of the crucial technologies to ensure the security for wireless sensor network(WSN). Parakh, et al. proposed a key agreement for WSN based on matrix decomposition. However, the study revealed that the protocol had security risks. A key recovery attack scheme against this protocol was proposed by using the properties of symmetric matrix and permutation matrix. Based on intercepting the row and column vector of the node, elementary transformation was performed to construct a linear algebraic attack algorithm and the equivalent key was obtained. The computational complexity is O(N6). Experimental results show that the method can recover the equivalent key of the above protocol within the polynomial computational complexity and the memory consumption is within an acceptable range. In addition, an improved scheme for key agreement was proposed to resist the linear algebraic attack by using a random disturbance matrix, and the correctness and security analysis were also carried out.
The key protocol is one of the crucial technologies to ensure the security for wireless sensor network(WSN). Parakh, et al. proposed a key agreement for WSN based on matrix decomposition. However, the study revealed that the protocol had security risks. A key recovery attack scheme against this protocol was proposed by using the properties of symmetric matrix and permutation matrix. Based on intercepting the row and column vector of the node, elementary transformation was performed to construct a linear algebraic attack algorithm and the equivalent key was obtained. The computational complexity is O(N6). Experimental results show that the method can recover the equivalent key of the above protocol within the polynomial computational complexity and the memory consumption is within an acceptable range. In addition, an improved scheme for key agreement was proposed to resist the linear algebraic attack by using a random disturbance matrix, and the correctness and security analysis were also carried out.
引文
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[22]RUJ S,SAKURAI K.Secure and privacy preserving hierarchical wireless sensor networks using hybrid key management technique[C]//Global Communications Conference.2014:402-407.
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[24]BECHKIT W,CHALLAL Y,BOUNABDALLAH A.A new class of Hash-Chain based key pre-distribution schemes for WSN[J].Computer Communications,2013,36(3):243-255.
[25]陈燕俐,杨庚.适合于无线传感器网络的混合式组密钥管理方案[J].通信学报,2010,31(11):56-64.CHEN Y L,YANG G.Hybird group key management scheme for wireless sensor networks[J].Journal on Communications,2010,31(11):56-64.
[26]张永,温涛,郭权,等.WSN中基于全同态加密的对偶密钥建立方案[J].通信学报,2012,33(10):101-109.ZHONG Y,WEN T,GUO Q,et al.Pair-wise key establishment for wireless sensor networks based on fully homomorphic encryption[J].Journal on Communications,2012,33(10):101-109.
[27]SINGH A,AWASTHI A K,SINGH K.A key agreement algorithm based on ECDSA for wireless sensor network[C]//Proceedings of 3rd International Conference on Advanced Computing,Networking and Informatics.Springer India.2016:143-149.
[28]LIU J H,ZHANG H G,JIA J W,et al.Cryptanalysis of an asymmetric cipher protocol using a matrix decomposition problem[J].Science China Information Sciences,2016,46(5):1-11.
[29]LIU J H,ZHANG H G,JIA J W.A linear algebra attack on the non-commuting cryptography class based on matrix power function[C]//International Conference on Information Security and Cryptology.2016:343-354.
[30]刘金会,张焕国,贾建卫,等.HKKS密钥交换协议分析[J].计算机学报,2016,39(3):516-528.LIU J H,ZHANG H G,JIA J W,et al.Cryptanalysis of HKKS key exchange protocols[J].Chinese Journal of Computers,2016,39(3):516-528.
[31]张焕国,毛少武,吴万青,等.量子计算复杂性理论综述[J].计算机学报,2016,39(12):2403-2428.ZHANG H G,MAO S W,WU W Q,et al.Overview of quantum computation complexity theory[J].Chinese Journal of Computers,2016,39(12):2403-2428.
[2]罗军舟,杨明,凌振,等.网络空间安全体系与关键技术[J].中国科学:信息科学,2016,46(8):939-968.LUO J Z,YANG M,LING Z,et al.Architecture and key technologies of cyberspace security[J].Science China Information Sciences,2016,46(8):939-968.
[3]陈帅,钟先信,巫正中,等.无线传感器网络混沌分组密码研究[J].中国科学:信息科学,2009,39(3):357-362.CHEN S,ZHONG X X,WU Z Z,et al.Chaos block cipher for wireless sensor network[J].Science China Information Sciences,2009,39(3):357-362.
[4]曾建电,王田,贾维嘉,等.传感云研究综述[J].计算机研究与发展,2017,54(5):925-939.ZENG J D,WANG T,JIA W J,et al.A survey on sensor-cloud[J].Journal of Computer Research and Development,2017,54(5):925-939.
[5]付帅,马建峰,李洪涛,等.无线传感器网络中匿名的聚合节点选举协议[J].通信学报,2015,36(2):88-97.FU S,MA J F,LI H T,et al.Anonymous aggregator election protocol for wireless sensor networks[J].Journal on Communications,2015,36(2):88-97.
[6]ARAFATH M S,KHAN K U R.Opportunistic sensor networks:Asurvey on privacy and secure routing[C]//International Conference on Anti-Cyber Crimes.IEEE,2017:41-46.
[7]HAMZA T,KADDOUM G,MEDDEB A,et al.A survey on intelligent MAC layer jamming attacks and countermeasures in WSN[C]//2016IEEE 84th Vehicular Technology Conference(VTC-Fall).IEEE,2016:1-5.
[8]TEJASWINI B S,BHAT G J.Survey on various attacks and message authentication schemes in WSN[J].International Journal of Scientific Research Engineering&Technology(IJSRET),2015,4(3):148-152.
[9]RAYMOND D R,MARCHANY R C,BROWNFIELD M,et al.Effects of denial-of-sleep attacks on wireless sensor network MAC Protocols[J].IEEE Transactions on Vehicular Technology,2009,58(1):367-380.
[10]GANDINO F,FERRERO R,REBAUDENGO M.A Key distribution scheme for mobile wireless sensor networks:q-s-composite[J].IEEETransactions on Information Forensics&Security,2017,12(1):34-47.
[11]HAYOUNI H,HAMDI M,KIM T H.A survey on encryption schemes in wireless sensor networks[J].J Chem Eng Data,2014,3(1):91-92.
[12]RAVI K,KHANAI R,PRAVEEN K.Survey on pairing based cryptography for wireless sensor networks[C]//International Conference on Inventive Computation Technologies.IEEE,2016:1-4.
[13]SHIM K A.A survey of public-key cryptographic primitives in wireless sensor networks[J].IEEE Communications Surveys&Tutorials,2016,18(1):577-601.
[14]MALEH Y,EZZATI A.A lightweight symmetric cryptography scheme for Identifying compromised node in WSN[J].Indonesian Journal of Electrical Engineering and Computer Science,2016,2(2):431-451.
[15]YAGAN O,MAKOWSKI A M.Wireless sensor networks under the random pairwise key pre-distribution scheme:can resiliency be achieved with small key rings[J].IEEE/ACM Transactions on Networking,2016,24(6):3383-3396.
[16]PARAKH A,KAK S.New key agreement techniques for sensor networks[J].Infocommunications Journal,2015,7(1):15-21.
[17]SINGH A,AWASTHI A K,SINGH K.A key agreement algorithm based on ECDSA for wireless sensor network[C]//Proceedings of 3rd International Conference on Advanced Computing,Networking and Informatics.2016:143-149.
[18]CHAPHEKAR P P.Survey of key distribution schemes for wireless sensor networks[J].Computer Science,2014,1(1):1-14.
[19]CHEN C Y,CHAO H.A survey of key distribution in wireless sensor networks[J].Security and Communication Networks,2015,7(12):2495-2508.
[20]CASOLA V,BENEDICTIS A D,DRAGO A,et al.Analysis and comparison of security protocols in wireless sensor networks[C]//IEEE,Symposium on Reliable Distributed Systems Workshops.2011:52-56.
[21]JR M A S,BARRETO P S L M,MARGI C B,et al.A survey on key management mechanisms for distributed wireless sensor networks[J].Computer Networks,2010,54(15):2591-2612.
[22]RUJ S,SAKURAI K.Secure and privacy preserving hierarchical wireless sensor networks using hybrid key management technique[C]//Global Communications Conference.2014:402-407.
[23]SALZO S,VILLA S.SPIKE:a novel session key management protocol with time-varying secure cluster formation in wireless sensor networks[C]//Eleventh International Conference on Privacy,Security and Trust.2013:151-160.
[24]BECHKIT W,CHALLAL Y,BOUNABDALLAH A.A new class of Hash-Chain based key pre-distribution schemes for WSN[J].Computer Communications,2013,36(3):243-255.
[25]陈燕俐,杨庚.适合于无线传感器网络的混合式组密钥管理方案[J].通信学报,2010,31(11):56-64.CHEN Y L,YANG G.Hybird group key management scheme for wireless sensor networks[J].Journal on Communications,2010,31(11):56-64.
[26]张永,温涛,郭权,等.WSN中基于全同态加密的对偶密钥建立方案[J].通信学报,2012,33(10):101-109.ZHONG Y,WEN T,GUO Q,et al.Pair-wise key establishment for wireless sensor networks based on fully homomorphic encryption[J].Journal on Communications,2012,33(10):101-109.
[27]SINGH A,AWASTHI A K,SINGH K.A key agreement algorithm based on ECDSA for wireless sensor network[C]//Proceedings of 3rd International Conference on Advanced Computing,Networking and Informatics.Springer India.2016:143-149.
[28]LIU J H,ZHANG H G,JIA J W,et al.Cryptanalysis of an asymmetric cipher protocol using a matrix decomposition problem[J].Science China Information Sciences,2016,46(5):1-11.
[29]LIU J H,ZHANG H G,JIA J W.A linear algebra attack on the non-commuting cryptography class based on matrix power function[C]//International Conference on Information Security and Cryptology.2016:343-354.
[30]刘金会,张焕国,贾建卫,等.HKKS密钥交换协议分析[J].计算机学报,2016,39(3):516-528.LIU J H,ZHANG H G,JIA J W,et al.Cryptanalysis of HKKS key exchange protocols[J].Chinese Journal of Computers,2016,39(3):516-528.
[31]张焕国,毛少武,吴万青,等.量子计算复杂性理论综述[J].计算机学报,2016,39(12):2403-2428.ZHANG H G,MAO S W,WU W Q,et al.Overview of quantum computation complexity theory[J].Chinese Journal of Computers,2016,39(12):2403-2428.