防污染和防窃听的网络编码
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摘要
近年来,网络编码越来越成为业界的研究热点。网络编码技术极大的提高了网络的传输速率、吞吐量和可靠性,对路由器基础设施以及无线网状网络等都有重要意义。但直接应用网络编码存在不可忽视的安全问题,主要包括污染和窃听两类问题,其中污染主要由恶意节点和信道噪声引起,窃听是指攻击者通过窃听网络中的部分或者全部信道来获取网络中传输的消息。这些安全问题很大程度上限制了其应用范围,阻碍了它在实际中的应用和推广。论文研究了应用网络编码时存在的污染和窃听问题,并设计了有效的安全网络编码体制,主要包括以下几个方面:
(1)提出了一种防窃听的网络编码算法。应用该算法,窃听者得不到关于信源任何有意义的信息,称之为弱安全。该算法通过舍弃少量带宽使得随机网络编码能以很高的概率达到弱安全的要求。另外,当信源和信宿共享有一个低速率秘密信道或公钥加密体制时,设计了一种可以达到网络最大流的弱安全网络编码体制。应用随机网络编码时,该编码体制防窃听的概率为1。
(2)现有的防窃听网络编码存在两方面的问题。首先,要达到信息论安全的防窃听目的必须牺牲部分带宽,以致无法达到网络的最大流。其次,应用随机网络编码时,编码安全的概率较低。文中设计了一种能同时达到网络的最大流和信息论安全条件的网络编码体制。同时,该编码体制是一个确定性模型而非概率模型,即:应用随机网络编码时,该编码体制信息论安全的概率为1。
(3)提出了一种验证消息完整性的同态签名体制。首先,取一些公开参数作为原始信源消息每个信息包的Hash值,当在原始信息包中加入少量冗余时,其Hash值便是取定的公开参数,省去Hash值的分发,很大程度上降低了该签名体制的通信开销。其次,当网络拓扑简单且固定时,用一个所有节点所共享的随机数产生器来产生编码向量,省去了编码向量的分发。当Hash值和编码向量的分发都省去时,该种签名体制的通信开销是几乎可以忽略的。
(4)利用消息向量张成线性空间的思想,设计了一种概率模型下的防污染随机网络编码算法。当信源和信宿共享有一个线性空间时,在信源消息中加入部分冗余,使得新信源向量张成的空间与信源和信宿共享的空间正交,达到正确译码的目的。
(5) Koetter和Kschischang利用有限域上的线性多项式从线性空间的角度设计了一种网络纠错编码体制,但其编码体制的通信开销较高(100%),使其很难在现实中应用。文中对其编码体制进行了改进,在其基础上设计了一种低通信开销的网络纠错编码体制。该编码体制的通信开销与经典随机网络编码相同。另外,文中同时考虑了窃听问题,并在此基础上设计了一种防污染和防窃听的网络编码体制。
In recent years, there has been increasing attention to the theory of network coding.Network coding is beneficial for the basic router infrastructure and wireless network, sinceit greatly improved the multicast rate, throughput and robust of the network. However,direct application of network coding may su?er from two kinds of adversaries: contamina-tion and eavesdropping. Here contamination refers to the distortion on the transmission,such as random errors and malicious modifications. Eavesdropping referring to the adver-sary aims to get the transfer of information by eavesdropping on some or all the channelsover a network. The application and promotion of the network coding are greatly re-stricted by these two kinds of adversaries. In this dissertation, we study these two kindsof adversaries and design some secure network coding schemes to conquer them. Themain results of this dissertation are as follows:
(1) An algorithm that targets eavesdropping adversaries is presented. By means of thisalgorithm, an eavesdropper is unable to get any meaningful information about thesource, which we call weak security. We show that if we give up a small amountof overall capacity, then a random code achieves the weak security condition ata much higher probability. Besides, when there is a low rate secret channel or apublic encryption scheme between the source and destination, an algorithm thatnot only achieves the max-?ow but also the weak security condition is proposed.The probability of the coding scheme to be security is 1, when random codingscheme is used.
(2) There are two main problems in the present secure network coding schemes. Firstly,in order to achieve the information security condition, some network capacity mustbe sacrificed and the max-?ow of the network could not be achieved. Secondly, whenrandom coding scheme is used, the probability of the coding scheme to be security islow. A max-?ow achieved information secure network coding scheme is proposed inthis dissertation. The coding scheme is a deterministic model instead of probabilitymodel i.e, the probability of the coding scheme to be information security is one,when random coding scheme is used.
(3) A homomorphic hash scheme to verify the integrity of the received packets is pre-sented. Firstly, the public parameters are selected as the“intended”hash values.The original packets are padded so that they are hashed to the public parameters.In this way the distribution of the hash values is avoided and hence the communica-tion overhead is reduced. Secondly, when the topology of the network is fixed, the code coe?cients can be generated by a shared pseudo-random number generator sothat the distribution of the coe?cients can also be avoided. When the distributionof the hash values and the code coe?cients are both avoided, we indicate that thecommunication overhead of the scheme is negligible compared with previous works.
(4) A random network coding scheme against the contamination adversary is proposed,using the idea that the message packets span a vector space. The proposed securescheme is a probability model. When the source and the destinations share a linearvector space, some redundancy is added to the source message. In this way, thevector space spanned by the padded message is orthogonal to the shared vectorspace and the original source message can be decoded.
(5) Koetter and Kschischang proposed an error correcting network coding scheme viathe vector space perspective using the linearized polynomials over finite field. Itis noted that, the communication overhead of their scheme is high, actually 100%,which greatly restricted its application. Based on their coding scheme, we propose alow communication overhead error correcting network coding scheme in this disser-tation. The overhead of the proposed coding scheme is the same as the standard ran-dom network coding. Furthermore, the eavesdropping adversary is also consideredand a secure network coding scheme against the contamination and eavesdroppingadversary is proposed.
(1)提出了一种防窃听的网络编码算法。应用该算法,窃听者得不到关于信源任何有意义的信息,称之为弱安全。该算法通过舍弃少量带宽使得随机网络编码能以很高的概率达到弱安全的要求。另外,当信源和信宿共享有一个低速率秘密信道或公钥加密体制时,设计了一种可以达到网络最大流的弱安全网络编码体制。应用随机网络编码时,该编码体制防窃听的概率为1。
(2)现有的防窃听网络编码存在两方面的问题。首先,要达到信息论安全的防窃听目的必须牺牲部分带宽,以致无法达到网络的最大流。其次,应用随机网络编码时,编码安全的概率较低。文中设计了一种能同时达到网络的最大流和信息论安全条件的网络编码体制。同时,该编码体制是一个确定性模型而非概率模型,即:应用随机网络编码时,该编码体制信息论安全的概率为1。
(3)提出了一种验证消息完整性的同态签名体制。首先,取一些公开参数作为原始信源消息每个信息包的Hash值,当在原始信息包中加入少量冗余时,其Hash值便是取定的公开参数,省去Hash值的分发,很大程度上降低了该签名体制的通信开销。其次,当网络拓扑简单且固定时,用一个所有节点所共享的随机数产生器来产生编码向量,省去了编码向量的分发。当Hash值和编码向量的分发都省去时,该种签名体制的通信开销是几乎可以忽略的。
(4)利用消息向量张成线性空间的思想,设计了一种概率模型下的防污染随机网络编码算法。当信源和信宿共享有一个线性空间时,在信源消息中加入部分冗余,使得新信源向量张成的空间与信源和信宿共享的空间正交,达到正确译码的目的。
(5) Koetter和Kschischang利用有限域上的线性多项式从线性空间的角度设计了一种网络纠错编码体制,但其编码体制的通信开销较高(100%),使其很难在现实中应用。文中对其编码体制进行了改进,在其基础上设计了一种低通信开销的网络纠错编码体制。该编码体制的通信开销与经典随机网络编码相同。另外,文中同时考虑了窃听问题,并在此基础上设计了一种防污染和防窃听的网络编码体制。
In recent years, there has been increasing attention to the theory of network coding.Network coding is beneficial for the basic router infrastructure and wireless network, sinceit greatly improved the multicast rate, throughput and robust of the network. However,direct application of network coding may su?er from two kinds of adversaries: contamina-tion and eavesdropping. Here contamination refers to the distortion on the transmission,such as random errors and malicious modifications. Eavesdropping referring to the adver-sary aims to get the transfer of information by eavesdropping on some or all the channelsover a network. The application and promotion of the network coding are greatly re-stricted by these two kinds of adversaries. In this dissertation, we study these two kindsof adversaries and design some secure network coding schemes to conquer them. Themain results of this dissertation are as follows:
(1) An algorithm that targets eavesdropping adversaries is presented. By means of thisalgorithm, an eavesdropper is unable to get any meaningful information about thesource, which we call weak security. We show that if we give up a small amountof overall capacity, then a random code achieves the weak security condition ata much higher probability. Besides, when there is a low rate secret channel or apublic encryption scheme between the source and destination, an algorithm thatnot only achieves the max-?ow but also the weak security condition is proposed.The probability of the coding scheme to be security is 1, when random codingscheme is used.
(2) There are two main problems in the present secure network coding schemes. Firstly,in order to achieve the information security condition, some network capacity mustbe sacrificed and the max-?ow of the network could not be achieved. Secondly, whenrandom coding scheme is used, the probability of the coding scheme to be security islow. A max-?ow achieved information secure network coding scheme is proposed inthis dissertation. The coding scheme is a deterministic model instead of probabilitymodel i.e, the probability of the coding scheme to be information security is one,when random coding scheme is used.
(3) A homomorphic hash scheme to verify the integrity of the received packets is pre-sented. Firstly, the public parameters are selected as the“intended”hash values.The original packets are padded so that they are hashed to the public parameters.In this way the distribution of the hash values is avoided and hence the communica-tion overhead is reduced. Secondly, when the topology of the network is fixed, the code coe?cients can be generated by a shared pseudo-random number generator sothat the distribution of the coe?cients can also be avoided. When the distributionof the hash values and the code coe?cients are both avoided, we indicate that thecommunication overhead of the scheme is negligible compared with previous works.
(4) A random network coding scheme against the contamination adversary is proposed,using the idea that the message packets span a vector space. The proposed securescheme is a probability model. When the source and the destinations share a linearvector space, some redundancy is added to the source message. In this way, thevector space spanned by the padded message is orthogonal to the shared vectorspace and the original source message can be decoded.
(5) Koetter and Kschischang proposed an error correcting network coding scheme viathe vector space perspective using the linearized polynomials over finite field. Itis noted that, the communication overhead of their scheme is high, actually 100%,which greatly restricted its application. Based on their coding scheme, we propose alow communication overhead error correcting network coding scheme in this disser-tation. The overhead of the proposed coding scheme is the same as the standard ran-dom network coding. Furthermore, the eavesdropping adversary is also consideredand a secure network coding scheme against the contamination and eavesdroppingadversary is proposed.
引文
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