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arXiv 1303.0930cs.CRcs.ITmath.IT
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基于线性码的网络中子空间码认证方案

An Authentication Scheme for Subspace Codes over Network Based on Linear Codes

Jun Zhang, Xinran Li, Fang-Wei Fu

摘要:

网络编码具有最大限度地利用网络资源的优点,在未来的网络通信中具有很大的应用前景。然而,网络编码的特性也使得污染攻击更加严重。本文给出了一个基于线性码$C$的网络编码无条件安全认证方案。Safavi-Naini和Wang给出了多个接收者和多个消息的认证码。我们注意到Safavi-Naini和Wang的方案本质上是用Reed-Solomon码构造的。并对它们的构造作了一些修改,使之能用于线性网络上的子空间码的认证。同时,我们推广了线性码的构造。将Shamir的秘密共享方案推广到线性码上具有与将Shamir的秘密共享方案推广到基于线性码的线性秘密共享方案相似的优点。这种推广的一个优点是,对于一个固定的消息空间,我们的计划允许任意多个接收器来检查自己的消息的完整性,而与里德-所罗门码的计划有一个限制验证接收器的数量。另一个优点是我们在推广方案中引入了访问结构。Massey用第一分量为1的二元码中的最小码字来刻画线性秘密共享方案的访问结构。我们稍微修改了最小码字的定义。令$C$是$[V,k]$线性码。对于任何坐标$i\in \{1,2,\cdots,V\}$,如果码字$\vec{c}$在第$i$个坐标处具有分量1,并且不存在第$i$个分量为1的其它码字,并且支持严格包含在$\vec{c}$的支持中,则$C$中的码字$\vec{c}$被称为关于$i$的最小值。然后,我们的认证方案中接收方$R_i$的安全性由双码$C^\bot$中相对于$i$的最小码字来表征。

英文摘要:

Network coding provides the advantage of maximizing the usage of network resources, and has great application prospects in future network communications. However, the properties of network coding also make the pollution attack more serious. In this paper, we give an unconditional secure authentication scheme for network coding based on a linear code $C$. Safavi-Naini and Wang gave an authentication code for multi-receivers and multiple messages. We notice that the scheme of Safavi-Naini and Wang is essentially constructed with Reed-Solomon codes. And we modify their construction slightly to make it serve for authenticating subspace codes over linear network. Also, we generalize the construction with linear codes. The generalization to linear codes has the similar advantages as generalizing Shamir's secret sharing scheme to linear secret sharing sceme based on linear codes. One advantage of this generalization is that for a fixed message space, our scheme allows arbitrarily many receivers to check the integrity of their own messages, while the scheme with Reed-Solomon codes has a constraint on the number of verifying receivers. Another advantage is that we introduce access structure in the generalized scheme. Massey characterized the access structure of linear secret sharing scheme by minimal codewords in the dual code whose first component is 1. We slightly modify the definition of minimal codewords. Let $C$ be a $[V,k]$ linear code. For any coordinate $i\in \{1,2,\cdots,V\}$, a codeword $\vec{c}$ in $C$ is called minimal respect to $i$ if the codeword $\vec{c}$ has component 1 at the $i$-th coordinate and there is no other codeword whose $i$-th component is 1 with support strictly contained in that of $\vec{c}$. Then the security of receiver $R_i$ in our authentication scheme is characterized by the minimal codewords respect to $i$ in the dual code $C^\bot$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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