2 research outputs found
Security Analysis on "An Authentication Code Against Pollution Attacks in Network Coding"
We analyze the security of the authentication code against pollution attacks
in network coding given by Oggier and Fathi and show one way to remove one very
strong condition they required. Actually, we find a way to attack their
authentication scheme. In their scheme, they considered that if some malicious
nodes in the network collude to make pollution in the network flow or make
substitution attacks to other nodes, they thought these malicious nodes must
solve a system of linear equations to recover the secret parameters. Then they
concluded that their scheme is an unconditional secure scheme. Actually, note
that the authentication tag in the scheme of Oggier and Fathi is nearly linear
on the messages, so it is very easy for any malicious node to make pollution
attack in the network flow, replacing the vector of any incoming edge by linear
combination of his incoming vectors whose coefficients have sum 1. And if the
coalition of malicious nodes can carry out decoding of the network coding, they
can easily make substitution attack to any other node even if they do not know
any information of the private key of the node. Moreover, even if their scheme
can work fruitfully, the condition in their scheme in a network
can be removed, where is the sum of numbers of the incoming edges at
adversaries. Under the condition , may be large, so we need
large parameter which increases the cost of computation a lot. On the other
hand, the parameter can not be very large as it can not exceed the length
of original messages.Comment: 9 pages. arXiv admin note: text overlap with arXiv:0909.3146 by other
author
An Authentication Scheme for Subspace Codes over Network Based on Linear Codes
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 .
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 be a linear code. For any coordinate , a
codeword in is called minimal respect to if the codeword
has component 1 at the -th coordinate and there is no other
codeword whose -th component is 1 with support strictly contained in that of
. Then the security of receiver in our authentication scheme is
characterized by the minimal codewords respect to in the dual code
.Comment: 18 page