ISSN 0032-9460, Problems of Information Transmission, 2013, Vol. 49, No. 2, pp. 179–191.
Pleiades Publishing, Inc., 2013.
Original Russian Text
E.M. Gabidulin, N.I. Pilipchuk, B. Honary, H. Rashwan, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49,
No. 2, pp. 92–106.
Information Security in a Random
Network Coding Network
E. M. Gabidulin
, N. I. Pilipchuk
Moscow Institute of Physics and Technology (State University)
Lancaster University, United Kingdom
Received April 24, 2012; in ﬁnal form, December 4, 2012
Abstract—We consider a communication network with random network coding which can
be attacked by adversaries of two types. One of them can wiretap original packets outgo-
ing from source to destination. The other can insert its own packets into information ﬂow,
which are wrong messages for the receiver. To provide secure communication, we use a scheme
based on combining the GPT (Gabidulin–Paramonov–Tretjakov) public key cryptosystem and
SKK (Silva–Kschischang–Koetter) codes. Encrypted packets are transmitted to the destination
through wired channels. Performance of this system is investigated. The main result is that
the proposed scheme is secure against wiretapping and insertion attacks under some conditions
which depend on rank code parameters.
1.1. New Approach and Problems
The concept of network coding was ﬁrst proposed in . Random network coding is well de-
scribed in [2–6]. Random network coding was shown to be an eﬃcient way for network communi-
cation, since it allows to increase network throughput.
At unicast and multicast transmission, a network can be represented as a directed acyclic graph,
where graph vertices are network nodes and graph edges are network channels. One of the nodes
is a source of messages, and one or several nodes are destinations (receivers). Other nodes are
intermediate (inner) nodes. The source node generates messages as a sequence of packets. The
destination receives packets and extracts information from them. Inner nodes relay received packets.
In a traditional network (without network coding), inner nodes receive packets, save them in a
buﬀer for a while, and then transmit them to the next node without any modiﬁcation. When using
network coding, transmission procedure is principally diﬀerent. Packets are treated as elements of
a ﬁnite ﬁeld. Inner nodes create new packets as algebraic linear combinations of received packets
and then transmit the new packets to the next node. Each inner node performs this procedure
independently. Therefore, the destination receives a set of linear combinations of original source
Assume that a source node transmits a message with n information packets of length m to a
destination. The transmitted message can be represented as a matrix M of size n × m.Two
scenarios for transmitting packets from the source node to the destination are considered. The ﬁrst
scenario assumes that the destination receives a matrix Y = AM,whereA is an n
× n matrix.
Supported in part by the Russian Foundation for Basic Research, project no. 12-07-00122-a.