  We propose a secure scheme for wireless network coding, called the algebraic
watchdog. By enabling nodes to detect malicious behaviors probabilistically and
use overheard messages to police their downstream neighbors locally, the
algebraic watchdog delivers a secure global self-checking network. Unlike
traditional Byzantine detection protocols which are receiver-based, this
protocol gives the senders an active role in checking the node downstream. The
key idea is inspired by Marti et al.'s watchdog-pathrater, which attempts to
detect and mitigate the effects of routing misbehavior.
  As an initial building block of a such system, we first focus on a two-hop
network. We present a graphical model to understand the inference process nodes
execute to police their downstream neighbors; as well as to compute, analyze,
and approximate the probabilities of misdetection and false detection. In
addition, we present an algebraic analysis of the performance using an
hypothesis testing framework that provides exact formulae for probabilities of
false detection and misdetection.
  We then extend the algebraic watchdog to a more general network setting, and
propose a protocol in which we can establish trust in coded systems in a
distributed manner. We develop a graphical model to detect the presence of an
adversarial node downstream within a general multi-hop network. The structure
of the graphical model (a trellis) lends itself to well-known algorithms, such
as the Viterbi algorithm, which can compute the probabilities of misdetection
and false detection. We show analytically that as long as the min-cut is not
dominated by the Byzantine adversaries, upstream nodes can monitor downstream
neighbors and allow reliable communication with certain probability. Finally,
we present simulation results that support our analysis.
