  This paper considers a network where a node wishes to transmit a source
message to a legitimate receiver in the presence of an eavesdropper. The
transmitter secures its transmissions employing a sparse implementation of
Random Linear Network Coding (RLNC). A tight approximation to the probability
of the eavesdropper recovering the source message is provided. The proposed
approximation applies to both the cases where transmissions occur without
feedback or where the reliability of the feedback channel is impaired by an
eavesdropper jamming the feedback channel. An optimization framework for
minimizing the intercept probability by optimizing the sparsity of the RLNC is
also presented. Results validate the proposed approximation and quantify the
gain provided by our optimization over solutions where non-sparse RLNC is used.
