Untrusting network coding

In networks that perform linear network coding, an intermediate network node may receive a much larger number of linear equations of the source symbols than the number of messages it needs to send. For networks constructed by untrusted nodes, we propose a relaxed measure of security: we want to be untrusting, and allow each intermediate node to only learn as much information as the number of independent messages it needs to send. In this paper we formulate this problem and provide sufficient and necessary conditions for classes of combination networks.