Inspired by problems in Private Information Retrieval, we consider the setting where two users need to establish a communication protocol to transmit a secret without revealing it to external observers. This is a question of how large a linear code can be, when it is required to agree with a prescribed code on a collection of coordinate sets. We show how the efficiency of such a protocol is determined by the derived matroid of the underlying linear communication code. Furthermore, we provide several sufficient combinatorial conditions for when no secret transmission is possible.
翻译:受私人信息检索系统问题的影响,我们考虑了两个用户需要建立通信协议,在不向外部观察者透露秘密的情况下传递秘密的场合,这是一个线性代码有多大的问题,当需要同意关于一组坐标的指定代码时,线性代码会有多大。我们展示了这种协议的效率如何由底线性通信代码的衍生的假体来决定。此外,我们为无法进行秘密传输的情况提供了几个充分的组合条件。