Mathematical Model and Framework of Physical Layer Encryption for Wireless Communications

As a response to serious transmission security problems in wireless communications, physical layer encryption (PLE) provides an effective security measure which is very different from upper layer cryptography technologies. PLE can take advantage of the effects of channel and noise and the processing objects are complex vector signals, which are essentially different from Boolean algebra based traditional cryptography. This paper establishes mathematical models, design frameworks and cryptographic primitives for PLE. Two design frameworks are proposed: stream PLE and block PLE. For stream PLE, a new 3D security constellation mapping is derived. For block PLE, two types of sub-transforms are defined: isometry transformations and stochastic transformations. The proposed PLE framework has a large cipher signal space and key space; it provides more freedom in design and can resist known plaintext attacks and chosen-plaintext attacks.