Shannon described encryption as a set of reversible (nonsingular) transformations from one space to another space, so that a potential cryptanalyst would not be able to decipher the message unless they had access to the encryption key. Encryption has since been developed along two distinct routes. The prominent approach is based on the generation of coding schemes that are practically unbreakable because of their computational complexity, thus combining encryption with complexity theory. Along the second path lie information theoretic approaches, allowing for theoretic perfect secrecy. Analyses for the wireless fading channel and MIMO systems have established non-zero secrecy capacities for such systems, although on average the eavesdropper's channel can be better than the legitimate user's channel. Furthermore, information theoretic dirty paper coding (helping interferer or jamming) approaches have recently been proposed. In this talk, we present a dirty paper encryption scheme, specifically for OFDM signals.

We call the scheme Masked-OFDM, as OFDM signals are masked through faster than Nyquist signalling. Secrecy capacity that approximates the underlying OFDM capacity is attained, due to the ill-conditioning of the overall system linear statistical model. The proposed scheme compromises neither the bandwidth efficiency nor the error performance of the underlying OFDM in AWGN and slow fading channels, at the cost of increased transmission power.

The main motivation behind the proposed approach stems from the fact that problems modeled by ill-posed operators prevent the extraction of accurate estimates as a result of their instability. The mutual information between the transmitter and any potential unlicensed receiver is small, irrespective of the signal dimensions, so that almost perfect secrecy is attained.