We propose a threshold secret sharing scheme for secure communications in multiple input and multiple output wireless networks. In the proposed scheme, the base station divides the secret data into Nmin parts using a polynomial of degree T-1 (T≤Nmin) and transmits the divided data to the legitimate user by beamforming with multiple spatial dimensions. Then, at the user, the secret data can be reconstructed with a sufficient number (≥T) of divided parts by using the Lagrange interpolating polynomial. However, it is difficult for the eavesdropper to correctly estimate the T parts due to the difference between the main channel with beamforming and the eavesdropping channel in the physical layer, which results in the failure of secret data reconstruction. The numerical results show that the eavesdropping probability of the proposed scheme is lower than those of conventional schemes. Moreover, we analyze the symbol-error-rate and show that the theoretical result is well aligned with simulation results.
Threshold Secret Sharing Transmission against Passive Eavesdropping in MIMO Wireless Networks