Secure Nested Lattices for MIMO Broadcast Channel With Confidential Messages

In this letter, our focus is on the strong secrecy over the two-user multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM). Different from existing works on the broadcast channel, we explore the strong secrecy of multiuser case with confidential constraints. In this scenario, each transmitter aims to send secure messages to the corresponding receiver while keeping them private from the other receiver, ensuring the transmitted messages remain confidential. In the transmission scheme, the confidential message associated the auxiliary message is encoded to the point of the nested lattice. The encoded message is sent in the null space of the channel to achieve secure transmission. The decoding scheme that attains secrecy with confidential constraints is provided. Applying information theoretic methods, we derive a new outer bound on the quantity of leaked information, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}\frac {n_{r}}{nk}\log {V(\boldsymbol {\Lambda }_{e})}$ </tex-math></inline-formula>. According to the new outer bound, the information leakage rises with the number of receiving antennas and the volume of fundamental region of the nested lattices, but is not affected by the transmitting antennas.