An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> E. Transmit Signal Design Based on Channel Reciprocity <s> We propose the new technique of physical-layer cryptography based on using a massive MIMO channel as a key between the sender and desired receiver, which need not be secret. The goal is for low-complexity encoding and decoding by the desired transmitter-receiver pair, whereas decoding by an eavesdropper is hard in terms of prohibitive complexity. The decoding complexity is analyzed by mapping the massive MIMO system to a lattice. We show that the eavesdropper's decoder for the MIMO system with M-PAM modulation is equivalent to solving standard lattice problems that are conjectured to be of exponential complexity for both classical and quantum computers. Hence, under the widely-held conjecture that standard lattice problems are hard to solve in the worst-case, the proposed encryption scheme has a more robust notion of security than that of the most common encryption methods used today such as RSA and Diffie-Hellman. Additionally, we show that this scheme could be used to securely communicate without a pre-shared secret and little computational overhead. Thus, by exploiting the physical layer properties of the radio channel, the massive MIMO system provides for low-complexity encryption commensurate with the most sophisticated forms of application-layer encryption that are currently known. <s> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> E. Transmit Signal Design Based on Channel Reciprocity <s> A new technique is presented for securing a space-time block code in the presence of an eavesdropper without channel state information (CSI) at the transmitter. Assuming channel reciprocity between the transmitter and the intended receiver, we use the receive signal strength indicator, which is much easier to estimate reliably than CSI, to randomly rotate the information symbols at each transmit antenna without increasing the transmit signal's peak-to-average ratio. It is shown that the proposed scheme guarantees full diversity to an intended recipient while reducing the diversity order of an eavesdropper to zero even in the presence of perfect channel state information. <s> BIB002 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> E. Transmit Signal Design Based on Channel Reciprocity <s> In this paper, we consider the wire-tap channel model consisting of three users, namely, a transmitter, a legal receiver, and an eavesdropper, where the eavesdropper has possible unlimited centralized or distributed multiple antennas, while the legal user has just a single antenna. With this model, we study the realization of strict positive secrecy rate through Rayleigh flat fading channels using M-ary phase shift keying (PSK) and orthogonal space-time block code (OSTBC) based on channel reciprocal principle. We demonstrate that the information rate at the eavesdropper can be reduced to zero and a positive communication rate at the legal receiver can be realized if the transmitter employs a proper phase precoder based on the channel reciprocal, and uses OSTBC and M-ary PSK modulations for data transmissions. Application examples of space-time codes for positive secrecy rate are illustrated. As we have given the eavesdropper more capabilities than the legal receiver and thus captured a worst case scenario, any positive secrecy rate that is achieved serves as a lower bound on the secrecy capacity. <s> BIB003 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> E. Transmit Signal Design Based on Channel Reciprocity <s> The generation of secret keys from reciprocal wireless channel by exploiting their randomness nature, is an emerging area of interest to provide secure communication. One of the main challenges in this domain is to increase the secret key length, extracted from the shared channel coefficients between two legitimate communication parties, while maintaining its randomness and uniformity. In this work, we develop a practical key generation method, based on channel quantization with singular value decomposition (CQSVD), which is capable of significantly increasing the generated secret key in MIMO systems. This is achieved through quantizing the phases and amplitudes of the estimated MIMO channel coefficient's matrix by using an alternative form of SVD, where the key sequence is extracted from the orthogonal basis functions of the decomposed channel. In this method, it is shown that for an M ×M antenna system, with M ::: 2 ::: independent channel fading coefficients, a secret key sequence of length 2M ::: 3 ::: can be generated. The extracted key sequence is transformed to a random phase sequence, which is then used to manipulate the transmitted data on a symbol level basis rather than bit level-basis, to provide more secure communication. The comparative simulation results show that the proposed CQSVD method outperforms the state of the art secret key generation methods. <s> BIB004
A group of transmission strategies in the literature of physical layer security rely on the assumption of channel reciprocity, that is, the transmitter and the legitimate receiver observe the same channel, simultaneously. For systems working in time division duplex (TDD) mode, this property can be used to enable the transmitter to obtain the MCSI using pilot signals transmitted from the legitimate receiver. In BIB003 , a secure transmission scheme is proposed over a MIMO wiretap channel under the assumption that no training signals are transmitted by Alice, and hence, no CSI is available at Bob or Eve. Alice realizes an orthogonal space-time block coded PSK transmission and uses the CSI she obtains from the reverse channel estimation to design a phase shifting precoder, which compensates the phase shift by the channel. Therefore, Bob can recover the transmitted messages with no need to CSI. On the other hand, Eve who observes an independent channel can only recover the information with non-coherent detection, ensuring positive secrecy rates over MIMO wiretap channels. In the scenarios with channel reciprocity, when channel estimation is carried out both in the forward (from Alice to Bob) and the reverse (from Bob to Alice) directions, the channel between Alice and Bob can serve as a source of common randomness, which can further improve secrecy. This common randomness is used in BIB004 for generation of a random phase sequence, which is then used to manipulate the transmitted symbols (by simply multiplying them with the obtained random phase terms). Since the eavesdropper is unable to find out these random phase values, an enhanced secrecy is attained. Allen et al. BIB002 propose a secure Alamouti scheme using channel reciprocity. In their proposed approach, after performing a two-way probing, the legitimate users exchange a secret key based on their received signal strength indicator, and this key is used for rotation of the PSK constellation from one codeword to the next. A cross-layer analysis of secure MIMO transmission is given in BIB001 . It is shown that when using the main channel as a (not necessarily secret) key between the legitimate users, complexity of the eavesdropper's decoding of the legitimate receiver's message is as hard as solving standard lattice problems, and it grows exponentially in the number of transmit antennas.