Shuiyin Liu

Practical Secrecy using Artificial Noise

In this paper, we consider the use of artificial noise for secure communications. We propose the notion of practical secrecy as a new design criterion based on the behavior of the eavesdroppers error probability P_{E}, as the signal-to-noise ratio goes to infinity. We then show that the practical secrecy can be guaranteed by the randomly distributed artificial noise with specified power. We show that it is possible to achieve practical secrecy even when the eavesdropper can afford more antennas than the transmitter.

Artificial Noise Revisited

The artificial noise (AN) scheme, proposed by Goel and Negi, is being considered as one of the key enabling technology for secure communications over multiple-output multiple-input wiretap channels. However, the decrease in secrecy rate due to the increase in the number of Eves antennas is not well understood. In this paper, we develop an analytical framework to characterize the secrecy rate of the AN scheme as a function of Eves SNR, Bobs SNR, the number of antennas in each terminal, and the power allocation scheme. We first derive a closed-form expression for the average secrecy rate. We then derive a closed-form expression for the asymptotic instantaneous secrecy rate with large number of antennas at all terminals. Finally, we derive simple lower and upper bounds on the average/instantaneous secrecy rate that provide a tool for the system design.

Unshared Secret Key Cryptography

Current security techniques can be implemented with either secret key exchange or physical-layer wiretap codes. In this paper, we investigate an alternative solution for MIMO wiretap channels. Inspired by the artificial noise (AN) technique, we propose the unshared secret key (USK) cryptosystem, where the AN is redesigned as a one-time pad secret key aligned within the null space between a transmitter and a legitimate receiver. The proposed USK cryptosystem is a new physical-layer cryptographic scheme, which was obtained by combining traditional network-layer cryptography and physical-layer security. Unlike previously studied AN techniques, rather than ensuring nonzero secrecy capacity, the USK is valid for an infinite lattice input alphabet and guarantees Shannons ideal secrecy and perfect secrecy without the need for secret key exchange. We then show how ideal secrecy can be obtained for finite lattice constellations with an arbitrarily small outage.

Guaranteeing Positive Secrecy Capacity for MIMOME Wiretap Channels With Finite-Rate Feedback Using Artificial Noise

While the impact of finite-rate feedback on the capacity of fading channels has been extensively studied in the literature, not much attention has been paid to this problem under secrecy constraint. In this work, we study the ergodic secret capacity of a multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channel with quantized channel state information (CSI) at the transmitter and perfect CSI at the legitimate receiver, under the assumption that only the statistics of eavesdropper CSI is known at the transmitter. We refine the analysis of Lin et al.s random vector quantization (RVQ) based artificial noise (AN) scheme, where a heuristic upper bound on the secrecy rate loss (compared to the perfect CSI case) was given. We propose a lower bound on the ergodic secrecy capacity. We show that the lower bound and the secrecy capacity with perfect CSI coincide asymptotically as the number of feedback bits and the AN power go to infinity. For practical applications, we propose a very efficient quantization codebook construction method for the two transmit antennas case.

Artificial noise revisited: When Eve has more antennas than Alice

We consider secure communications over MIMO wiretap channels, in the presence of a passive eavesdropper with an unlimited number of antennas. In this scenario, we characterize the performance of the artificial noise scheme proposed by Goel et al., and show that non-zero secrecy capacity is available even when the eavesdropper has more antennas than the transmitter. Our results are derived based on the fraction of the transmission power used for artificial noise and the ratio of the channel noise variances of the eavesdropper and the intended receiver. Finally, we investigate the attack option for the eavesdropper to drive the secrecy rate to zero by increasing the number of antennas.

Unshared Secret Key Cryptography: Finite constellation inputs and ideal secrecy outage

The Unshared Secret Key Cryptography (USK), recently proposed by the authors, guarantees Shannons ideal secrecy and perfect secrecy for MIMO wiretap channels, without requiring secret key exchange. However, the requirement of infinite constellation inputs limits its applicability to practical systems. In this paper, we propose a practical USK scheme using finite constellation inputs. The new scheme is based on a cooperative jamming technique, and is valid even if the eavesdropper has more antennas than the transmitter. We show that Shannons ideal secrecy can be achieved with an arbitrarily small outage probability.

Unshared secret key cryptography: Achieving Shannon's ideal secrecy and perfect secrecy

In cryptography, a shared secret key is normally mandatory to encrypt the confidential message. In this work, we propose the unshared secret key (USK) cryptosystem. Inspired by the artificial noise (AN) technique, we align a one-time pad (OTP) secret key within the null space of a multiple-output multiple-input (MIMO) channel between transmitter and legitimate receiver, so that the OTP is not needed by the legitimate receiver to decipher, while it is fully affecting the eavesdroppers ability to decipher the confidential message. We show that the USK cryptosystem guarantees Shannons ideal secrecy and perfect secrecy, if an infinite lattice input alphabet is used.

Polar Codes for Block Fading Channels

In this paper, we consider the design of polar codes for block fading channels. The key idea is to treat the fading process as a natural polarization, i.e., the reliability of a symbol in a fading block varies with its fading coefficient. This new viewpoint inspires us to construct polar codes tailored for fading channels by matching code polarization with fading polarization. The resulting codes enjoy an explicit construction, and are shown to provide significant gain with respect to conventional polar BICM schemes and LDPC codes.

Adaptive polar coding with high order modulation for block fading channels

We consider the design of polar codes for block fading channels. The key idea is to combine modulation, fading, and coding in a single entity. This design is based on two facts: (i) for each fading block, symbols with different fading coefficient has different reliability; (ii) for each symbol, different bit levels of a high order modulation observe different noise levels. In other words, the bit channels are partially polarized by modulation and fading. This new viewpoint inspires us to construct polar codes by matching code polarization perfectly with modulation polarization and fading polarization. The resulting codes adapt to the channel quality fluctuation, thus provide better performance than conventional polar BICM schemes and LDPC codes.

Wiretap channel with finite-rate feedback

While the impact of finite-rate feedback on the capacity of fading channels has been extensively studied in the literature, not much attention has been paid to this problem under secrecy constraint. This paper provides a survey of recent research on physical-layer security considering quantized channel state information (CSI) at the transmitter and perfect CSI at the legitimate receiver, under the assumption that only the statistics of eavesdropper CSI is known at the transmitter. We start by introducing the classical notion of secrecy capacity. Then we show how finite-rate feedback degrades the secrecy capacity.