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arXiv:1411.2367 · International Conference on Communications

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

Shuiyin Liu, Yi Hong, Emanuele Viterbo

Published Jun 1, 2015• 2 citations
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Abstract

The Unshared Secret Key Cryptography (USK), recently proposed by the authors, guarantees Shannon's 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 Shannon's ideal secrecy can be achieved with an arbitrarily small outage probability.

DOI
10.1109/icc.2015.7248978

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The Unshared Secret Key Cryptography (USK), recently proposed by the authors, guarantees Shannon's 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 Shannon's ideal secrecy can be achieved with an arbitrarily small outage probability.
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 Shannon's 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.
Current security techniques can be implemented either by requiring a secret key exchange or depending on assumptions about the communication channels. In this paper, we show that, by using a physical layer technique known as artificial noise, it is feasible to protect secret data without any form of secret key exchange and any restriction on the communication channels. Specifically, we analyze how the artificial noise can achieve practical secrecy. By treating the artificial noise as an unshared one-time pad secret key, we show that the proposed scheme also achieves Shannon's perfect secrecy. Moreover, we show that achieving perfect secrecy is much easier than ensuring non-zero secrecy capacity, especially when the eavesdropper has more antennas than the transmitter. Focusing on the practical applications, we show that practical secrecy and strong secrecy can be guaranteed even if the eavesdropper attempts to remove the artificial noise. We finally show the connections between traditional cryptography and physical layer security.
In this paper, assuming an interference-limited eavesdropper scenario, the secrecy outage performance of multiple-input multiple-output wiretap channels with transmit antenna selection is investigated.Considering that the transmitter (Tx) and the receiver (Rx) are equipped with NA and NB antennas, respectively, while the passive eavesdropper is set with NE antennas, closed-form expressions for the secrecy outage probability and non-zero secrecy rate are derived.In our analysis, a selection combining (SC) scheme is employed at the Rx, while the eavesdropper uses a maximal-ratio combining (MRC) one.The derived outage expressions hold for arbitrary power distributed jamming signals.An asymptotic analysis is carried out to show the impact of the number of jamming signals and number of antennas on the secrecy outage performance.Interestingly, our results show that the diversity order equals to min(M, NANB), with M denoting the number of jamming signals.
A practical uncoordinated cooperative jamming (UCJ) scheme with multiple single-antenna helpers is proposed in this paper to enhance the physical layer security of single-input-multiple-output (SIMO) wiretap channel. In the scheme, both the intended receiver and the eavesdropper are equipped with multiple antennas and apply the minimum mean-square error (MMSE) combiner. The multiple uncoordinated single-antenna helpers transmit jamming signals independently to confound the eavesdropper, and we focus on power allocation for the helpers to solve the secrecy rate maximization (SRM) problem. Assuming that the statistical channel state information (CSI) concerning the eavesdropper is available, a convex conservative secrecy outage probability (SOP) constraint is derived and then used to solve the SRM problem with DC (difference of convex function) programming method. Furthermore, a bisection-like refinement method is provided to find a quality solution of the SRM problem with the original SOP constraint. Numerical results show that the proposed scheme has good secrecy performance especially when the number of helpers is large.
Abstract—This paper addresses secure communications over MIMO wiretap channels with the help of multiple cooperative jammers. The worst-case scenario for Alice, Bob and jammers is considered: Eve has the knowledge of all channel matrices, while neither her channel matrix nor her location is known to the remaining terminals. We propose an artificial noise aided cooperative jamming (AN-CJ) scheme, allowing the total jamming signals to be nulled at Bob. The new scheme is valid for the case where the eavesdropper has more antennas than the transmitter. To evaluate the performance of the AN-CJ scheme, we first derive a closed-form expression for the achievable ergodic secrecy rate with Gaussian input alphabets. Then, we show how Gaussian input alphabets achieve the ergodic secrecy capacity. I.