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arXiv:1410.5021 · IEEE Transactions on Wireless Communications

Unshared Secret Key Cryptography

Shuiyin Liu, Yi Hong, Emanuele Viterbo

Published Oct 20, 2014• 28 citations
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Abstract

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.

DOI
10.1109/twc.2014.2364022

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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.
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 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.
Artificial noise (AN) is an efficient way to enhance physical layer security of multiantenna wiretap channels with a passive eavesdropper (ED) whose channel state information is unavailable. However, the AN is known to be vulnerable to the eavesdropping attack with a large antenna array. To tackle the problem, the artificial fast fading (AFF) scheme has been developed to deliberately randomize the ED's effective channel so as to disrupt its channel estimation. Some recent progress has been made for the secrecy-rate performance of the AFF scheme in the multi-input single-output wiretap channels. However, it turns out that the performance is over-estimated. In this correspondence, we provide a comprehensive analysis on the secrecy-rate of the AFF scheme in general multi-input multi-output wiretap channels. Unfortunately, our analysis reveals a negative result that the conventional AFF is no better than the AN methods, without some pre-shared information among the legitimate parties. This is in fact in stark contrast to the previous observations. Motivated by our analysis, we propose a novel cross layer design by combining the AFF in the physical layer with the secret-keys in the upper layer crypto systems. Then, we mathematically prove that our method asymptotically nullifies the information leakage to the ED in the physical layer for any number of ED antennas even without the aid of the wiretap codes, while further enhancing the upper layer security, and thus provides an enhanced security over the layers. Finally, numerical results demonstrate the accuracy of our analysis and the efficiency of the proposed scheme.
In physical-layer security, communication secrecy is commonly achieved by providing the legitimate receiver a physical-layer advantage over the eavesdropper or, equivalently, by making the eavesdropper's channel more degraded than the legitimate receiver's, a setting traditionally known as the degraded wiretap channel. There may be situations, however, where such advantages cannot be guaranteed. One example is the wireless channel where the legitimate receiver's channel may be more degraded than the eavesdropper's owing to a deep fade (outage), additive interference at the edge of a network cell, etc. To our knowledge, such scenarios have not been remedied in the related literature. Thus, we propose in this work the first physical-layer security scheme that achieves communication in a setting where the eavesdropper has the physical-layer advantage over the legitimate receiver, a scenario that we call the reversely-degraded wiretap channel. Precisely, we show that by constraining the transmitter's input to be discrete uniformly distributed (such as an on-off keying modulation) and by using nonlinear threshold-based signal detection, the legitimate receiver is guaranteed to have a positive secrecy capacity even though the eavesdropper has a better signal-to-noise ratio (SNR). The former requirement on the input distribution is to limit the capacity gains of the eavesdropper at high SNR. The latter requirement allows the communication channel to exhibit supra-threshold stochastic resonance, a phenomenon whereby noise improves signal detection and increases the mutual information. A numerical example is provided to confirm our claims.
In MIMO wireless channels, channel estimation can provide a source of randomness common to sender and receiver that may be used to generate secret keys. These keys can provide information theoretically secure communication. Alternatively, a known MIMO channel allows transmitting artificial noise in the null space of the main channel to secure communication. In this paper, we show that both methods can be combined to further enhance secrecy. Symbols encrypted at the transmitter simultaneously act as message for the intended receiver and as noise for any potential eavesdroppers. We derive expressions for the minimum-guaranteeable secrecy rate as a function of number of symbols encrypted. Given at least one symbol can be encrypted, our proposed method outperforms the standard artificial noise scheme in terms of both secrecy rate and power expenditure. We first analyze the system assuming keys can be instantaneously extracted from channel measurements. We then derive bounds for rates assuming the overhead time required for key generation produces a Gaussian channel-estimation error.