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Unshared Secret Key Cryptography: (Invited Paper)

Shuiyun Liu, Yi Hong, Emanuele Viterbo

Published Jan 1, 2014• 0 citations
Publisher

Abstract

Abstract—Inspired by the artificial noise technique by Goel et al., we propose an unshared secret key (USK) cryptosystem, where the artificial noise is redesigned as a one-time pad secret key aligned within the null space between transmitter and legitimate receiver. Unlike previously studied artificial noise techniques, rather than ensuring non-zero secrecy capacity, the USK cryptosystem guarantees Shannon’s perfect secrecy without the need of secret key exchange. I.

DOI
10.3929/ethz-a-010094663

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Abstract—Inspired by the artificial noise technique by Goel et al., we propose an unshared secret key (USK) cryptosystem, where the artificial noise is redesigned as a one-time pad secret key aligned within the null space between transmitter and legitimate receiver. Unlike previously studied artificial noise techniques, rather than ensuring non-zero secrecy capacity, the USK cryptosystem guarantees Shannon’s perfect secrecy without the need of secret key exchange. I.
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.
The basic problems We saw in Chapter 5 that the one-time pad is a cryptosystem that provides perfect secrecy, so why not use it? The obvious reason is that the key needs to be as long as the message and the users need to decide on this secret key in advance using a secure channel. Having introduced public key cryptography in Chapter 7 one might wonder why anyone would want to use a symmetric cryptosystem. Why not simply use RSA or some other public key cryptosystem and dispense with the need to exchange secret keys once and for all? The problem with this approach is that symmetric cryptosystems are generally much faster. For example in 1996, DES was around 1000 times faster than RSA. In situations where a large amount of data needs to be encrypted quickly or the users are computationally limited, symmetric cryptosystems still play an important role. A major problem they face is how to agree a common secret key to enable communications to begin. This basic ‘key exchange problem’ becomes ever more severe as communication networks grow in size and more and more users wish to communicate securely. Indeed while one could imagine. Alice and Bob finding a way to exchange a secret key securely the same may not be true if you have a network with 1000 users.
The broadcast channel with independent secret keys is studied. In this scenario, a common message has to be securely broadcast to two legitimate receivers in the presence of an eavesdropper. The transmitter shares with each legitimate receiver an independent secret key of arbitrary rate. These keys can either be used as one-time pads to encrypt the common message or can be interpreted as fictitious messages used as randomization resources for wiretap coding. Both approaches are discussed and the secrecy capacity is derived for various cases. Depending on the qualities of the legitimate and eavesdropper channels, either a one-time pad, wiretap coding, or a combination of both turns out to be capacity-achieving.
In Chapter 3, we considered the transmission of information over a noisy broadcast channel subject to reliability and security constraints; we showed that appropriate coding schemes can exploit the presence of noise to confuse the eavesdropper and guarantee some amount of information-theoretic security. It is important to note that the wiretap channel model assumes that all communications occur over the channel, hence communications are inherently rate-limited and one-way. Consequently, the results obtained do not fully capture the role of noise for secrecy; in particular, for situations in which the secrecy capacity is zero, it is not entirely clear whether this stems from the lack of any “physical advantage” over the eavesdropper or the restrictions imposed on the communication schemes. The objective of this chapter is to study more precisely the fundamental role of noise in information-theoretic security. Instead of studying how we can communicate messages securely over a noisy channel, we now analyze how much secrecy we can extract from the noise itself in the form of a secret key. Specifically, we assume that the legitimate parties and the eavesdropper observe the realizations of correlated random variables and that the legitimate parties attempt to agree on a secret key unknown to the eavesdropper. To isolate the role played by noise, we remove restrictions on communication schemes and we assume that the legitimate parties can distill their key by communicating over a two-way, public, noiseless , and authenticated channel at no cost.