Authentication over Noisy Channels

In this work, message authentication over noisy channels is studied. The model developed in this paper is the authentication theory counterpart of Wyner's wiretap channel model. Two types of opponent attacks, namely impersonation attacks and substitution attacks, are investigated for both single message and multiple message authentication scenarios. For each scenario, information theoretic lower and upper bounds on the opponent's success probability are derived. Remarkably, in both scenarios, lower and upper bounds are shown to match, and hence the fundamental limit of message authentication over noisy channels is fully characterized. The opponent's success probability is further shown to be smaller than that derived in the classic authentication model in which the channel is assumed to be noiseless. These results rely on a proposed novel authentication scheme in which key information is used to provide simultaneous protection again both types of attacks.Comment: Appeared in the Proceedings of the 45th Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, September 26 - 28, 200

Quantum authentication with key recycling

We show that a family of quantum authentication protocols introduced in [Barnum et al., FOCS 2002] can be used to construct a secure quantum channel and additionally recycle all of the secret key if the message is successfully authenticated, and recycle part of the key if tampering is detected. We give a full security proof that constructs the secure channel given only insecure noisy channels and a shared secret key. We also prove that the number of recycled key bits is optimal for this family of protocols, i.e., there exists an adversarial strategy to obtain all non-recycled bits. Previous works recycled less key and only gave partial security proofs, since they did not consider all possible distinguishers (environments) that may be used to distinguish the real setting from the ideal secure quantum channel and secret key resource.Comment: 38+17 pages, 13 figures. v2: constructed ideal secure channel and secret key resource have been slightly redefined; also added a proof in the appendix for quantum authentication without key recycling that has better parameters and only requires weak purity testing code

Message Authentication Code over a Wiretap Channel

Message Authentication Code (MAC) is a keyed function $f_K$ such that when Alice, who shares the secret $K$ with Bob, sends $f_K(M)$ to the latter, Bob will be assured of the integrity and authenticity of $M$. Traditionally, it is assumed that the channel is noiseless. However, Maurer showed that in this case an attacker can succeed with probability $2^{-\frac{H(K)}{\ell+1}}$ after authenticating $\ell$ messages. In this paper, we consider the setting where the channel is noisy. Specifically, Alice and Bob are connected by a discrete memoryless channel (DMC) $W_1$ and a noiseless but insecure channel. In addition, an attacker Oscar is connected with Alice through DMC $W_2$ and with Bob through a noiseless channel. In this setting, we study the framework that sends $M$ over the noiseless channel and the traditional MAC $f_K(M)$ over channel $(W_1, W_2)$. We regard the noisy channel as an expensive resource and define the authentication rate $\rho_{auth}$ as the ratio of message length to the number $n$ of channel $W_1$ uses. The security of this framework depends on the channel coding scheme for $f_K(M)$. A natural coding scheme is to use the secrecy capacity achieving code of Csisz\'{a}r and K\"{o}rner. Intuitively, this is also the optimal strategy. However, we propose a coding scheme that achieves a higher $\rho_{auth}.$ Our crucial point for this is that in the secrecy capacity setting, Bob needs to recover $f_K(M)$ while in our coding scheme this is not necessary. How to detect the attack without recovering $f_K(M)$ is the main contribution of this work. We achieve this through random coding techniques.Comment: Formulation of model is change

On the Achievable Error Region of Physical Layer Authentication Techniques over Rayleigh Fading Channels

For a physical layer message authentication procedure based on the comparison of channel estimates obtained from the received messages, we focus on an outer bound on the type I/II error probability region. Channel estimates are modelled as multivariate Gaussian vectors, and we assume that the attacker has only some side information on the channel estimate, which he does not know directly. We derive the attacking strategy that provides the tightest bound on the error region, given the statistics of the side information. This turns out to be a zero mean, circularly symmetric Gaussian density whose correlation matrices may be obtained by solving a constrained optimization problem. We propose an iterative algorithm for its solution: Starting from the closed form solution of a relaxed problem, we obtain, by projection, an initial feasible solution; then, by an iterative procedure, we look for the fixed point solution of the problem. Numerical results show that for cases of interest the iterative approach converges, and perturbation analysis shows that the found solution is a local minimum

Analysis of Channel-Based User Authentication by Key-Less and Key-Based Approaches

User authentication (UA) supports the receiver in deciding whether a message comes from the claimed transmitter or from an impersonating attacker. In cryptographic approaches messages are signed with either an asymmetric or symmetric key, and a source of randomness is required to generate the key. In physical layer authentication (PLA) instead the receiver checks if received messages presumably coming from the same source undergo the same channel. We compare these solutions by considering the physical-layer channel features as randomness source for generating the key, thus allowing an immediate comparison with PLA (that already uses these features). For the symmetric-key approach we use secret key agreement, while for asymmetric-key the channel is used as entropy source at the transmitter. We focus on the asymptotic case of an infinite number of independent and identically distributed channel realizations, showing the correctness of all schemes and analyzing the secure authentication rate, that dictates the rate at which the probability that UA security is broken goes to zero as the number of used channel resources (to generate the key or for PLA) goes to infinity. Both passive and active attacks are considered and by numerical results we compare the various systems