Construction of Codes for Wiretap Channel and Secret Key Agreement from Correlated Source Outputs by Using Sparse Matrices
Jun Muramatsu, Shigeki Miyake
备注：
A part of this paper is presented in part at 2009 IEEE Information Theory Workshop (ITW2009), Taormina, Italy, pp.105-109, 2009. This paper is submitted to IEEE Transactions on Information Theory. 34 pages
发表信息：
IEEE Transactions on Information Theory, vol. 58, no. 2, pp. 671-692, Feb. 2012
The aim of this paper is to prove coding theorems for the wiretap channel coding problem and secret key agreement problem based on the the notion of a hash property for an ensemble of functions. These theorems imply that codes using sparse matrices can achieve the optimal rate. Furthermore, fixed-rate universal coding theorems for a wiretap channel and a secret key agreement are also proved.
We consider the problem of multiterminal secret key agreement (SKA) in wiretapped source model where terminals have access to samples of correlated random variables from a publicly known joint probability distribution. The adversary has access to a side information variable, that is correlated with terminals' variables. We focus on a special type of terminal variables in this model, known as Tree-PIN, where the relation between variables of the terminals can be represented by a tree. The study of Tree-PIN source model is of practical importance as it can be realized in wireless network environ…
While the wiretap secret key capacity remains unknown for general source models even in the two-user case, we obtained a single-letter characterization for a large class of multi-user source models with a linear wiretapper who can observe any linear combinations of the source. We introduced the idea of irreducible sources to show existence of an optimal communication scheme that achieves perfect omniscience with minimum leakage of information to the wiretapper. This implies a duality between the problems of wiretap secret key agreement and secure omniscience, and such duality potentially holds…
In this paper we consider a wiretap channel with a secret key buffer. We use the coding scheme of [1] to enhance the secrecy rate to the capacity of the main channel, while storing each securely transmitted message in the secret key buffer. We use the oldest secret bits from the buffer to be used as a secret key to transmit a message in a slot and then remove those bits. With this scheme we are able to prove stronger results than those in [1]. i.e., not only the message which is being transmitted currently, but all the messages transmitted in last $N_1$ slots are secure with respect to all the…
We analyze arbitrarily varying classical-quantum wiretap channels.These channels are subject to two attacks at the same time: one passive (eavesdropping), and one active (jamming). We progress on previous works by introducing a reduced class of allowed codes that fulfills a more stringent secrecy requirement than earlier definitions. In addition, we prove that non-symmetrizability of the legal link is suficient for equality of the deterministic and the common randomness assisted secrecy capacities. At last, we focus on analytic properties of both secrecy capacities: We completely characterize …
The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret key distillation capacity aga…
The coding problem for wiretap channels with causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied. We are concerned here particularily with the problem of achievable secret-message secret-key rate pairs under the semantic security criterion. Our main result extends all the previous results on achievable rates as given by Chia and El Gamal [10], Fujita [11], and Han and Sasaki [23]. In order to do this, we first derive a unifying theorem (Theorem 2) with causal CSI at Alice, which follows immediately by leveraging the unifying seminal theor…
We consider a network coding problem where the destination wants to recover the sum of the signals (Gaussian random variables or random finite field elements) at all the source nodes, but the sum must be kept secret from an eavesdropper that can wiretap on a subset of edges. This setting arises naturally in sensor networks and federated learning, where the secrecy of the sum of the signals (e.g. weights, gradients) may be desired. While the case for finite field can be solved, the case for Gaussian random variables is surprisingly difficult. We give a simple conjecture on the necessary and suf…
It is a well-known fact that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this work, an achievable scheme for the wiretap channel with generalized feedback is presented. This scheme, which uses the feedback signal to generate a shared secret key between the legitimate users, encrypts the message to be sent at the bit level. New capacity results for a class of channels are provided, as well as some new insights into the secret key agreement problem. Moreover, this scheme recovers previ…
Security constraint results in \textit{rate-loss} in wiretap channels. In this paper we propose a coding scheme for two user Multiple Access Channel with Wiretap (MAC-WT), where previous messages are used as a key to enhance the secrecy rates of both the users until we achieve the usual capacity region of a Multiple Access Channel (MAC) without the wiretapper (Shannon capacity region). With this scheme all the messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal we introduce secret key buffers at both the user…
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievabili…
We consider the secret key agreement problem under the multiterminal source model proposed by Csiszár and Narayan. A single-letter characterization of the secrecy capacity is desired but remains unknown except in the extreme case with unlimited public discussion and without wiretapper's side information. Taking the problem to the opposite extreme by requiring the public discussion rate to be zero asymptotically, we obtain the desired characterization under surprisingly general setting with wiretapper's side information, silent users, trusted and untrusted helpers. An immediate consequence of t…
This paper considers the problem of secret-key agreement with public discussion subject to a peak power constraint $A$ on the channel input. The optimal input distribution is proved to be discrete with finite support. The result is obtained by first transforming the secret-key channel model into an equivalent Gaussian wiretap channel with better noise statistics at the legitimate receiver and then using the fact that the optimal distribution of the Gaussian wiretap channel is discrete. To overcome the computationally heavy search for the optimal discrete distribution, several suboptimal scheme…
The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed in which a common message has to be broadcast to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of sufficiently high rates with both legitimate receivers, which can be used in different ways: they can be used as one-time pads to encrypt the common message, as fictitious messages for wiretap coding, or as a hybrid of these. In this paper, capacity results are established when the broadcast channels involv…
An artificial-noise (AN)-aided beamformer specific to correlated main and wiretap channels is designed in this paper. We consider slow-fading multiple-input-single-output (MISO) wiretap channels with a passive single-antenna eavesdropper, in which independent transmitter-side and correlated receiver-side are assumed. Additionally, the source has accurate main channel information and statistical wiretap channel information. To reduce the secrecy loss due to receiver-side correlation, this paper proposes the scheme of channel-correlation-enabled transmit optimization. Particularly, the correlati…
This paper presents a detailed secrecy outage performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single input multiple output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U…
For the multiterminal secret key agreement problem, new single-letter lower bounds are obtained on the public discussion rate required to achieve any given secret key rate below the secrecy capacity. The results apply to general source model without helpers or wiretapper's side information but can be strengthened for hypergraphical sources. In particular, for the pairwise independent network, the results give rise to a complete characterization of the maximum secret key rate achievable under a constraint on the total discussion rate.
The coding problem for wiretap channels with causal channel state information available at the encoder and/or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to naive wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and investigated in details from the viewpoint of achievable rates with strong secrecy. The general wiretap channel with various directions of channel state info…
We consider wiretap channels with uncertainty on the eavesdropper channel under (i) noisy blockwise type II, (ii) compound, or (iii) arbitrarily varying models. We present explicit wiretap codes that can handle these models in a unified manner and only rely on three primitives, namely source coding with side information, universal hashing, and distribution approximation. Our explicit wiretap codes achieve the best known single-letter achievable rates, previously obtained non-constructively, for the models considered. Our results are obtained for strong secrecy, do not require a pre-shared secr…
We propose a new secure transmission scheme for uplink multiple-input single-output (MISO) orthogonal-frequency multiplexing (OFDM) systems in the presence of multiple eavesdroppers. Our proposed scheme utilizes the sub-channels orthogonality of OFDM systems to simultaneously transmit data and secret key symbols. The base station, Bob, shares secret key symbols with the legitimate user, Alice, using wiretap coding over a portion of the sub-channels. Concurrently, Alice uses the accumulated secret keys in her secret-key queue to encrypt data symbols using a one time pad (OTP) cipher and transmi…
Information leakage in Wyner's wiretap channel model is usually defined as the mutual information between the secret message and the eavesdropper's received signal. We define a new quantity called "conditional information leakage given the eavesdropper's received signals," which expresses the amount of information that eavesdropper gains from his/her received signal. A benefit of introducing this quantity is that we can develop a fast algorithm for computing the conditional information leakage, which has linear complexity in the code length $n$, while the complexity for computing the usual inf…
The conventional channel resolvability problem refers to the determination of the minimum rate required for an input process so that the output distribution approximates a target distribution in either the total variation distance or the relative entropy. In contrast to previous works, in this paper, we use the (normalized or unnormalized) Rényi divergence (with the Rényi parameter in $[0,2]\cup\{\infty\}$) to measure the level of approximation. We also provide asymptotic expressions for normalized Rényi divergence when the Rényi parameter is larger than or equal to $1$ as well as (lower and u…
In this paper, new two-user multiple access wiretap channel models are studied. First, the multiple access wiretap channel II with a discrete memoryless main channel, under three different wiretapping scenarios, is introduced. The wiretapper, as in the classical wiretap channel II model, chooses a fixed-length subset of the channel uses on which she obtains noise-free observations of one of the codewords, a superposition of the two codewords, or each of the two codewords. These thus extend the recently examined wiretap channel II with a noisy main channel to a multiple access setting with a va…
The problem of sending a secret message over the Gaussian multiple-input multiple-output (MIMO) wiretap channel is studied. While the capacity of this channel is known, it is not clear how to construct optimal coding schemes that achieve this capacity. In this work, we use linear operations along with successive interference cancellation to attain effective parallel single-antenna wiretap channels. By using independent scalar Gaussian wiretap codebooks over the resulting parallel channels, the capacity of the MIMO wiretap channel is achieved. The derivation of the schemes is based upon joint t…
In this paper, we consider the transmitter optimization problem in slow fading multiple-input-single-output (MISO) wiretap channel. The source transmits a secret message intended for $K$ users in the presence of $J$ non-colluding eavesdroppers, and operates under a total power constraint. The channels between the source and all users and eavesdroppers are assumed to be slow fading, and only statistical channel state information (CSI) is known at the source. For a given code rate and secrecy rate pair of the wiretap code, denoted by $(R_{D}, R_{s})$, we define the non-outage event as the joint …
A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems in the presence of a bath. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret key agreement between two quantum systems. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity called the bidirectional max-Rains information. Our upper bound on the secret-key-agreement capacity of a bipartite quantum interaction is given by a related quantity calle…
A polar coding scheme is proposed for the Wiretap Broadcast Channel with two legitimate receivers and one eavesdropper. We consider a model in which the transmitter wishes to send different confidential (and non-confidential) information to each legitimate receiver. First, we compare two inner-bounds on the achievable region of this model from the literature, and then we design a polar coding scheme that achieves the stronger one. In the proposed scheme, the encoding uses polar-based Marton's coding, where one inner-layer must be reliably decoded by both legitimate receivers, and each receiver…
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted codeword symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by sol…
Composable, unconditional security without a Quantum secret key: public broadcast channels and their conceptualizations, adaptive bit transmission rates, fidelity pruning under wiretaps
This paper investigates the problem of secret key generation over a wiretap channel when the terminals observe correlated sources. These sources are independent of the main channel and the users overhear them before the transmission takes place. A novel achievable scheme is proposed, and its optimality is shown under certain less-noisy conditions. This result improves upon the existing literature where the more stringent condition of degradedness is required. Furthermore, numerical evaluation of the proposed scheme and previously reported results for a binary model are presented; a comparison …
This paper employs equal-image-size source partitioning techniques to derive the capacities of the general discrete memoryless wiretap channel (DM-WTC) under four different secrecy criteria. These criteria respectively specify requirements on the expected values and tail probabilities of the differences, in absolute value and in exponent, between the joint probability of the secret message and the eavesdropper's observation and the corresponding probability if they were independent. Some of these criteria reduce back to the standard leakage and variation distance constraints that have been pre…
