Wyner's elegant model of wiretap channel exploits noise in the communication channel to provide perfect secrecy against a computationally unlimited eavesdropper without requiring a shared key. We consider an adversarial model of wiretap channel proposed in [18,19] where the adversary is active: it selects a fraction @math of the transmitted codeword to eavesdrop and a fraction @math of the codeword to corrupt by "adding" adversarial error. It was shown that this model also captures network adversaries in the setting of 1-round Secure Message Transmission [8]. It was proved that secure communication (1-round) is possible if and only if @math . In this paper we show that by allowing communicants to have access to a public discussion channel (authentic communication without secrecy) secure communication becomes possible even if @math . We formalize the model of protocol and for two efficiency measures, information rate and message round complexity derive tight bounds. We also construct a rate optimal protocol family with minimum number of message rounds. We show application of these results to Secure Message Transmission with Public Discussion (SMT-PD), and in particular show a new lower bound on transmission rate of these protocols together with a new construction of an optimal SMT-PD protocol.
Maurer's @cite_18 introduced channels first in the context of over wiretap channels; this was also independently considered in @cite_20 . Since the channel is considered free, the established key can be used to send the message securely over this channel and so the communication cost of the message transmission will stay the same as that of the key establishment. In a key agreement protocol, the goal of Alice and Bob is to generate a common random key.
@cite_18 @cite_20
2211831180 1916886752 2217772850 2060644465
Suppose that Alice wishes to send messages to Bob through a communication channel C1, but her transmissions also reach an eavesdropper Eve through another channel C2. This is the wiretap channel model introduced by Wyner in 1975. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of the mutual information between the message and Eve's observations. Wyner showed that the situation is characterized by a single constant Cs, called the secrecy capacity, which has the following meaning: for all e >; 0, there exist coding schemes of rate R ≥ Cs-e that asymptotically achieve the reliability and security objectives. However, his proof of this result is based upon a random-coding argument. To date, despite consider able research effort, the only case where we know how to construct coding schemes that achieve secrecy capacity is when Eve's channel C2 is an erasure channel, or a combinatorial variation thereof. Polar codes were recently invented by Arikan; they approach the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. In this paper, we use polar codes to construct a coding scheme that achieves the secrecy capacity for a wide range of wiretap channels. Our construction works for any instantiation of the wiretap channel model, as long as both C1 and C2 are symmetric and binary-input, and C2 is degraded with respect to C1. Moreover, we show how to modify our construction in order to provide strong security, in the sense defined by Maurer, while still operating at a rate that approaches the secrecy capacity. In this case, we cannot guarantee that the reliability condition will also be satisfied unless the main channel C1 is noiseless, although we believe it can be always satisfied in practice. Assuming that Alice and Bob use a secret noisy channel (modelled by a binary symmetric channel) to send a key, reconciliation is the process of correcting errors between Alice's and Bob's version of the key. This is done by public discussion, which leaks some information about the secret key to an eavesdropper. We show how to construct protocols that leak a minimum amount of information. However this construction cannot be implemented efficiently. If Alice and Bob are willing to reveal an arbitrarily small amount of additional information (beyond the minimum) then they can implement polynomial-time protocols. We also present a more efficient protocol, which leaks an amount of information acceptably close to the minimum possible for sufficiently reliable secret channels (those with probability of any symbol being transmitted incorrectly as large as 15 ). This work improves on earlier reconciliation approaches [R, BBR, BBBSS]. We consider the MIMO wiretap channel, where a legitimate transmitter (Alice) wishes to communicate a confidential message to the legitimate receiver (Bob) over a MIMO channel, while its messages are being eavesdropped by Eve through another MIMO channel. Supposing that Alice uses the nested lattice code proposed in [8], we characterize the expected value of amount of information leakage to Eve, and from minimizing this expected value, we derive a code design criterion for MIMO lattice wiretap codes. The special cases of block and fast fading channels are also studied. We also illustrate our lattice code design criterion using the Alamouti Code as the simplest MIMO code available in the literature. We consider MIMO (Multiple Input Multiple Output) wiretap channels, where a legitimate transmitter Alice is communicating with a legitimate receiver Bob in the presence of an eavesdropper Eve, and communication is done via MIMO channels. We suppose that Alice's strategy is to use an infinite lattice codebook, which then allows her to perform coset encoding. We analyze Eve's probability of correctly decoding the message Alice meant to Bob, and from minimizing this probability, we derive a code design criterion for MIMO lattice wiretap codes. The case of block fading channels is treated similarly, and fast fading channels are derived as a particular case. The Alamouti code is carefully studied as an illustration of the analysis provided.