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.
The scheme is information-theoretic security. Key agreement protocol in @cite_18 is over the binary symmetic channel and @cite_20 is over discrete memoryless channel. The adversary is passive and only evasdrop the transmission, which is same as wiretap channel with passive adversary.
@cite_18 @cite_20
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Consider the following scenario: Alice and Bob, two parties who share no secret key initially but whose goal it is to generate a (large amount of) information-theoretically secure (or unconditionally secure) shared secret key, are connected only by an insecure public channel to which an eavesdropper Eve has perfect (read) access. Moreover, there exists a satelite broadcasting random bits at a very low signal power. Alice and Bob can receive these bits with certain bit error probabilities ?A and ?B, respectively (e.g. ?A = ?B = 30 ) while Eve is assumed to receive the same bits much more reliably with bit error probability ?E ? ?A, ?B (e.g. ?E = 1 ). The errors on the three channels are assumed to occur at least partially independently. Practical protocols are discussed by which Alice and Bob can generate a secret key despite the facts that Eve possesses more information than both of them and is assumed to have unlimited computational resources as well as complete knowledge of the protocols.The described scenario is a special case of a much more general setup in which Alice, Bob and Eve are assumed to know random variables X, Y and Z jointly distributed according to some probability distribution PXYZ, respectively. The results of this paper suggest to build cryptographic systems that are provably secure against enemies with unlimited computing power under realistic assumptions about the partial independence of the noise on the involved communication channels. As the first part of a study of problems involving common randomness at distance locations, information-theoretic models of secret sharing (generating a common random key at two terminals, without letting an eavesdropper obtain information about this key) are considered. The concept of key-capacity is defined. Single-letter formulas of key-capacity are obtained for several models, and bounds to key-capacity are derived for other models. >