The Concept Clause Examples

The Concept. In an information-theoretic key agreement problem, generally, some legitimate parties on a communication network wish to share a secret (key) reliably by using a (block) key agreement coding scheme such that wiretappers are unable to gain any information about the key. To do this, some signals are to be communicated between authorized parties (subject to constraints of the network) in presence of the wiretappers. This step, which is known as key exchange, is usually performed prior to the transmission of messages. At the end of the key exchange step, each authorized party retrieves his/her own key by decoding total available signals at his/her terminal. The agreed keys are finally to be exploited for symmetric-key cryptography [8] in the step of the transmission of messages [17, 18, 20]. Hence, the keys are selected from a same alphabet (key) set with a finite size, which is denoted by K in this thesis. Moreover, the agreed keys must satisfy the AR condition and the AS condition in the same way as messages (M, Mˆ ) ∈ M2 do in Definition 1.3 and Definition 1.8, respectively. Further to these two conditions, any key is required to look like a uniformly distributed random variable as the third condition; thus, the key is often called a secure common randomness in the literature, e.g., [3, 18, 19, 21]. This condition is called the asymptotic randomness condition (ARN) as block length n → ∞. Near uniformity of a RV with a finite size can be measured in various ways; one popular way in information theory, which is used in our work, is to compare the entropy rate of the RV with that of a uniformly distributed RV with the same size [3, Ch. 17].