Problem Definitions. In this section, we define the key agreement problem over the DM model. Before we present the DM model, let us define a two-way (authenticated) public channel with given capacity in each direction. As a special case, a one-way public channel is also specified in the following definition. Definition 3.1 (Public channel). Assume n ∈ N is time duration, and side information a and b is available at Xxxxx and Xxx, respectively. Let p1 , (P11, P12, . . . , P1n) ∈ P11 × P12 × . . . P1n and p2 , (P21, P22, . . . , P2n) ∈ P21 × P22 × . . . P2n be the forward public message sequence and the backward public message sequence, respectively, where P1τ and P2τ are the alphabet set of the forward message and that of the backward message at time τ ∈ {1, . . . , n}, respectively. A public channel with a given capacity pair (CP1 , CP2 ) is a noiseless channel between Xxxxx and Xxx which consists of a noiseless forward channel from P Xxxxx to Bob with capacity C and a noiseless backward channel from Bob to Xxxxx with P capacity C such that • at time instant τ ∈ {1, . . . , n}, the forward message P1τ is sent from Xxxxx to Bob (in the forward direction), and the backward message P2τ is sent from Bob to Xxxxx (in the backward direction); • P1τ is a function of all available information at Xxxxx up to time τ — 1, i.e., it is a (stochastic) function of a and (P21, P22, . . . , P2(τ−1)), where P20 , 0; • P2τ is a function of all available information at Bob up to time τ — 1, i.e., it is a (stochastic) function of b, (P11, P12, . . . , P1(τ−1)), where P10 , 0, and (Y1, Y2, . . . , Yτ−1), if there exists a wiretap channel connected from Xxxxx to Bob with output symbol Yτ at time τ ; • p1 and p2 are intercepted by Xxx; • the communication rate over the public channel is subject to forward capacity constraint: lim sup log(|P1|) ≤ C , (3.1a) n P1 n→∞ backward capacity constraint: lim sup log(|P2|) ≤ C , (3.1b) n P2 n→∞ where P1 , P11 × . . . × P1n and P2 , P21 × . . . × P2n. P If C = 0, the public channel is called a (one-way) forward public channel; if C P = 0, the public channel is called a (one-way) backward public channel. As sketched in Figure 3.1, the DM model consists of two parallel channels: a discrete memoryless state-dependent wiretap channel (DM-SWC) with non-causally known CSI at the transmitter and a forward public channel. In the following, the DM-SWC is defined.
Problem Definitions. The following standard problem definitions will apply to the Service provided under the terms of this SLA. Problem Priority Status Impact Severity 1 Downtime Critical Inability to (a) access the User Interface, or (b) send a Notification across all modalities.
Problem Definitions. The following standard problem definitions will apply to the Service provided under the terms of this SLA.
