High-level structure. The route choice model is developed as a discrete choice model, a random utility model framework (XxXxxxxx, 1974). Such model assumes that each traveler as- sociates a utility to each path alternative between an origin and destination and then selects, out of a set of discrete path alternatives, the one that maximizes his/her utility. A route choice model has two main components: 1) pathset generation and 2) a route choice model estimation. The first component consists of generating a set of possible route alternatives between each origin and destination while the second component calculates the probability of a given route being selected from the pathset.
High-level structure. An instance of the combinatorial model is characterized by a tuple (n, k, tmax, C0) and a sequence (Ut, Ct)tmax , where n, k, tmax ∈ N, C0 ⊆ [n], and Ut, Ct ⊆ [n] for all t. Intuitively, this corresponds to setting up the group G = [n] and in round 0 corrupting the set of users C0. The se- quence (Ut, Ct)tmax determines the operations performed in the following tmax rounds, where - Ut is the set of users performing an update in round t, and - Ct is the set of users corrupted at the end of round t. ∈ { } ∈ ∈ Integer k determines the safety requirement imposed on the CGKA scheme. More precisely, we aim to capture CGKA schemes that recover from corruption after k updates, meaning that if every user did at least k updates since the last round in which they were corrupted, then the group must agree on a secure key. Formally, consider an instantiation of the combinatorial model with respect to (n, k, tmax, C0) and (Ut, Ct)t as described above. We say that a round t 0, . . . , tmax is safe, if for every user u G such that u Ct′ for some t′ there exist rounds t1, . . . , tk such that
