Final answer:
Routers use a larger set of information by periodically updating routing tables and calculating the shortest path to each destination, typically using Dijkstra's algorithm.
Step-by-step explanation:
Each router on a network uses a larger set of information primarily by calculating the shortest path to each destination (C). Routers periodically update their routing tables to maintain a current view of the network (A), but they don't typically broadcast the entire network topology as it would be inefficient and could pose a security risk. The algorithm often used for calculating the shortest path is known as Dijkstra's algorithm. However, it is also important to note that routers generally do not encrypt routing information for the purpose of network routing; encryption is used to secure data packets, not routing information itself (D).