This article considers the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs. For this minimal secure computation problem, the authors propose a novel coding scheme built from two steps. First, the function to be computed is expanded such that it can be recovered while additional information might be leaked. Second, a randomization step is applied to the expanded function such that the leaked information is protected. The authors implement this expand-and-randomize coding scheme with two algebraic structures—the finite field and the modulo ring of integers, where the expansion step is realized with the addition operation and the randomization step is realized with the multiplication operation over the respective algebraic structures.

Article presenting fundamental insights into the design of air corridors with high operational efficiency as well as zero collisions. It begins with the definitions of air cube, skylane or track, intersection, vertiport, gate, and air corridor. Then a multi-layered air corridor model is proposed. Traffic at intersections is analyzed in detail with examples of vehicles turning in different directions. The concept of capacity of an air corridor is introduced along with the nature of distribution of locations of vehicles in the air corridor and collision probability inside the corridor are discussed. Finally, results of traffic flow simulations are presented.