Cryptography by Cellular Automata or How Fast Can Complexity Emerge in Nature?

Computation in the physical world is restricted by the following spatial locality constraint: In a single unit of time, information can only travel a bounded distance in space. A simple computational model which captures this constraint is a cellular automaton: A discrete dynamical system in which cells are placed on a grid and the state of each cell is updated via a local deterministic rule that depends only on the few cells within its close neighborhood. Cellular automata are commonly used to model real world systems in nature and society. Cellular automata were shown to be capable of a highly complex behavior. However, it is not clear how fast this complexity can evolve and how common it is with respect to all possible initial configurations. We examine this question from a computational perspective, identifying "complexity" with computational intractability. More concretely, we consider an n-cell automaton with a random initial configuration, and study the minimal number...

• Type: Conference
• Year: 2010
• Where: ICS
• Authors: Benny Applebaum, Yuval Ishai, Eyal Kushilevitz
• Keywords: ICS 2010, Theoritical Computer Science